Theoretical Computer Science最新文献

{"title":"The Convex Set Forming Game","authors":"Caroline Brosse ,&nbsp;Nicolas Martins ,&nbsp;Nicolas Nisse ,&nbsp;Rudini Sampaio","doi":"10.1016/j.tcs.2025.115323","DOIUrl":"10.1016/j.tcs.2025.115323","url":null,"abstract":"<div><div>In 1984, Frank Harary introduced the first graph convexity game, focused on the geodesic convexity. A set <span><math><mi>S</mi><mo>⊆</mo><mi>V</mi></math></span> of vertices of a graph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> is convex if every shortest path between two vertices of <em>S</em> is also included in <em>S</em>. We introduce the Convex Set Forming Game CFG: two players alternately select vertices in such a way that the set of selected vertices is always a convex set. In the normal (resp., misère) variant, the last player to be able to select a vertex wins (resp., loses). We also define a new graph invariant <span><math><mi>gc</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> as the largest integer <em>k</em> such that the first player has a strategy ensuring that, at the end of the game, at least <em>k</em> vertices of the graph <em>G</em> have been selected. We first show that the problems of deciding the outcome (does the first player win?) of the game in both variants (normal and misère), as well as the problem of deciding whether <span><math><mi>gc</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≥</mo><mi>k</mi></math></span>, are PSPACE-complete. As a by-product, we prove that the optimization variant of the classical <span>Kayles</span> game is PSPACE-complete. Then, we focus on convexable graphs, i.e., <em>n</em>-node graphs <em>G</em> for which <span><math><mi>gc</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>n</mi></math></span>. For this purpose, we say that a set <span><math><mi>S</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mo>|</mo><mi>S</mi><mo>|</mo></mrow></msub><mo>}</mo><mo>⊆</mo><mi>V</mi></math></span> in a graph <em>G</em> admits a Convex Elimination Ordering (CEO) if <span><math><mo>{</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>}</mo></math></span> is convex for every <span><math><mn>1</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mo>|</mo><mi>S</mi><mo>|</mo></math></span>. We show that the class of graphs whose vertex-set admits a CEO coincides with the chordal graphs and that this class strictly contains the convexable graphs. Moreover, every graph which is Ptolemaic (distance-hereditary chordal) or unit interval is convexable. Finally, we give a polynomial-time algorithm for computing a largest set admitting a CEO in outerplanar graphs, which gives upper bounds on <span><math><mi>gc</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> in outerplanar graphs <em>G</em>.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1046 ","pages":"Article 115323"},"PeriodicalIF":0.9,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106600","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":"Monodic fragments of probabilistic first-order temporal logic with bounded semantics","authors":"Georgios Kourtis,&nbsp;Clare Dixon,&nbsp;Michael Fisher","doi":"10.1016/j.tcs.2025.115319","DOIUrl":"10.1016/j.tcs.2025.115319","url":null,"abstract":"<div><div>We extend (type-2) probabilistic first-order logic with temporal operators, interpreted over fixed-length initial segments of (discrete) time. Given a formula <em>φ</em> of the resulting logic and a natural number <em>N</em>, we ask: is <em>φ</em> satisfiable over a space of length <span><math><mi>N</mi><mo>+</mo><mn>1</mn></math></span> sequences of states (first-order structures)? We show the problem to be decidable for monodic fragments of the logic whose first-order part has a decidable satisfiability problem and we also establish the problem's computational complexity when the first-order part is among some well-known decidable fragments of first-order logic.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1046 ","pages":"Article 115319"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144083987","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":"Locating two facilities on a square with a minimum distance requirement","authors":"Weian Li ,&nbsp;Yu Zhou","doi":"10.1016/j.tcs.2025.115310","DOIUrl":"10.1016/j.tcs.2025.115310","url":null,"abstract":"<div><div>Classic works on facility location problems have been focused on the basic model where facilities and agents are distributed on one line. In this work, we study a new model where one facility or two facilities with a minimum distance requirement are to be located on a square (e.g., a plaza) to serve the agents who are distributed on a line (e.g., a street) that crosses the square. The actual positions of the agents are their private information, and our goal is to design strategyproof mechanisms that decide the locations to build the facilities such that the agents are incentivized to report their true positions and the social welfare is (approximately) maximized. We study different settings, where the facilities can be favorable or obnoxious and the distance metrics can be Manhattan or Euclidean. Interestingly, for Manhattan distances, all but one of our mechanisms achieve the optimal social welfare. For Euclidean distances, however, the optimal algorithms are not strategyproof. Accordingly, for each setting with Euclidean distances, we design strategyproof mechanisms that guarantee constant approximations of the optimal social welfare.