Theoretical Computer Science最新文献

{"title":"Computational power of autonomous robots: Transparency vs. opaqueness","authors":"Caterina Feletti ,&nbsp;Lucia Mambretti ,&nbsp;Carlo Mereghetti ,&nbsp;Beatrice Palano","doi":"10.1016/j.tcs.2025.115153","DOIUrl":"10.1016/j.tcs.2025.115153","url":null,"abstract":"<div><div>The research on distributed computing by robot swarms has formalized different models where robots act through a sequence of <em>Look-Compute-Move</em> cycles in the Euclidean plane. Models mostly under study differ for <em>(i)</em> the possibility of storing constant-size information, <em>(ii)</em> the possibility of communicating constant-size information, <em>(iii)</em> the synchronization mode, and <em>(iv)</em> the visibility of robots. By varying features <em>(i)</em> and <em>(ii)</em>, we obtain the noted four base models: <span><math><mi>OBLOT</mi></math></span> (silent and oblivious robots), <span><math><mi>FSTA</mi></math></span> (silent and finite-state robots), <span><math><mi>FCOM</mi></math></span> (oblivious and finite-communication robots), and <span><math><mi>LUMI</mi></math></span> (finite-state and finite-communication robots). Feature <em>(iii)</em> comprehends the three main synchronization modes: <em>fully synchronous</em>, <em>semi-synchronous</em>, and <em>asynchronous</em>. According to robot visibility <em>(iv)</em>, models can assume robots to be <em>transparent</em> (thus enjoying <em>complete visibility</em>) or <em>opaque</em> (thus experiencing <em>obstructed visibility</em> in case of collinearities). By combining features <em>(i-iv)</em>, we obtain 24 models. Extensive research has studied the <em>computational power</em> of the 12 transparent models, proving the hierarchical relations among them; to this regard, it is worth noticing that robots have been assumed to be collision-tolerant.</div><div>In this work, we assume our robots to be <em>collision-intolerant</em> and we lay down the computational hierarchy by considering all 24 models. Firstly, we study the relations between the transparent and the opaque framework, focusing on how obstructed visibility affects the computational power of a model. Then, we introduce five witness problems that prove most of the computational relations among the 24 models.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1036 ","pages":"Article 115153"},"PeriodicalIF":0.9,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bribery in elections with randomly selected voters: Hardness and algorithm","authors":"Liangde Tao ,&nbsp;Lin Chen ,&nbsp;Lei Xu ,&nbsp;Weidong Shi ,&nbsp;Md Mahabub Uz Zaman ,&nbsp;Ahmed Sunny","doi":"10.1016/j.tcs.2025.115150","DOIUrl":"10.1016/j.tcs.2025.115150","url":null,"abstract":"<div><div>Many research works in computational social choice assume a fixed set of voters in an election and study the resistance of different voting rules against electoral manipulation. In recent years, however, a new technique known as <em>random sample voting</em> has been adopted in many multi-agent systems. One of the most prominent examples is blockchain. Many proof-of-stake based blockchain systems like Algorand will randomly select a subset of participants of the system to form a committee, and only the committee members will be involved in the decision of some important system parameters. This can be viewed as running an election where the voter committee (i.e., the voters whose votes will be counted) is randomly selected. It is generally expected that the introduction of such randomness should make the election more resistant to electoral manipulation, despite the lack of theoretical analysis. In this paper, we present a systematic study on the resistance of an election with a randomly selected voter committee against bribery. Since the committee is randomly generated, by bribing any fixed subset of voters, the designated candidate may or may not win. Consequently, we consider the problem of finding a feasible solution that maximizes the winning probability of the designated candidate. We show that for most voting rules, this problem becomes extremely difficult for the briber as even finding any non-trivial solution with non-zero objective value becomes NP-hard. However, for plurality and veto, there exists a polynomial time approximation scheme that computes a near-optimal solution efficiently. The algorithm builds upon a novel integer programming formulation together with techniques from <em>n</em>-fold integer programming, which may be of separate interest.