This talk studies the Unimodal-Cost $k$-Median problem: given $n$ piecewise-linear
unimodal functions $f_1,\ldots,f_n: \mathbb{R} \to \mathbb{R}$, choose $k$ facilities $y_1,\ldots,y_k$ in $\mathbb{R}$ to minimize $\sum_i \min_r f_i(y_r)$. The classical special case $f_i(y)=w_i|y-z_i|$ arises in facility placement and has been well studied [Love 1976; Hassin & Tamir 1991; Chen & Wang 2014]. We consider general unimodal costs, allowing asymmetry.

For $k=2$, we give an $O((n+k\log k)\log n)$ exact algorithm via total monotonicity and divide-and-conquer. For general $k$, we reduce the problem to a minimum-weight $k$-link path with Monge costs, and combine a direct $k$-stage DP with the frameworks of Aggarwal et al. [1993] and Schieber [1998], using batched column-minimum primitives in place of $O(1)$ edge-weight access. With $m$ total breakpoints, the overall time is

Since it was systematically developed for parameterized algorithms in [Fomin et al., JACM 2016], the Representative Family technique has become a powerful tool in parameterized algorithm design. In this talk, I will introduce the Representative Family technique, including its core definitions, underlying intuition, and the key ideas behind efficient computation. I will then present its application to the Kidney Exchange Problem, where Representative Family leads to a deterministic algorithm improving the running time from $O^*(14.34^t)$ to $O^*(6.855^t)$. ($t$ is the solution size.) This example illustrates how the technique can be used to speed up exponential-time dynamic programming algorithms, thereby transforming them into fixed-parameter tractable algorithms.

The Generalized Independent Set (GIS) problem extends the classical maximum independent set problem by incorporating profits for vertices and penalties for edges. This generalized problem has been identified in diverse applications in fields such as forest harvesting, competitive facility location, social network analysis, and even machine learning.However, solving the GIS problem in large-scale, real-world networks remains computationally challenging. In this paper, we explore data reduction techniques to address this challenge. We first propose 14 reduction rules that can reduce the input graph with rigorous optimality guarantees. We then present a reduction-driven local search (RLS) algorithm that integrates these reduction rules into the pre-processing, the initial solution generation, and the local search components in a computationally efficient way. The RLS is empirically evaluated on 278 graphs drawn from different application scenarios. The results indicate that the RLS is highly competitive. For most graphs, it achieves significantly superior solutions compared to other known solvers, and it effectively provides solutions for graphs exceeding 260 million edges, a task at which every other known method fails. Analysis also reveals that data reduction plays a key role in achieving such a competitive performance.

Large language models are useful research assistants in theoretical computer science — generating examples, writing scripts, triaging literature, stress-testing conjectures, and contributing to proofs. This talk gives a brief overview of recent advances in AI for mathematics, then focuses on how to use these tools effectively in practice: what to prompt, when to trust, and how to verify. I will illustrate these ideas through a recent result obtained with significant AI assistance, walking through the real process of discovery, failure, and iteration that led to it.

One of the most sighificant achievements in the study of Constraint Satisfaction Problems (CSPs) is a result due to Bulatov [ECCC 2002], which establishes that every constraint language $\Gamma$ – a set of relations over a finite domain-that is invariant under a Mal’tsev operation, i.e.,a ternary operation $p$ satisfying

gives rise to a tractable problem class. This result both subsumes and generalizes several previously known tractable fragments of the CSP, including affine constraint problems [JACM 1997, STOC 1978] and constraint satisfaction problems over finite groups with near-subgroups and their cosets [SIAM J. Computing 1998]. Moreover, it has become a cornerstone of more recent developments in the field, most notably the complete complexity classification of CSPs over three-element domains [FOCS 2002] and the resolution of the conservative CSP [LICS 2003].
This talk presents the simplified proof of tractability for CSPs admitting a Mal’tsev polymorphism, following the treatment of Bulatov and Dalmau [SIAM J. Computing 2006).

Computational problems exhibit a wide range of behaviors in terms of how efficiently they can be solved. What underlying mathematical structure in a problem enables an efficient algorithm, and what structural obstacles lead to intractability? While one might not expect a universal theory explaining the sources of algorithmic easiness and hardness across all problems, a remarkably clean answer emerges in the setting of constraint satisfaction problems (CSPs). CSPs provide a unifying framework for a broad class of problems. In this talk, we introduce the basic framework of CSP and illustrate it through several classical examples, such as graph coloring, Horn-SAT, and linear equations. We then explain how the complexity of a CSP is governed by certain algebraic operations called polymorphisms, which capture hidden structure in the space of solutions.