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1047 ","pages":"Article 115310"},"PeriodicalIF":0.9,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138117","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":"Sampling and output estimation in distributed algorithms and LCAs","authors":"Leonid Barenboim ,&nbsp;Tzalik Maimon","doi":"10.1016/j.tcs.2025.115311","DOIUrl":"10.1016/j.tcs.2025.115311","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We consider the distributed message-passing model and the Local Computational Algorithms (LCA) model. In both models a network is represented by an &lt;em&gt;n&lt;/em&gt;-vertex graph &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. We focus on labeling problems, such as vertex-coloring, edge-coloring, maximal independent set (MIS) and maximal matching. In the distributed model the vertices of &lt;em&gt;v&lt;/em&gt; perform computations in parallel in order to compute their own solution for solving the problem for &lt;em&gt;G&lt;/em&gt;. In contrast, in the LCA model probes are performed on certain vertices in order to compute their labels in a solution to a given problem. In this work we study the possibility of estimating a solution produced by an algorithm, much before the algorithm terminates. This estimation not only allows for size approximation of a solution, but also for early detection of failure in randomized algorithms. We do this such that a correcting procedure can be executed. To this end, we propose a sampling technique, in which the labels in the sampling are distributed proportionally to the distribution in the algorithm's output. However, the sampling running time is significantly smaller than that of the algorithm in hand.&lt;/div&gt;&lt;div&gt;We achieve the following results, in terms of the maximum degree Δ and the arboricity &lt;em&gt;a&lt;/em&gt; of the input graph. The running time of our procedures is &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, for sampling vertex-coloring, edge-coloring, maximal matching and MIS. This significantly improves upon previous sampling techniques, which incur additional dependency on the maximum degree Δ that can be much higher than the arboricity, as well as more significant dependency on &lt;em&gt;n&lt;/em&gt;. Not only that, we also show that our technique extends naturally for the power graph &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; for any constant integer &lt;span&gt;&lt;math&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; for the problems of MIS and coloring.&lt;/div&gt;&lt;div&gt;Our techniques for sampling in the distributed model provide a powerful and general tool for estimation in the LCA model. In this setting the goal is estimating the size of a solution to a given problem, by making as few vertex probes as possible. For the above-mentioned problems, we achieve estimations with probe complexity &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Our results extend as wel","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1046 ","pages":"Article 115311"},"PeriodicalIF":0.9,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106599","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":"Generalised Nyldon words","authors":"Pamela Fleischmann,&nbsp;Annika Huch,&nbsp;Dirk Nowotka","doi":"10.1016/j.tcs.2025.115320","DOIUrl":"10.1016/j.tcs.2025.115320","url":null,"abstract":"<div><div>One of the most studied famous classes of words is the class of Lyndon words. Their studies are mainly motivated by the property that they factorise the free monoid as shown in the famous Chen-Fox-Lyndon Theorem. Several generalisations of Lyndon words as anti-Lyndon words, Nyldon words or inverse Lyndon words were made over time. In 2014, Grinberg introduced <em>Nyldon words</em> as a new perspective on the factorisation of the free monoid of words. In particular, for Nyldon words the famous Chen-Fox-Lyndon Theorem is considered w.r.t. a reversed lexicographical order, i.e., a lexicographically non-decreasing factorisation where each factor is smaller or equal than its successor. Further, a <em>generalised lexicographical order</em> is defined by equipping each position <em>i</em> in a word in <span><math><msup><mrow><mi>Σ</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> with a total order <span><math><msub><mrow><mo>◃</mo></mrow><mrow><mi>i</mi></mrow></msub></math></span> on Σ. For combining the concept of a generalised order as for generalised Lyndon words and the class of Nyldon words, we investigate a non-decreasing factorisation of the free monoid w.r.t. this generalised ordering and introduce <em>generalised Nyldon words</em>. We show that those words even force a unique non-decreasing factorisation, form a right Hall set, and coincide with the anti-Lyndon words.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1046 ","pages":"Article 115320"},"PeriodicalIF":0.9,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144069443","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":"Hamiltonian path in permutation graphs","authors":"Krishna Daripa ,&nbsp;Alak Kumar Datta","doi":"10.1016/j.tcs.2025.115301","DOIUrl":"10.1016/j.tcs.2025.115301","url":null,"abstract":"<div><div>Hamiltonian path problem is NP-Complete for general graphs. There are some polynomial time algorithms for the problem in some special graphs, such as interval graphs, co-comparability graphs, etc. The existing best algorithm for the Hamiltonian path problem in a permutation graph requires <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> time. We introduce the notion of a follow-up vertex in a permutation graph with respect to its Hasse diagram. We also provide a necessary and sufficient condition for the existence of a Hamiltonian path in a permutation graph in terms of the existence of a follow-up vertex. This finding leads to the design of an improved algorithm for the Hamiltonian path problem in a permutation graph that takes <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> time.