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1036 ","pages":"Article 115150"},"PeriodicalIF":0.9,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weighted connected matchings","authors":"Guilherme C.M. Gomes ,&nbsp;Bruno P. Masquio ,&nbsp;Paulo E.D. Pinto ,&nbsp;Vinicius F. dos Santos ,&nbsp;Jayme L. Szwarcfiter","doi":"10.1016/j.tcs.2025.115149","DOIUrl":"10.1016/j.tcs.2025.115149","url":null,"abstract":"<div><div>A matching <em>M</em> of a graph is a <span><math><mi>P</mi></math></span>-matching if the subgraph induced by the endpoints of the edges of <em>M</em> satisfies property <span><math><mi>P</mi></math></span>. As examples, for appropriate choices of <span><math><mi>P</mi></math></span>, the problems <span>Induced Matching</span>, <span>Uniquely Restricted Matching</span>, <span>Connected Matching</span> and <span>Disconnected Matching</span> arise. For many of these problems, finding a <span><math><mi>P</mi></math></span>-matching of a given size is a known <figure><img></figure> problem, with few exceptions, such as <span>Connected Matching</span>, which has the same time complexity as the usual <span>Maximum Matching</span> problem. The weighted variant of <span>Maximum Matching</span> has been studied for decades, with many applications, including the well-known <span>Assignment</span> problem. Motivated by this fact and by some recent research in weighted versions of acyclic and induced matchings, we study <span>Maximum Weight Connected Matching</span> and its decision version, <span>Weighted Connected Matching</span>. The former problem asks for a matching <em>M</em> such that the endpoints of its edges induce a connected subgraph and the sum of the edge weights of <em>M</em> is maximum, while the latter asks if there is an <em>M</em> of at least a given weight. Unlike the unweighted <span>Connected Matching</span> problem, which is in ¶ for general graphs, we show that <span>Weighted Connected Matching</span> is <figure><img></figure> even for bounded diameter bipartite graphs, starlike graphs, planar bipartite graphs, and 3-regular planar graphs, while solvable in linear time for trees and for graphs of maximum degree at most two. When we restrict edge weights to be non-negative, we show that the problem turns out to be polynomially solvable for chordal graphs, while it remains <figure><img></figure> for most of the other cases. In addition, we consider the parameterized complexity of the problem. On the positive side, we present a single-exponential time algorithm when parameterized by treewidth. As for kernelization, we show that, even when restricted to binary weights, <span>Weighted Connected Matching</span> does not admit a polynomial kernel when parameterized by vertex cover number under standard complexity-theoretical hypotheses.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1036 ","pages":"Article 115149"},"PeriodicalIF":0.9,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Notes on Smyth-completes and local Yoneda-completes","authors":"Zhenhua Jia,&nbsp;Qingguo Li","doi":"10.1016/j.tcs.2025.115148","DOIUrl":"10.1016/j.tcs.2025.115148","url":null,"abstract":"<div><div>In this paper, we first introduce the notion of <em>d</em>-net which is obtained being inspired by an elegant characterization: a quasi-metric space <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></span> is Smyth-complete if and only if <span><math><mi>B</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></span> is sober in its open ball topology. Then, we obtain the characterizations of Smyth-complete quasi-metric spaces via <em>d</em>-nets in quasi-metric spaces. Or rather, we prove that a quasi-metric space is Smyth-complete if and only if every <em>d</em>-net has a <em>d</em>-limit and converges to its <em>d</em>-limit. For a local Yoneda-complete quasi-metric space, we provide a necessary and sufficient condition such that the open ball topology coincides with the Scott topology on its formal ball space. In addition, we show that local Yoneda-completeness is preserved by some constructions, such as coproducts, products, function spaces, formal ball spaces and so on. Finally, we prove that the formal ball construction <strong>B</strong> induces the monads on the categories of Smyth-complete quasi-metric spaces with 1-Lipschitz maps, local Yoneda-complete quasi-metric spaces with 1-Lipschitz maps, Smyth-complete quasi-metric spaces with Y-continuous maps and local Yoneda-complete quasi-metric spaces with Y-continuous maps.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1036 ","pages":"Article 115148"},"PeriodicalIF":0.9,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sequential decision based learning method for influence maximization","authors":"Zizhen Zhang ,&nbsp;Deying Li ,&nbsp;Yongcai Wang ,&nbsp;Wenping Chen ,&nbsp;Yuqing Zhu","doi":"10.1016/j.tcs.2025.115147","DOIUrl":"10.1016/j.tcs.2025.115147","url":null,"abstract":"<div><div>Influence maximization (IM) involves choosing an initial group of users within a social network to optimize the expected spread of influence across other users. Recently, learning-based combinatorial optimization (CO) methods have been developed to learn generalized policies for specific CO problems on graphs. However, current learning-based algorithms struggle with diverse diffusion patterns, which restricts their generalization ability. In this paper, we apply reverse influence sampling to simplify the IM problem, reducing it to a stochastic maximum coverage problem using hyperedges. We then model this as a Markov decision process and propose two sequential decision-based learning methods. These methods leverage the symmetry of solutions with respect to sequence order and utilize the submodular reward function. By jointly training on multiple graphs, our approach learns a transferable seed selection policy that generalizes effectively to previously unseen test graphs. Extensive experiments demonstrate that our method outperforms recent learning-based approaches as well as traditional methods on both real and synthetic datasets for the IM problem.