We study automatic presentations of the structures $(\mathbb{N}; S)$, $(\mathbb{N}; E_S)$, $(\mathbb{N}; \leq)$, and their expansions by a unary predicate $U$. Here $S$ is the successor function, $E_S$ is the undirected version of $S$, and $\leq$ is the natural order. We call these structures word structures. Our goal is three-fold. First, we study the isomorphism problem for automatic word structures by focusing on the following three problems. The first problem asks to design an algorithm that, given an automatic structure $\mathcal A$, decides if $\mathcal A$ is isomorphic to $(\mathbb{N}; S)$. The second asks to design an algorithm that, given two automatic presentations of $(\mathbb{N}; S, U_1)$ and $(\mathbb{N}; S, U_2)$, where $U_1$ and $U_2$ are unary predicates, decides if these structures are isomorphic. The third problem investigates if there is an algorithm that, given two automatic presentations of $(\mathbb{N}; \leq, U_1)$ and $(\mathbb{N}; \leq, U_2)$, decides whether $U_1\cap U_2\neq \emptyset$. We show that these problems are undecidable.

The Stacker Crane Problem (SCP) is a variant of the Traveling Salesman Problem where a crane must traverse a graph with designated pairs of pickup and delivery points, moving objects from each pickup location to its corresponding delivery point. The objective is to minimize the total travel distance. SCP is known to be NP-hard, even on trees. Polynomial-time results are limited to graphs topologically equivalent to a path or cycle. In this work, we propose an algorithm that is optimal for each fixed topology, with near-linear runtime. This is made possible by showing that SCP is fixed-parameter tractable (FPT) when parameterized by cycle rank and the number of branch vertices.

A $k$-defective clique of an undirected graph $G$ is a subset of its vertices that induces a nearly complete graph with a maximum of $k$ missing edges. The maximum $k$-defective clique problem, which asks for the largest $k$-defective clique from the given graph, is important in many applications, such as social and biological network analysis. In the paper, we propose a new branching algorithm that takes advantage of the structural properties of the $k$-defective clique and uses the efficient maximum clique algorithm as a subroutine. As a result, the algorithm has a better asymptotic running time than the existing ones. We also investigate upper-bounding techniques and propose a new upper bound utilizing the conflict relationship between vertex pairs. Because the conflict relationship is common in many graph problems, we believe that this technique can be potentially generalized. Finally, experiments show that our algorithm outperforms state-of-the-art solvers on a wide range of open benchmarks. Our source code, as well as the experiment data, is open source and available https://github.com/cy-Luo000/Maximum-k-Defective-Clique.git

Lexicographic Ranking SuperMartingale (LexRSM) is a probabilistic extension of Lexicographic Ranking Function (LexRF), which is a widely accepted technique for verifying program termination. In this paper, we are the first to propose sound probabilistic extensions of LexRF with a weaker non-negativity condition, which is called single-component non-negativity. It is known that such an extension, if it exists, will be nontrivial due to the intricacies of the probabilistic circumstances.
As the basis of technical development, we first devise a novel notion of rescalability, which ensures that a LexRSM does not take negative values in a “harmful” way. This notion yields a sound probabilistic extension of single-component non-negative LexRF for general stochastic processes. Toward the application to automated verification, we then introduce another extension, called lazy LexRSM. Linear lazy LexRSM is sound for probabilistic programs with linear arithmetics, and its subclass is amenable to automated synthesis algorithms via linear programming. Experiments show an advantage of the algorithm over existing LexRSM synthesis algorithms.

This is a joint work with Libo Zhang, Changjiang Wang, and Jiamou Liu.

The talk introduces Presburger arithmetic $\mathrm{PrA}$, the theory of natural numbers with addition, and Büchi arithmetics $\mathrm{BA}_n$, a series of algorithmically decidable extensions of $\mathrm{PrA}$. The main logical and algorithmic properties of these theories and their fragments are explored, both classical and recently obtained. Various expressibility results are introduced as well as some data on the structure of the non-standard models of $\mathrm{PrA}$ and $\mathrm{BA}_n$. We discuss the Büchi-Bruyère theorem, establishing the direct connection between interpretations in Büchi arithmetics and automatic structures, as well as the Cobham-Semënov theorem, allowing to compare the expressive powers of $\mathrm{BA}_n$ for different $n$. The speaker’s result on the non-existence of interpretations from $\mathrm{BA}_n$ to itself unless isomorphic to the trivial one is presented and put in context.

In the MaxSAT problem, given a CNF formula $\mathcal{F}$ with $m$ clauses and an integer $k$, we are asked whether there is a truth assignment that satisfies at least $k$ clauses of $\mathcal{F}$. The natural and well-studied parameterization of the MaxSAT problem takes $k$ as the parameter. In this work, we study the following parameterization of the MaxSAT problem: Given a CNF formula $\mathcal{F}$ with $m$ clauses, decide whether at least $m/2 + \mu$ clauses in $\mathcal{F}$ could be satisfied, where $\mu$ is the excess of the number of satisfied clauses over the trivial lower bound $m/2$ and is taken as the parameter. This perspective is known as the “above guarantee” parameterization. Since its introduction by Mahajan and Raman in 1999, the analysis of parameterization above guarantee has become a highly active and fruitful line of research. In this paper, we develop a new algorithm with runtime $O^*(2.1479^{\mu})$, improving the previous best upper bound $O^*(5.4064^{\mu})$ for this problem. Here, the $O^*$ notation omits polynomial factors.

