Theoretical Computer Science最新文献

{"title":"Complete decomposition of symmetric tensors in linear time and polylogarithmic precision","authors":"Pascal Koiran , Subhayan Saha","doi":"10.1016/j.tcs.2025.115159","DOIUrl":"10.1016/j.tcs.2025.115159","url":null,"abstract":"<div><div>We study symmetric tensor decompositions, i.e., decompositions of the form <span><math><mi>T</mi><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>r</mi></mrow></msubsup><msubsup><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow><mrow><mo>⊗</mo><mn>3</mn></mrow></msubsup></math></span> where <em>T</em> is a symmetric tensor of order 3 and <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. In order to obtain efficient decomposition algorithms, it is necessary to require additional properties from the <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>. In this paper we assume that the <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> are linearly independent. This implies <span><math><mi>r</mi><mo>≤</mo><mi>n</mi></math></span>, i.e., the decomposition of <em>T</em> is <em>undercomplete</em>. We will moreover assume that <span><math><mi>r</mi><mo>=</mo><mi>n</mi></math></span> (we plan to extend this work to the case <span><math><mi>r</mi><mo><</mo><mi>n</mi></math></span> in a forthcoming paper).</div><div>We give a randomized algorithm for the following problem: given <em>T</em>, an accuracy parameter <em>ε</em>, and an upper bound <em>B</em> on the <em>condition number</em> of the tensor, output vectors <span><math><msubsup><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow><mrow><mo>′</mo></mrow></msubsup></math></span> such that <span><math><mo>|</mo><mo>|</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>−</mo><msubsup><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mo>|</mo><mo>|</mo><mo>≤</mo><mi>ε</mi></math></span> (up to permutation and multiplication by phases) with high probability. The main novel features of our algorithm are:<ul><li><span>•</span><span><div>We provide the first algorithm for this problem that works in the computation model of finite arithmetic and requires only poly-logarithmic (in <span><math><mi>n</mi><mo>,</mo><mi>B</mi></math></span> and <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>ε</mi></mrow></mfrac></math></span>) many bits of precision.</div></span></li><li><span>•</span><span><div>Moreover, this is also the first algorithm that runs in linear time in the size of the input tensor. It requires <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> arithmetic operations for all accuracy parameters <span><math><mi>ε</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mtext>poly</mtext><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfrac></math></span>.</div></span></li></ul></div><div>In order to obtain these results, we rely on a mix of techniques from algorithm design and algorithm analysis. The algorithm is a modified version of simultaneous diagonalisation algorithm for symmetric ","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1037 ","pages":"Article 115159"},"PeriodicalIF":0.9,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636584","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":"(min⁡,+) matrix and vector products for inputs decomposable into few monotone subsequences","authors":"Andrzej Lingas , Mia Persson","doi":"10.1016/j.tcs.2025.115158","DOIUrl":"10.1016/j.tcs.2025.115158","url":null,"abstract":"<div><div>We study the time complexity of computing the <span><math><mo>(</mo><mi>min</mi><mo>⁡</mo><mo>,</mo><mo>+</mo><mo>)</mo></math></span> matrix product of two <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> integer matrices in terms of <em>n</em> and the number of monotone subsequences the rows of the first matrix and the columns of the second matrix can be decomposed into. In particular, we show that if each row of the first matrix can be decomposed into at most <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> monotone subsequences and each column of the second matrix can be decomposed into at most <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> monotone subsequences such that all the subsequences are non-decreasing or all of them are non-increasing then the <span><math><mo>(</mo><mi>min</mi><mo>⁡</mo><mo>,</mo><mo>+</mo><mo>)</mo></math></span> product of the matrices can be computed in <span><math><mi>O</mi><mo>(</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mi>n</mi></mrow><mrow><mn>2.569</mn></mrow></msup><mo>)</mo></math></span> time. On the other hand, we observe that if all the rows of the first matrix are non-decreasing and all columns of the second matrix are non-increasing or <em>vice versa</em> then this case is as hard as the general one. We also present six cases of the restrictions on the input integer matrices under which the problem of computing the <span><math><mo>(</mo><mi>min</mi><mo>⁡</mo><mo>,</mo><mo>+</mo><mo>)</mo></math></span> matrix product is equally hard as that of computing the minimum and maximum witnesses of Boolean matrix product.