图1：“委托人-中介-代理人”模型示例图，展示委托人、中介与代理人之间的合约与机制交互流程

作者完整求解了该模型的子博弈完美均衡，发现委托人的最优合约可等价转化为虚拟价值定价问题，并证明了线性合约的最优性。图2展示了已知与未知市场大小两种情形下，中介参与带来的效用损失上界：当市场大小已知时，损失仅取决于工人成本的分布特征，在理想情况下可被控制在常数倍以内；当委托人只知道市场大小的范围时，损失还会额外受到该范围宽度的放大影响，不确定性越大，效率损失越严重。

图2：已知与未知市场大小时的双重边际化价格与无序价格界限对比

电子科技大学算法与逻辑团队由欧洲科学院院士、新西兰院士Bakh Khoussainov教授和算法专家肖鸣宇教授共同组建，现有许超教授、Toru Takisaka教授、周毅副教授、郝东副教授等多位骨干成员。团队长期深耕算法设计与分析（包括近似算法、参数算法、精确算法、在线算法等），逻辑、图论与图算法，组合优化，算法工程，机制设计与算法博弈论，形式化方法与认证等理论方向，近年来在LICS、CAV、WINE、SODA等理论计算机科学领域顶级会议上连续发表高水平成果，研究实力和学术影响力稳步提升。此次EC 2026论文的录用，进一步彰显了团队在计算经济学前沿领域的国际竞争力。
算法与逻辑团队将以此次突破为契机，继续聚焦算法博弈论与机制设计的基础理论问题，深化国际合作，产出更多原创性成果，为推动我国在计算经济学领域的发展贡献成电智慧。

论文信息如下 (按照理论计算机科学/计算经济学国际学术惯例，论文作者按照姓氏首字母排序)：

Contracting with a Mechanism Designer

Authors: Tian Bai, Yiding Feng, Yaohao Liu*, Mengfan Ma, Mingyu Xiao

论文链接：https://arxiv.org/pdf/2507.12054

该论文研究了著名的布尔可满足性问题（SAT问题）的算法与计算复杂性，得到该问题精确求解中，以问题输入CNF公式的总长度L为度量的当前最佳运行时间上界，改进了十余年前Chen和Liu于2009年给出的结果。本文给出的时间运行界和历史上该问题的运行时间界如表1中所示。

SAT问题是第一个被证明的NP完全问题，在计算复杂性理论里扮演着重要角色，也在人工智能、运筹学和电子设计工程等众多领域中有着重要且基础的应用。该经典问题的运行时间上界在过去几十年里一直被深入研究。作者们通过设计新的分支算法，并运用测量治之（Measure-and-Conquer）的分析技术深入分析，最终取得了这项突破。

彭俊强同学为计算机（网安）学院2021级直博研究生。他从本科阶段开始进入算法与逻辑团队学习，在肖鸣宇教授的指导下从事SAT及其相关问题的研究工作。在博士学习的前两年已经发表两篇CCF A类和一篇CCF B类论文。

算法与逻辑团队由欧洲科学院院士、新西兰院士Bakh Khoussainov教授和肖鸣宇教授共同组建，周毅副教授、郝东副教授和许超助理教授、日籍Toru Takisaka副研究员等多位老师参与。该团队致力于基础理论研究，以探索算法难题和解决重要的科学问题为宗旨，激发和培养学生及青年老师对算法和基础理论的兴趣，为算法及相关研究方向感兴趣的师生提供一个交流平台。团队目前重点关注的研究方向包括：算法设计与分析（包括近似算法、参数算法、精确算法、在线算法等）、逻辑、图论与图算法、组合优化、算法工程、机制设计与算法博弈论、形式化方法与认证等。

团队以科研育人为首要任务，培养出了众多优秀的学生。近两年本科生第一作者在WWW、IJCAI、SODA、COCOON、Discrete Mathematics等CCF A类会议和重要刊物上发表5篇论文。除论文外，团队学生还在多项科技竞赛中斩获重要奖项，仅2023年上半年就获得2023年华为软件精英挑战赛全球总决赛冠军，2023年全国大学生数学竞赛（非数学类）全国第一名，IEEE极限编程竞赛世界第四名（第五次进入世界前十名）等。