Muller games form a well-established class of games for model checking and verification. These games are played on directed graphs $\mathcal G$ where Player 0 and Player 1 play by generating an infinite path through the graph. The winner is determined by the set $X$ consisting of all vertices in the path that occur infinitely often. If $X$ belongs to $\Omega$, a specified collection of subsets of $\mathcal G$, then Player 0 wins. Otherwise, Player 1 claims the win. These games are determined, enabling the partitioning of $\mathcal G$ into two sets $W_0$ and $W_1$ of winning positions for Player 0 and Player 1, respectively. Numerous algorithms exist that decide Muller games $\mathcal G$ by computing the sets $W_0$ and $W_1$. In this paper, we introduce two novel algorithms that outperform all previously known methods for deciding explicitly given Muller games, especially in the worst-case scenarios. The previously known algorithms either reduce Muller games to other known games (e.g. safety games) or recursively change the underlying graph $\mathcal G$ and the collection of sets in $\Omega$. In contrast, our approach does not employ these techniques but instead leverages subgames, the sets within $\Omega$, and their interactions. This distinct methodology sets our algorithms apart from prior approaches for deciding Muller games. Additionally, our algorithms offer enhanced clarity and ease of comprehension. Importantly, our techniques are applicable to improving the performance of existing algorithms that handle other game classes, including coloured Muller games, McNaughton games, Rabin games, and Streett games..

The maximum vertex-weighted clique problem (MVWCP) and the maximum edge-weighted clique problem (MEWCP) are two natural extensions of the fundamental maximum clique problem. In this paper, we systematically study MEWCP and make the following major contributions: (1) We show that MEWCP is NP-hard even when the minimum degree of the graph is $n-2$, in contrast to MVWCP which is polynomial-time solvable when the minimum degree of the graph is at least $n-3$. This result distinguishes the complexity of the two problems for the first time. (2) To address MEWCP, we develop an efficient branch-and-bound algorithm called MEWCat with both practical and theoretical performance guarantees. In practice, MEWCat utilizes a new upper bound tighter than existing ones, which allows for more efficient pruning of branches. In theory, we prove a running-time bound of $O^*(1.4423^n)$ for MEWCat, which breaks the trivial bound of $O^*(2^n)$ in the research line of practical exact MEWCP solvers for the first time. (3) Empirically, we evaluate the performance of MEWCat on various benchmark instances. The experiments demonstrate that MEWCat outperforms state-of-the-art exact solvers significantly. For instance, on 16 DIMACS graphs that the state-of-the-art solver BBEWC fails to solve within 7200 seconds, MEWCat solves all of them with an average time of less than 1000 seconds. On real-world graphs, MEWCat achieves an average speedup of over 36x.

In the field of graph mining, the $k$-plex is a well-known extension of the clique model. A $k$-plex is nearly a clique except that each vertex is allowed to be not adjacent to at most $k$ vertices, with $k$ being a positive integer. When $k=1$, a $k$-plex is equivalent to a clique. Fundamental problems related to the $k$-plex include how to enumerate all maximal $k$-plexes and how to find the maximum $k$-plexes in a given graph. In this talk, I will present some of our recent results on these problems from the perspective of algorithm engineering. I will also introduce how techniques in the design of exact and parameterized algorithms assist in the analysis of practical $k$-plex algorithms.

Cut games are among the most fundamental strategic games in algorithmic game theory. It is well-known that computing an exact pure Nash equilibrium in these games is PLS-hard, so research has focused on computing approximate equilibria. We present a polynomial-time algorithm that computes 2.7371-approximate pure Nash equilibria in cut games. This is the first improvement to the previously best-known bound of 3, due to the work of Bhalgat, Chakraborty, and Khanna from EC 2010. Our algorithm is based on a general recipe proposed by Caragiannis, Fanelli, Gravin, and Skopalik from FOCS 2011 and applied on several potential games since then. The first novelty of our work is the introduction of a phase that can identify subsets of players who can simultaneously improve their utilities considerably. This is done via semidefinite programming and randomized rounding. In particular, a negative objective value to the semidefinite program guarantees that no such considerable improvement is possible for a given set of players. Otherwise, randomized rounding of the SDP solution is used to identify a set of players who can simultaneously improve their strategies considerably and allows the algorithm to make progress. The way rounding is performed is another important novelty of our work. Here, we exploit an idea that dates back to a paper by Feige and Goemans from 1995, but we take it to an extreme that has not been analyzed before.

Speaker Bio:

Zhile jiang is a second-year PhD student at Aarhus University, advised by Prof. Ioannis Caragiannis. Currently, he is working on various problems in algorithmic game theory, such as equilibrium computation and pricing.