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1036 ","pages":"Article 115147"},"PeriodicalIF":0.9,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discrete evacuation in graphs with multiple exits","authors":"Piotr Borowiecki ,&nbsp;Shantanu Das ,&nbsp;Dariusz Dereniowski ,&nbsp;Łukasz Kuszner","doi":"10.1016/j.tcs.2025.115141","DOIUrl":"10.1016/j.tcs.2025.115141","url":null,"abstract":"<div><div>In this paper, we consider the problem of efficient evacuation of mobile agents from distinct nodes in a graph to multiple exit nodes, while avoiding congestion and bottlenecks, and minimizing the total evacuation time. Each node in the graph can only hold one agent at a time, so the agents must choose their movements based on the locations of other agents to optimize the evacuation process. We consider two scenarios: the centralized (offline) and the distributed (online) setting. In the former one, the agents have complete information about the initial positions of other agents. In the distributed setting, agents lack prior knowledge of other agents' locations but can communicate locally with nearby agents and must adapt their strategy in an online fashion as they move and gather more information. In this study, we propose an offline polynomial time solution for determining the optimal evacuation strategy for all agents. In the online case, where agents can communicate at a distance of two in the graph, a constant-competitive algorithm is presented. Additionally, we demonstrate that when agents are heterogeneous and each type of agent can access only a certain subgraph of the original graph, computing the optimal strategy becomes NP-hard, even with full global knowledge. This result remains true even if there are only two types of agents or, even if the optimal evacuation time is a small constant.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1035 ","pages":"Article 115141"},"PeriodicalIF":0.9,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143489036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inoculation strategies for bounded degree graphs","authors":"Mason DiCicco,&nbsp;Henry Poskanzer,&nbsp;Daniel Reichman","doi":"10.1016/j.tcs.2025.115142","DOIUrl":"10.1016/j.tcs.2025.115142","url":null,"abstract":"<div><div>We study the inoculation game, a game-theoretic abstraction of epidemic containment played on an undirected graph <em>G</em>: each player is associated with a node in <em>G</em> and can either acquire protection from a contagious process or risk infection. After decisions are made, an infection starts at a random node <em>v</em> and propagates through all unprotected nodes reachable from <em>v</em>. It is known that the price of anarchy (PoA) in <em>n</em>-node graphs can be as large as <span><math><mi>Θ</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>. Our main result is a tight upper bound of <span><math><mi>O</mi><mo>(</mo><msqrt><mrow><mi>n</mi><mi>Δ</mi></mrow></msqrt><mo>)</mo></math></span> on the PoA, where Δ is the <em>maximum degree</em> of the graph. Indeed, we provide constructions of graphs with maximum degree Δ for which the PoA is <span><math><mi>Ω</mi><mo>(</mo><msqrt><mrow><mi>n</mi><mi>Δ</mi></mrow></msqrt><mo>)</mo></math></span>. We also study additional factors that can reduce the PoA, such as higher thresholds for contagion and varying the costs of becoming infected vs. acquiring protection.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1035 ","pages":"Article 115142"},"PeriodicalIF":0.9,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143478538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Post-quantum secure compact deterministic wallets from isogeny-based signatures with rerandomized keys","authors":"Surbhi Shaw,&nbsp;Ratna Dutta","doi":"10.1016/j.tcs.2025.115127","DOIUrl":"10.1016/j.tcs.2025.115127","url":null,"abstract":"<div><div>A deterministic wallet is a specialized type of cryptocurrency wallet designed to simplify key management and enhance security. In their research presented at CCS'19, Das et al. introduced a general framework for building deterministic wallets based on signature schemes with rerandomizable keys (rerandomizable signatures). This advanced form of signature scheme allows for independent yet consistent rerandomization of signing and public key. Additionally, they provided an instantiation of their framework using rerandomizable signatures derived from BLS and ECDSA. However, these wallet schemes reveal vulnerability to quantum threats, primarily because of their reliance on the discrete logarithm problem which poses a significant challenge to the security landscape.