论文链接：https://www.sciencedirect.com/science/article/pii/S0890540123000883

　　k-Plex是一种松弛团模型，相比于传统团模型提高了对数据噪声的容忍度，在社区发现算法中常被用于社区的图论建模。最大k-Plex问题旨在搜索图中规模最大的k-Plex，该问题属于NP难问题。该论文基于参数算法理论，给出了一个快速的最大k-Plex的搜索算法，可以在大规模稀疏图中高效地搜索出最大k-Plex。

　　论文揭示了大规模稀疏图中存在的小参数——退化差，并设计了相应的固定参数可解（Fixed-Parameter Tractable，FPT）算法。即在退化差参数有界的情况下，最大k-Plex问题能够在多项式时间内求解。此外，论文通过广泛地实验证明，退化差参数通常在输入图规模的对数数值范围内，并且所提出的固定参数可解算法达到了目前的最优性能。

　　该论文中所提出的固定参数可解算法，其算法框架和运行实例分别如算法1和表1所示。

IJCAI是人工智能领域顶级会议，位列中国计算机学会推荐国际会议CCF-A类。本年度会议投稿超过4500篇，录用率仅为15%，会议将于8月在中国澳门召开。除以上介绍的这篇论文以外，算法与逻辑团队的研究生彭俊强以第一作者身份撰写的另一篇论文《Fast Algorithms for SAT with Bounded Occurrences of Variables》也被IJCAI 2023接收。

　　王正仁，2022年度“成电杰出学生（本科生）”，现计算机学院大四本科生。他从大一开始以学院拔尖人才计划的形式进入算法与逻辑团队学习，主要专注于算法工程与理论方向上的前沿问题，以第一作者身份在CCF-A类会议WWW 2022和IJCAI 2023上发表两篇论文。

　　电子科技大学算法与逻辑团队由新西兰院士Bakh Khoussainov教授和肖鸣宇教授共同组建，周毅副教授、郝东副教授和许超助理教授等多位老师参与。该团队致力于基础理论研究，以探索算法难题和解决重要的科学问题为宗旨，激发和培养学生及青年老师对算法和基础理论的兴趣，为算法及相关研究方向感兴趣的师生提供一个交流平台。团队目前重点关注的研究方向包括：算法设计与分析（包括近似算法、参数算法、精确算法、在线算法等）、逻辑、图论与图算法、组合优化、算法工程、机制设计与算法博弈论、形式化方法与认证等。

　　每年有10余名对算法和数学感兴趣的本科生进入团队学习，科研能力明显提升，高水平论文等学术成果层出不穷。长期以来，学生在多项科技竞赛中斩获奖项，多名学生在程序设计竞赛和数学建模竞赛中取得非常优异的成绩。在ACM程序设计竞赛中，团队多名学生打进了世界总决赛；在IEEE极限编程竞赛中团队学生连续两年获得世界第二名，五次进入世界前十名；团队学生在2021年和2023年分别获得华为软件精英挑战赛全球总决赛冠军。

Title: The (3, 3)-colorability of planar graphs without 4-cycles and 5-cycles

Authors: Yuhao Liu and Mingyu Xiao

In this paper, we study the colorability of a special kind of planar graph. A graph $G$ is called $(d_1, \ldots, d_r)$-colorable if its vertex set can be partitioned into $r$ sets $V_1, \ldots, V_r$ such that the maximum degree of the induced subgraph $G[V_i]$ of $G$ is at most $d_i$ for $i \in \{1, \ldots, r\}$. The problem we study is a variant of famous Steinberg’s conjecture. Steinberg conjectured that every planar graph without 4-cycles and 5-cycles are $(0,0,0)$-colorable. Unfortunately, the conjecture does not hold. Based on it, there are a large number of research results. It is known that every planar graph without 4-cycles and 5-cycles is $(3,4)$-colorable or $(2,6)$-colorable. In this paper, we reduce the gap by proving that every planar graph without 4-cycles and 5-cycles is $(3,3)$-colorable.