The paper introduces two player connectivity games played on finite bipartite graphs. Algorithms that solve these connectivity games can be used as subroutines for solving Müller games. Müller games constitute a well established class of games in model checking and verification. In connectivity games, the objective of one of the players is to visit every node of
the game graph infinitely often. The first contribution of this paper is our proof that solving connectivity games can be reduced to the incremental strongly connected component maintenance (ISCCM) problem, an important problem in graph algorithms and data structures. The second contribution is that we non-trivially adapt two known algorithms for the ISCCM problem to provide two efficient algorithms that solve the connectivity games problem. Finally, based on the techniques developed, we
recast Horn’s polynomial time algorithm that solves explicitly given Müller games and provide the first correctness proof of the algorithm. Our algorithms are more efficient than that of Horn’s algorithm. Our solution for connectivity games is used as a subroutine in the algorithm.

In the Cluster Vertex Deletion problem, we are given a graph $G$ and an integer $k$, and the goal is to determine whether we can delete at most $k$ vertices from $G$ to make the remaining graph a cluster, i.e., a graph with each connected component being a complete graph. In this talk, we show that Cluster Vertex Deletion can be solved in $O^*(1.7549^k)$ time, improving the previous result of $O^*(1.811^k)$. To obtain this result, one crucial step is to show that Cluster Vertex Deletion on graphs of maximum degree at most 4 can be solved in $O^*(1.7485^k)$ time. After this step, we know that the graph will always have a vertex of degree at least 5. Then by adopting the previous method of automated generation of searching trees, we can obtain the result on general graphs.

The paper introduces new combinatorial games, called topological network-control games, played on graphs. These games model the influence of competing two parties aiming to control a given network. In a such game given the network, the players move alternatively. At each turn, a player selects an unclaimed vertex and its unclaimed neighbours within distance $t$. The players obey the topological condition that all claimed vertices stay connected. The goal is to decide which player claims the majority of the vertices at the end of the play. We study greedy, symmetric and optimal strategies. We solve the topological network-control games on various classes of graphs. This progresses our understanding of combinatorial games played on graphs. We prove that finding an optimal winning strategy is a PSPACE-complete problem.

在大型稀疏网络中，少数几条边的随机故障可能导致网络断开，为了提高网络健壮性，可以选择性的保护特定边从而使整个网络的连通性保持到一定水平，然而资源总是有限的，不可能保护所有的边。我们设计了一种快速的算法，即通过深度遍历树快速定位到较小的割，并对这些割的边进行有选择性的保护，从而提高网络健壮性，传统算法利用线性规划，时间较慢，并且不能适用于大型网络，实验表明我们的算法能够抵御 99.99%的随机故障，有较好的加速效果。

Speaker Bio

汪鹏鹏现就读于河南工业大学信息科学与工程学院，研究方向为最小割，网络健壮性，稀疏割算法等。

This talk will cover some new advances in recent parallel algorithm research.  We will introduce a few new parallel algorithms on classic graph problems such as single-source shortest paths (the rho-stepping and the delta*-stepping algorithms), biconnectivity (the FAST-BCC algorithm), and strongly connected components (the BGSS algorithm). These algorithms are simple and have good theoretical guarantees on work, span, and space.  If time permits, we will cover recent advances in computational models for modern architectures, parallel data structures, machine learning applications, etc.

Speaker Bio

Yan Gu is an Assistant Professor in the Computer Science and Engineering (CSE) Department at the University of California, Riverside (UCR), since 2020. Prior to that, he was a postdoc associate at MIT CSAIL in 2019. Before that, he received his Ph.D. degree and Bachelor’s degree from Carnegie Mellon University in 2018 and Tsinghua University in 2012, respectively, both in computer science. His research interest is algorithm design, broadly on both the most canonical problems, and applications in databases, machine learning, graphics, architecture, etc. He has recently received the Best Paper Awards in PPoPP 2023 and ESA 2023, the Best Technical Paper Runner-up at VLDB 2023, and an Outstanding Paper Award from SPAA 2020.

Let $k$ be an integer and $M$ a matroid on groundset $E$.
There is a label function $\ell:E\to [k]$ that assigns a label to all elements.

We aim to identify a base where the sum of the labels equals $b \pmod k$.
An special case would be the identification of a spanning tree with even weight.

We demonstrate that this problem is Fixed Parameter Tractable (FPT) with respect to $k$, under the assumption of a specific conjecture proposed by Schrijver and Seymour.
This conjecture is already proven for instances where $k$ is a power of a prime.
We show under the conjecture, any base is close to a base of label $b\pmod k$
for each $b$ in terms of hamming distance.
This result can be generalizable to finite abelian groups.

We also plan to discuss the optimization version of this problem.

This is joint work with Siyue Liu.