</div><div>Similarly, we also study the time complexity of computing the <span><math><mo>(</mo><mi>min</mi><mo>⁡</mo><mo>,</mo><mo>+</mo><mo>)</mo></math></span> convolution of two <em>n</em>-dimensional integer vectors in terms of <em>n</em> and the number of monotone subsequences the two vectors can be decomposed into. We show that if the first vector can be decomposed into at most <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> monotone subsequences and the second vector can be decomposed into at most <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> subsequences such that all the subsequences of the first vector are non-decreasing and all the subsequences of the second vector are non-increasing or <em>vice versa</em> then their <span><math><mo>(</mo><mi>min</mi><mo>⁡</mo><mo>,</mo><mo>+</mo><mo>)</mo></math></span> convolution can be computed in <span><math><mover><mrow><mi>O</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mi>n</mi></mrow><mrow><mn>1.5</mn></mrow></msup><mo>)</mo></math></span> time. ","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1037 ","pages":"Article 115158"},"PeriodicalIF":0.9,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143637458","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":"Closure and decision properties for higher-dimensional automata","authors":"Amazigh Amrane ,&nbsp;Hugo Bazille ,&nbsp;Uli Fahrenberg ,&nbsp;Krzysztof Ziemiański","doi":"10.1016/j.tcs.2025.115156","DOIUrl":"10.1016/j.tcs.2025.115156","url":null,"abstract":"<div><div>We report some further developments regarding the language theory of higher-dimensional automata (HDAs). Regular languages of HDAs are sets of finite interval partially ordered multisets (pomsets) with interfaces. We show a pumping lemma which allows us to expose a class of non-regular languages. Concerning decision and closure properties, we show that inclusion of regular languages is decidable (hence is emptiness), and that intersections of regular languages are again regular. Yet complements of regular languages are not always regular. We introduce a width-bounded complement and show that width-bounded complements of regular languages are again regular.</div><div>We also study determinism and ambiguity. We show that it is decidable whether a regular language is accepted by a deterministic HDA and that there exist regular languages with unbounded ambiguity. Finally, we characterize one-letter deterministic languages in terms of ultimately periodic functions.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1036 ","pages":"Article 115156"},"PeriodicalIF":0.9,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549042","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":"Ordinal maximin guarantees for group fair division","authors":"Pasin Manurangsi ,&nbsp;Warut Suksompong","doi":"10.1016/j.tcs.2025.115151","DOIUrl":"10.1016/j.tcs.2025.115151","url":null,"abstract":"<div><div>We investigate fairness in the allocation of indivisible items among groups of agents using the notion of maximin share (MMS). While previous work has shown that no nontrivial multiplicative MMS approximation can be guaranteed in this setting for general group sizes, we demonstrate that ordinal relaxations are much more useful. For example, we show that if <em>n</em> agents are distributed equally across <em>g</em> groups, there exists a 1-out-of-<em>k</em> MMS allocation for <span><math><mi>k</mi><mo>=</mo><mi>O</mi><mo>(</mo><mi>g</mi><mi>log</mi><mo>⁡</mo><mo>(</mo><mi>n</mi><mo>/</mo><mi>g</mi><mo>)</mo><mo>)</mo></math></span>, while if all but a constant number of agents are in the same group, we obtain <span><math><mi>k</mi><mo>=</mo><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>/</mo><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span>. We also establish the tightness of these bounds and provide non-asymptotic results for the case of two groups. Our proofs leverage connections to combinatorial covering designs.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1036 ","pages":"Article 115151"},"PeriodicalIF":0.9,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549054","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":"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}