Link to the paper: https://doi.org/10.1016/j.disc.2022.113306

实验室本科生在离散数学著名期刊Discrete Mathematics发表研究成果

近日，电子科技大学英才实验学院2019级数理基础科学专业本科生刘宇豪撰写的论文《The (3, 3)-colorability of planar graphs without 4-cycles and 5-cycles》被离散数学方向国际著名期刊《Discrete Mathematics》录用，并在2023年第4期刊出。该论文是在计算科学与工程学院算法与逻辑团队的肖鸣宇教授指导下完成的。

该论文研究的是平面图着色方面的问题。著名的平面图四色定理指的是任意一个平面图都可以用4种颜色对图中顶点进行染色使得任意相邻两个顶点被染不同颜色。一个后续研究问题是：只用3种或者2种颜色对一个平面图进行着色会有什么性质？很容易证明对一般平面图，没办法只用3种颜色进行着色。通过一系列深入研究后，Steinberg于1976年提出著名的猜想：不含长度为4和5的圈的平面图（用P(4,5)来表示这类平面图）可以用3种颜色来着色使得任意相邻两个顶点被染不同颜色。直到2017年，Steinberg的猜想才被证明是不成立的。我们不能保证每对相邻的顶点都染不同的颜色，但是可以使得染同一种颜色的点构成的图的度数尽量小。之前已知的结果是：P(4,5)类图可以用3种颜色进行着色使得每种相同颜色的点构成的图的度数不超过1；若只用2种颜色对P(4,5)类图进行着色，则可以使得每种相同颜色的点构成的图的度数不超过4。本文延续图着色方向里这条研究路线，进一步证明了，P(4,5)类图可以用2种颜色进行着色使得每种相同颜色的点构成的图的度数不超过3，改进了原有结果4。

文中证明里用到的是权转移技术，我们先反设存在一个不能满足着色要求的图，然后对这个图上的顶点和面赋一种权值，使得图中所有顶点和面的权值总和是负的；然后通过一些规则在图中顶点和面之间进行权值的转移，在转移的过程中所有权值总和保持不变；但是转移全部完成后，我们可以计算出所有权值和为正的，得到这样一个矛盾，从而证明了这种不满足着色要求的图不存在。下图中给出了一些权转移的规则示例。

权转移的一些规则示例

学生作者刘宇豪于2019年转入电子科技大学英才实验学院数理基础科学专业，大二开始进入计算机科学与工程学院算法与逻辑团队进行科研训练，先后参与多项图论、算法、组合优化方向的基础研究，已经在相关领域高水平期刊和会议上发表论文2篇，另1篇论文发表在算法领域顶级会议SODA 2023上。

电子科技大学算法与逻辑团队是由新西兰院士Bakh Khoussainov教授和算法著名专家肖鸣宇教授共同组建，面向全校师生开放的、致力于基础理论研究的团队。该团队关注算法、图论、逻辑、组合优化、机制设计等方面的基础难题，培养和激发学生及青年老师的理论研究兴趣。每年有10余名对算法和数学感兴趣的本科生进入团队学习，科研能力明显提升，高水平论文等学术成果层出不穷。长期以来，学生在多项科技竞赛中斩获奖项，多名学生在程序设计竞赛和数学建模竞赛中取得非常优异的成绩；在ACM程序设计竞赛中，团队多名学生打进了世界总决赛；在IEEE极限编程竞赛中团队学生连续两年获得世界第二名，五次进入世界前十名。

转自成电新闻 (阅读原文)

• Facility Location Games with Entrance Fees, by Mengfan Ma (Ph.D. Student), Mingyu Xiao, Tian Bai (Ph.D. Student), Bakh Khoussainov.
• The Linear Distance Traveling Tournament Problem Allows an EPTAS, by Jingyang Zhao (Ph.D. Student), Mingyu Xiao.
• MSDC: Exploiting Multi-State Power Consumption in Non-intrusive load monitoring based on A Dual-CNN Model, by Jialing He, Jiamou Liu, Zijian Zhang, Yang Chen, Yiwei Liu, Bakh Khoussainov, Liehuang Zhu.

Title: Listing Maximal k-Plexes in Large Real-World Graphs

Authors: Zhengren Wang, Yi Zhou, Mingyu Xiao and Bakhadyr Khoussainov

In this paper, we study the problem of listing maximal k-plexes in large real-world graphs, which is highly significant in many domains such as data mining, bio-informatics and ad-hoc wireless network. We propose ListPlex, an algorithm that lists all maximal k-plexes with a guaranteed worst-case running time bound. From algorithmic perspective, we suggest strong prune rules to reduce the search space of our algorithm. From the computational system perspective, we propose new data structures to reduce cache misses and increase parallelism. Experiments show that ListPlex outperforms the state-of-the-art approaches and all optimization techniques bring evident speedup.