Designing strategyproof mechanisms in multi-unit diffusion auctions has posed a significant challenge, as each agent’s allocation and price can be easily influenced by their invitees and siblings. In our study, we contend that allocation monotonicity, regarding both valuation and diffusion, plays a pivotal role in the design of strategyproof diffusion auctions. Building on existing research in this field, we investigate monotonic allocation rules and their corresponding optimal payments within the context of two distinct types of belief preferences. Subsequently, we consolidate our findings into a general framework that facilitates the design of strategyproof diffusion auction mechanisms. Considering that optimal payment rules establish the upper bound of revenue under any deterministic monotonic allocation, this paradigm reveals the significance of prioritizing the search for a more efficient monotonic allocation, under a non-deficit restriction, rather than solely focusing on strategyproofness.

We introduce automatic structures. We provide examples and discuss several research directions. One direction of research is the isomorphism problem. The problem asks to design an algorithm that given two automatic structures decides if they are isomorphic. We explain the state of the art in this direction and provide our contribution. The other direction is concerned with finding exotic automatic presentations of automatic structures. These are examples of automatic structures that defy an intuition. Here provide examples of counter-intuitive automatic structures.
Our focus will be on structures of the type $(\omega; S, U)$, where $\omega$ is the set of natural numbers, $S$ is the successor function on the set $\omega$ of natural numbers, and $U$ is a unary predicate on $\omega$. These structures are called word structures.

We consider a large-scale incentive allocation problem where the entire trade-off curve between budget and profit has to be maintained approximately at all time. The application originally comes from assigning coupons to users of the ride-sharing apps, where each user can have a limit on the number of coupons been assigned. We consider a more general form, where the coupons for each user forms a matroid, and the coupon assigned to each user must be an independent set. We show the entire trade-off curve can be maintained approximately in near-real time.

We proposes a local search combined with DJD heuristic approach for the two-dimensional irregular bin packing problem (2DIBPP) with limited rotations. The objective of 2DIBPP is to pack a given set of irregular pieces into the minimum number of rectangular bins. This is a core problem of the Manufacturing Execution system. A little improvement can lead to a considerable reduction of raw material and labour source. To solve this problem, we merge pieces by customized fitness value, and use tabu search to prohibit poor merging. Finally, we use the DJD heuristic to place the merged pieces and the pieces that cannot be merged on the bins. The standard benchmark results show that our approach improves the results for most of the instances in the literature.

Diffusion auction is an emerging business model where a seller aims to incentivise buyers in a social network to diffuse the auction information thereby attracting potential buyers. We focus on designing mechanisms for multi-unit diffusion auctions. Despite several attempts at this problem, existing mechanisms are unsatisfactory in one way or another.
Here, we propose two new mechanisms for multi-unit diffusion auction: (1) MUDAN which satisfies IC and a weakened form of efficiency, and (2) MUDAR which satisfies efficiency and a weakened form of IC.
We define the mechanisms for the bottleneck case of the problem, namely when each buyer demands a single item, to which the more general multi-demand setting can be reduced.
Our mechanisms are the first multi-unit diffusion auctions that satisfy a range of desirable properties that include truthfulness and efficiency conditions. This closes the gap left open by the previous work.

The Edge Triangle Deletion problem asks whether we can delete at most $k$ edges from the input graph such that there is no triangle in the remaining graph. This problem is NP-hard and has been well studied in the parameterized complexity. A vertex kernel of size $6k$ was proved about 10 years ago. Last week, Zimo Sheng gave a $3k$ kernel for ETD by finding an approximate solution with some analysis. Today, we show that for any fixed $\epsilon > 0$ a polynomial-time algorithm can reduce the input instance to an equivalent instance of at most $(2+\epsilon)k$ vertices. The linear-vertex kernel is obtained using an extended crown decomposition combined with linear programming and other techniques.

Kernelization is a concept of data preprocessing which is possible to derive upper and lower bounds on sizes of reduced instance. Edge Triangle Covering is an important NP-hard problem that has been well studied in exact and parameterized complexity.In this paper, we study kernelization of the Edge Triangle Covering problem, which is to check whether a given graph has a edge-disjoint covering size of at most k. We prove a kernel of $3k$ vertices, improving the previous bound of $6k$.

A widely studied typical mobile edge computing (MEC) system network consists of a cloud server, some edge servers, and some user equipment, which promises a satisfactory user experience by offloading computing tasks to the servers. With the continuous innovation of distributed technology and the wide spread of the concept of collaborative development, network interconnection and resource sharing in multiple MEC system networks have become a trend. However, since the resources in multiple MEC systems are usually unbalanced, how to efficiently complete task scheduling and resource allocation for performance optimization becomes a challenge. In addition, the online network environment is also an urgent problem to be solved. In this paper, we study the joint cross-cell offloading and resource allocation problem in multi-cell MEC networks with the objective of optimizing the user’s quality of experience (QoE). We first propose an exact solution for the problem by formulating it as a mixed integer nonlinear programming (MINLP). Secondly, we devise an efficient distributed global optimal solution search DGOSS algorithm to solve the optimal task scheduling and resource allocation for the offline QoE optimization problem. We thirdly develop a decentralized online learning with dynamic threshold exploration DTE-DOL algorithm with a sub-linear bounded regret under dynamic computing task generation, dynamic server quota, and uncertain server-side information assumptions, by adopting the multi-user Multi-Armed Bandit (MAB) technique and distributed auction technique. We finally evaluated the performance of the proposed algorithms compared to state-of-the-art benchmarks. Results show that the proposed DGOSS and DTE-DOL algorithms outperform offline and online benchmarks by reducing the QoE around 5% and 18.75%, respectively..