</div><div>As signature schemes with perfectly rerandomizable keys are central to the construction of deterministic wallets, we begin by offering a generic construction of such scheme from signature schemes based on cryptographic (free) group actions. We present an in-depth security analysis of our scheme proving them secure against <em>existential unforgeability under chosen-message attack with honestly rerandomized keys</em>. To ensure post-quantum security, we instantiate our generic construction of rerandomizable signature from isogeny-based signature schemes <em>Commutative Supersingular Isogeny based Fiat-Shamir signature</em> (<span>CSI-FiSh</span>) and <span>CSI-FiSh</span> <em>with Sharing-friendly Keys</em> (<span>CSI-SharK</span>). We extend our techniques to adaptor signatures as well as to design an <em>adaptor signature with rerandomizable keys</em> from isogenies. Additionally, we seamlessly integrate our generic rerandomizable signature scheme into the development of the deterministic wallet. Finally, we instantiate our deterministic wallet from rerandomizable signature scheme from <span>CSI-FiSh</span> which gives the first isogeny-based deterministic wallet, distinguished by its compact key sizes.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1035 ","pages":"Article 115127"},"PeriodicalIF":0.9,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143478537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The min-move mutual visibility problem for disoriented asynchronous robots","authors":"Subhash Bhagat ,&nbsp;Krishnendu Mukhopadhyaya ,&nbsp;Rajarshi Ray","doi":"10.1016/j.tcs.2025.115125","DOIUrl":"10.1016/j.tcs.2025.115125","url":null,"abstract":"<div><div>We consider a distributed system of <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span> autonomous robots in the Euclidean plane under the <em>obstructed visibility model</em>. In the <em>obstructed visibility model</em>, robots are considered opaque, and if three robots lie on a straight line, the mid- dle robot blocks the vision of the two other robots. The <em>mutual visibility problem</em> requires the robots to coordinate their movements in such a way that all the robots in the system become mutually visible. This paper studies a constrained version of the mutual visibility problem, namely the <em>min-move mutual visibility problem</em>. The min-move mutual visibility problem asks to solve the mutual visibility problem by moving each robot at most once. One of the major implications of this constrained version of the mutual visibility problem is that it also addresses the issue of energy efficiency for the robots. We study the min-move mutual visibility problem for disoriented robots (i.e., robots not having any form of local axis agreement or common chirality). We study the problem under two of the strongest adversarial models, namely asynchronous scheduler and non- rigid movements. We first show that the min-move mutual visibility problem is not solvable for disoriented asynchronous robots with non-rigid movements in the absence of externally visible lights. Then, we analyze different characteristics of a min-move mutual visibility algorithm for disoriented robots with non-rigid movements. We use these properties to present a distributed algorithm that solves the problem for disoriented asynchronous robots with non-rigid movements and having externally visible lights (FALL light model). The algorithm uses only 7 colors for the lights. The proposed algorithm is collision-free and runs in <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> epochs.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1035 ","pages":"Article 115125"},"PeriodicalIF":0.9,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143478539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"For rational numbers with Suppes-Ono division, equational validity is one-one equivalent with Diophantine unsolvability","authors":"Jan A. Bergstra ,&nbsp;John V. Tucker","doi":"10.1016/j.tcs.2025.115124","DOIUrl":"10.1016/j.tcs.2025.115124","url":null,"abstract":"<div><div>Adding division to rings and fields leads to the question of how to deal with division by 0. From a plurality of options, we discuss in detail what we call <em>Suppes-Ono division</em> in which division by 0 produces 0. We explain the backstory of this semantic option and its associated notion of equality, and prove a result regarding the logical complexity of deciding equations over the rational numbers equipped with Suppes-Ono division. We prove that deciding the validity of the equations is computationally equivalent to the Diophantine Problem for the rational numbers, which is a longstanding open problem.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1034 ","pages":"Article 115124"},"PeriodicalIF":0.9,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}