Title: Multi-Unit Auction in Social Networks with Budgets

Authors: Mingyu Xiao, Yuchao Song, Bakh Khoussainov

In this paper, we study multi-unit auctions in social networks, where each buyer has a fixed budget and can spread the sale information to the network neighbors. We design a mechanism encouraging buyers to report their valuations truthfully and spread the sale information. Our design uses the idea of the clinching mechanism to decide the transaction price and can be viewed as a network version of the mechanism. Most of the previous clinching mechanisms search for the transaction prices by increasing the current price. Our mechanism directly computes the transaction prices in polynomial time. Furthermore, the mechanism applies a technique to iteratively activate new buyers in the network. This ensures utility preservations of the buyers and benefits the seller. We prove key properties of our mechanism, such as no-positive-transfers, individual rationality, incentive compatibility, non-wastefulness and social welfare preservation.

Title: Optimal Shielding to Guarantee Region-Based Connectivity under Geographical Failures

Authors: Binglin Tao, Mingyu Xiao, Bakhadyr Khoussainov, Junqiang Peng

In this paper, 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. Firstly, we establish the NP-hardness of the problem for multiple 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 multiple regions. The reviewers of this paper said that: The problem is interesting, and the paper has many theoretical contributions. The new algorithms are built on advanced combinatorial tools which can be also evaluated on various network topologies. The detailed complexity study reflects thorough research efforts and technical depth.

International Joint Conferences on Artificial Intelligence (IJCAI) is a top conference in AI. Our group got one paper accepted by IJCAI 2021.

The International Conferences on Theory and Applications of Satisfiability Testing (SAT) is the premier annual meeting for researchers focusing on the theory and applications of the propositional satisfiability problem, broadly construed. Our group got one paper accepted by SAT 2021.

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. Our group got one paper accepted by ICML 2021.

The three papers are:

1. The Traveling Tournament Problem with Maximum Tour Length Two: A Practical Algorithm with An Improved Approximation Bound, by Jingyang Zhao (master student), Mingyu Xiao.
2. A Fast Algorithm for SAT in Terms of Formula Length, by Junqiang Peng (undergraduate student), Mingyu Xiao.
3. From Local to Global Norm Emergence: Dissolving Self-reinforcing Substructures with Incremental Social Instruments, by Yiwei Liu, Jiamou Liu, KaibinWan, Zhan Qin, Zijian Zhang, Bakh Khoussainov, Liehuang Zhu.

Title: Efficient Reductions and a Fast Algorithm of Maximum Weighted Independent Set

Authors: Mingyu Xiao, Sen Huang, Yi Zhou, Bolin Ding

In this paper, we study the weighted version of the maximum independent set problem, one of the most extensively studied optimization problems in graph algorithms and social networks. By deeply studying the structural properties, we design a suite of efficient reduction rules and also propose a simple yet practical algorithm based on the reduction rules. The experimental results on known datasets show that our exact algorithm is not only faster than existing algorithms but also can exactly solve more hard instances with 1,000 seconds. For remaining infeasible instances, our reduction rules can also improve existing heuristic algorithms by producing higher-quality solutions using less time. Note that most of previous reduction rules were just used in theoretical analyses but not used to design fast solvers. The reviewers of this paper said that: it is quite appealing to see that a line of research which remained so far confined in the theory setting could actually lead to algorithms that can be implemented and executed on real instances, for producing non-trivial solutions, and the paper makes a very good point in this matter.

1. An Improved Upper Bound for SAT, by Huairui Chu (undergraduate student), Mingyu Xiao, and Zhe Zhang (undergraduate student).
2. Enhancing Balanced Graph Edge Partition with Effective Local Search, by Zhenyu Guo (master student), Mingyu Xiao, Yi Zhou, Dongxiang Zhang, and Kian-Lee Tan
3. Improving Maximum k-plex Solver via Second-Order Reduction and Graph Color Bounding, by Yi Zhou, Shan Hu (master student), Mingyu Xiao, and Zhang-Hua Fu