Resources

Joint cross-cell offloading and resource allocati

In a contest, a principal holding a task posts it to a crowd. People in the crowd then compete to win the principal’s rewards. Although a crowd is usually networked and people influence each other via social ties, existing contest theories do not aim to answer how interpersonal relationships influence people’s incentives and behaviors and thereby affect the contest performance. In this work, we take people’s social ties as a key factor in the modeling and designing of agents’ incentives in contest design. We establish two contest mechanisms by which the principal can impel the agents to invite their neighbors to contribute to the task. The first mechanism has a symmetric Bayesian Nash equilibrium, and it is very simple for agents to play and easy for the principal to predict the contest performance. The second mechanism has an asymmetric Bayesian Nash equilibrium, and agents’ behaviors in equilibrium show a vast diversity which is strongly related to their social relations. The Bayesian Nash equilibrium analysis of these new mechanisms reveals that, besides agents’ intrinsic abilities, the social relations among them also play a central role in a competitive environment. Moreover, we design an effective algorithm to automatically compute the Bayesian Nash equilibrium of the invitation contest and further adapt it to large graphs.

We introduce two player connectivity games played on finite bipartite graphs. Algorithms that solve these connectivity games can be used as subroutines for solving Müller games. Müller games constitute a well established class of games in model checking and verification. In connectivity games, the objective of one of the players is to visit every node of the game graph infinitely often. We provide a charaterization theorem that solving connectivity games can be reduced to the incremental strongly connected component maintenance (ISCCM) problem, an important problem in graph algorithms and data structures. We non-trivially adapt two known algorithms for the ISCCM problem to provide two efficient algorithms that solve the connectivity games problem.

We introduce Muller games. These are two player games played on finite graphs. They are used to model reactive systems that interact with enviroment. They are also used in model checking applications. To solve a Muller game means to find out the winner of the game that starts at a given vertex of the graph. In 2008 Florian Horn provided a polynomial time solution for Muller games. His proof, however, is unclear and contains many non-trivial gaps. We analyse Horn’s algorithm and provide an indpendent proof that Horn’s algorithm is correct.

We explain graph models (PGs) and regular path queries (RPQs). Then we introduce probability graph models (PGMs) and regular probability graph query language (PRPQs). We investigate three fundamental questions related to PRPQs: (1) the model checking problem (2) the satisfiability problem, and (3) the Validity problem.

Let $\mathbb{F}$ be any field, we consider solving $Ax=b$ for a matrix $A\in\mathbb{F}^{n\times n}$ of $m$ non-zero elements. If we are given a zero forcing set of $A$ of size $k$, we can solve the problem in $O(mk+k^\omega)$ time. The algorithm is inspired by the light chasing algorithm for grid graphs.

We study the minimum $k$-partition problem of submodular functions, i.e., given a finite set $V$ and a submodular function $f:2^V\to \R$, computing a $k$-partition $\{ V_1, \ldots, V_k \}$ of $V$ with minimum $\sum_{i=1}^k f(V_i)$.
The problem is a natural generalization of the minimum $k$-cut problem in graphs and hypergraphs. It is known that the problem is NP-hard for general $k$, and solvable in polynomial time for $k \leq 3$.
We construct the first polynomial-time algorithm for the minimum $4$-partition problem.

Diffusion auction is a business model where a seller aims to incentivise buyers in a social network to diffuse the auction information thereby attracting potential buyers. In this study, we focus on designing mechanisms for multi-unit diffusion auctions. Despite several attempts at this problem, existing mechanisms are unsatisfactory in one way or another. In particular, incentive compatibility seems to be hard to guarantee when a global diffusion tree structure is used to guide allocation. In this paper, we propose MUDA-1 and MUDA-m for single-demand and multi-demand cases of this problem, respectively. Our mechanism are the first multi-unit diffusion auction that is incentive compatible, individual rational, non-deficit and IDM-competitive. This closes the gap left open by the previous work. We also empirically analyse the effects of different graph exploration schemes to the auction outcomes.

Under the hypothesis $P \ne NP$, NP-complete problems cannot be solved in polynomial time. Under the ETH hypothesis, the SAT problem (the first NP-complete problem) cannot be solved in sub-exponential time. Under the SETH hypothesis, the SAT problem has no algorithm with running time better than the trivial bound $O(2^n)$, where n is the number of variables in the formula. However, some NP-complete problems allow algorithms with running time bound better than the trivial bound $O(2^n)$, and some can even be solved in sub-exponential time under ETH. In this talk, I will introduce the current status of exact algorithms and some techniques to break the border of $O(2^n)$ and also to design sub-exponential algorithms.

Speaker Bio

2008年在香港中文大学获得计算机博士学位之后进入电子科技大学工作，现在为电子科技大学计算机学院教授，副院长。主要从事算法分析与设计、机制设计与博弈论、人工智能中的基础算法理论等方向的研究，在Information and Computation、JCSS、Algorithmica、ACM/IEEE Trans.、ICALP、IJCAI、AAAI、WWW、INCOFOM等算法、人工智能领域顶级期刊和会议上发表论文超过100篇，撰写英文专著1部，主持（完成）国家自然科学基金项目5项。是参数算法和精确算法国内外知名的学者。

Inverse reinforcement learning (IRL) is used to automate reward design using demonstrated behaviours in cases where a reward function is not accessible to forward reinforcement learning agents. However, IRL becomes intractable in the face of a large number of agents due to the curse of dimensionality. The recent formalism of mean-field games provides a mathematically tractable model for modelling large-scale multi-agent systems by leveraging mean-field approximation to simplify the interactions among agents. In this talk, I will show how to conquer the problem of many-agent IRL using mean-field games as the framework. Specifically, I will introduce two IRL methods for mean-field games: the first is geometrically interpretable and builds the theoretical foundation for IRL in mean-field games; the second is based on the probabilistic inference that can further reason about uncertainties in agent behaviours. I will close the talk with the introduction of applications of IRL for mean-field games.

Schedule

• 16:20-17:20 (Time in Beijing)
• 21:20-22:20 (Time in Auckland)
• June 17, 2022 (Friday)

Let set $[\ell]=\{0,1,2,\ldots,\ell\}$. A subset $S$ of ring $\Z_n$ is called a $\ell$-covering set if $S[\ell] = \{ ab \mod n| a\in S, b\in [\ell]\} = \Z_n$. In the design of error correcting codes for limited-magnitude errors, small $\ell$-covering sets are used as a building block. We show there exists a $\ell$-covering sets of $\Z_n$ of size $O(\frac{n}{\ell}\log n\log \log n)$ for all $n$ and $\ell\leq n$ .
We consider a fast randomized construction algorithm that obtains a covering set of size at most $O(\log n)$ factor larger than the optimum covering set, and use on average $\tilde{O}(1)$ time per element in the $\ell$-covering set. We also show examples where the $\ell$-covering set must have size $\Omega(\frac{n}{\ell}\frac{\log n}{\log \log n})$. The proofs use results in sieve theory and symmetric linear programs.

Slides.

Schedule

• 16:20-17:20 (Time in Beijing)
• 21:20-22:20 (Time in Auckland)
• June 10, 2022 (Friday)

As networks and their inter-connectivity grow and become complex, failures in the networks impact society and industries more than ever. To address this limitation, we consider region-based connectivity to capture the local nature of failures under the geographical failure model, where failures may happen only on edges in a sub-network (region) and we want to shield some edges in regions to protect the connectivity. There may be several regions and in different regions the failures occur independently. Firstly, we establish the NP-hardness of the problem for l regions, answering a question proposed in previous papers. Secondly, we propose a polynomial-time algorithm for the special case of two regions based on the matroid techniques. Furthermore, we design an ILP-based algorithm to solve the problem for l regions. Experimental results on random and real networks show that our algorithms are much faster than previously known algorithms.

Schedule

• 16:20-17:20 (Time in Beijing)
• 21:20-22:20 (Time in Auckland)
• May 20, 2022 (Friday)

The increasing reliance on data-driven technologies has led to the formation of an economy that is built on data trading. A data marketplace is a platform that facilates data trading. It enables data consumers to query about privately-owned data by compensating the data owners for their loss of privacy. We call such transaction as private data query. There are challenges around private data queries: (1) data pricing, (2) privacy protection, and (3) secure implementation. In this talk, I will talk about the design and implementation of private data query mechanisms for a data marketplace.

Schedule

• 16:20-17:20 (Time in Beijing)
• 21:20-22:20 (Time in Auckland)
• May 13, 2022 (Friday)

Today graph neural networks (GNN) are widely used for processing complex graph data. However, GNN models are vulnerable in real-world scenarios as the input graphs are prone to noises, potentially distorting node representations.
I will introduce our work on Structural Entropy-based Robust learning method for Graph Neural Network. We show that by minimizing the structural entropy, the affect of noises in input graphs can be alleviated.

Schedule

• 16:20-17:20 (Time in Beijing)
• 21:20-22:20 (Time in Auckland)
• April 29, 2022 (Friday)

This talk discusses the algorithmic processes of creating ties in a social network. We view a social network as a graph where nodes represent agents and edges represent ties that allow direct interactions between two agents. The establishment of ties are important to the social network in different perpectives.
From the perspective of a single agent, creating ties enables an agent to gain centrality and thus a more advantageous position in the social network.
From the perspective of groups of agents, creating ties enhances interactions and resolves differences, thereby facilitating the emergence of “global norm”, i.e., unity of action among the agents. From the perspective of the entire network, creating ties fill the so-called “structural holes” and dissolves the community structure. In this talk, we will introduce tools to mathematically capture all three perspectives and discuss the corresponding algorithmic problems.

Schedule

• 16:20-17:20 (Time in Beijing)
• 21:20-22:20 (Time in Auckland)
• April 29, 2022 (Friday)

I give a talk about value iteration (VI) for stochastic games, which is one of the most widely used techniques in probabilistic verification. After a brief introduction to probabilistic verification, I talk about my result on an efficient VI algorithm [Phalakarn, Takisaka, Haas, Hasuo: CAV’20], and a related ongoing work.

[Phalakarn, Takisaka, Haas, Hasuo: CAV’20]
Kittiphon Phalakarn, Toru Takisaka, Thomas Haas and Ichiro Hasuo. Widest Paths and Global Propagation in Bounded Value Iteration for Stochastic Games. Proc. CAV 2020. https://doi.org/10.1007/978-3-030-01090-4_28

Schedule

• 16:20-17:20 (Time in Beijing)
• 21:20-22:20 (Time in Auckland)
• April 22, 2022 (Friday)

In the Capacitated Vehicle Routing Problem (CVRP), we are given an undirected complete graph $G=(V\cup{v_0}, E)$ with metric nonnegative edge weights, where there are $n$ nodes in $V$ representing $n$ customers, each customer $v_i$ with a demand $q_i\in\mathbb{N}_{\geq 1}$ and a vehicle located at the depot $v_0$ with a capacity of $k\in\mathbb{N}_{\geq 1}$. We wish to find a set of tours to cover the demand of every customer with a minimized total weight of edges such that each tour begins and ends at the depot and the sum deliveries for customers in each tour is at most $k$.

This problem has many results in different areas. I mainly consider the results of approximation algorithms in the metric case. In this talk, I will first summarize some current results and then I will introduce some new results.

Schedule

• 16:20-17:20 (Time in Beijing)
• 21:20-22:20 (Time in Auckland)
• April 15, 2022 (Friday)

This talk will give an introduction to the theory of automatic structures, a cutting-edge research topic in logic in computer science and computation. After introduction of the main concepts, many examples will be provided. We wll discuss several open questions, their history and motivation. Basic mathematics and computer science knowledge at undegraduate level suffices to follow the talk.

Schedule

• 16:20-17:20 (Time in Beijing)
• 21:20-22:20 (Time in Auckland)
• April 8, 2022 (Friday)

This talk is a report of our paper Listing Maximal k-Plexes in Large Real-World Graphs on WWW’2022.

K-plexes often serve as a kind of relaxed-clique model for community discovery, social network analysis and web mining tasks. Compared with cliques, k-plexes allow every vertex missing at most k-1 edges to other vertices for better data-noise tolerance.

In this talk, an introduction of background and primitives will be given first. Then, we will show the framework, motivation and details of our algorithm. Finally, we will take some further discussion.

Schedule

• 16:20-17:20 (Time in Beijing)
• 21:20-22:20 (Time in Auckland)
• April 1, 2022 (Friday)

This talk is about Automated Generation of Branching Rules, which helps avoid tedious case distinctions in the design of parameterized algorithms using branching methods. In this talk, we will introduce the general framework of this technique on graph modification problems. Also, to show the strengths and instructions for application of this technique , we will mention some new results about it. At last, some insights of this method in parameterized algorithm designing will be provided.

Schedule

• 16:20-17:20 (Time in Beijing)
• 21:20-22:20 (Time in Auckland)
• March 25, 2022 (Friday)

We introduce new combinatorial games played on graphs that we call network-control games. These games model the influence of competing two parties aiming to control the network. In a network-control game, the players move alternatively on a given undirected graph. At each turn, a player selects an unclaimed vertex and its unclaimed neighbours within distance $t$. The goal is to decide which player claims most of the vertices. We study greedy strategies, symmetric strategies, and fully solve network-control games played on multilines, cycles and a special class of caterpillars. We develop a framework that reduces the sizes of graphs by preserving the winner of the original game. Some proofs involve computer assisted techniques. We study a relaxed version of the network-control games and prove that finding the winner in such games is a PSPACE-complete problem. We show that by changing the underlying graph slightly (by using quasi-isometries), the network-control game can be solved efficiently in the modified graph.

Schedule

• 16:20-17:20 (Time in Beijing)
• 21:20-22:20 (Time in Auckland)
• March 18, 2022 (Friday)