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1046 ","pages":"Article 115301"},"PeriodicalIF":0.9,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144071454","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":"Approximation algorithm and mechanism design for bisubmodular welfare maximization problem","authors":"Yuanyuan Wang,&nbsp;Qingqin Nong,&nbsp;Wenjing Liu,&nbsp;Qizhi Fang","doi":"10.1016/j.tcs.2025.115302","DOIUrl":"10.1016/j.tcs.2025.115302","url":null,"abstract":"<div><div>In a combinatorial auction, <em>m</em> indivisible items are sold to multiple buyers. This paper explores the welfare maximization problem in combinatorial auctions with bisubmodular buyers. When buyers' valuations are public, we give a simple greedy algorithm that outputs an allocation achieving 2-approximation, and we prove a hardness result for the bisubmodular welfare maximization problem. When buyers are strategic individuals with valuations as private information, we give a dominant-strategy incentive compatible (DSIC) mechanism that can motivate buyers to provide truthful information and outputs an allocation achieving <span><math><mi>O</mi><mo>(</mo><msqrt><mrow><mi>m</mi></mrow></msqrt><mo>)</mo></math></span>-approximation.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1046 ","pages":"Article 115302"},"PeriodicalIF":0.9,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144069444","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":"Efficient deterministic algorithms for maximizing symmetric submodular functions","authors":"Zongqi Wan ,&nbsp;Jialin Zhang ,&nbsp;Xiaoming Sun ,&nbsp;Zhijie Zhang","doi":"10.1016/j.tcs.2025.115312","DOIUrl":"10.1016/j.tcs.2025.115312","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Symmetric submodular maximization is an important class of combinatorial optimization problems, including MAX-CUT on graphs and hyper-graphs. The state-of-the-art algorithm for the problem over general constraints has an approximation ratio of 0.432 &lt;span&gt;&lt;span&gt;[16]&lt;/span&gt;&lt;/span&gt;. The algorithm applies the canonical continuous greedy technique that involves a sampling process. It, therefore, suffers from high query complexity and is inherently randomized. In this paper, we present several efficient deterministic algorithms for maximizing a symmetric submodular function under various constraints. Specifically, for the cardinality constraint, we design a deterministic algorithm that attains a 0.432 ratio and uses &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; queries. Previously, the best deterministic algorithm attains a &lt;span&gt;&lt;math&gt;&lt;mn&gt;0.385&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; ratio and uses &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; queries &lt;span&gt;&lt;span&gt;[12]&lt;/span&gt;&lt;/span&gt;. For the matroid constraint, we design a deterministic algorithm that attains a &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; ratio and uses &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; queries. Previously, the best deterministic algorithm can also attain &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; ratio but it uses much larger &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; queries &lt;span&gt;&lt;span&gt;[24]&lt;/span&gt;&lt;/span&gt;. For the packing constraints with a large width, we design a deterministic algorithm that attains a &lt;span&gt;&lt;math&gt;&lt;mn&gt;0.432&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; ratio and uses &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; queries. To the best of our knowledge, there is no deterministic algorithm for the constraint previously. The last algorithm can be adapted to attain a 0.432 ratio for single knapsack constraint using &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; queries. Previously, the best deterministic algorithm attains a &lt;span&gt;&lt;math&gt;&lt;mn&gt;0.316&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; ratio and uses &lt;span&gt;&lt;math&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;˜&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; queries &lt;span&gt;&lt;span&gt;[2]&lt;/span&gt;&lt;/span&gt;.&lt;/div","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1046 ","pages":"Article 115312"},"PeriodicalIF":0.9,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143946854","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":"Cycles and global attractors of reactantless and inhibitorless reaction systems","authors":"Rocco Ascone ,&nbsp;Giulia Bernardini ,&nbsp;Luca Manzoni","doi":"10.1016/j.tcs.2025.115300","DOIUrl":"10.1016/j.tcs.2025.115300","url":null,"abstract":"<div><div>We explore the computational complexity of deciding the existence of fixed points and cycles that can be reached from any other states (called <em>global attractors</em>) in the dynamics of inhibitorless and reactantless reaction systems. The problems we consider are all known to be <span><math><mtext>PSPACE</mtext></math></span>-complete in the case of unconstrained reaction systems; in this paper, we show that some of them become polynomially solvable when limited to inhibitorless and reactantless reaction systems, while others remain <strong>PSPACE</strong>-complete. Specifically, we prove that the problems of deciding (i) if a given state belongs to a cycle, (ii) whether two reaction systems have at least one cycle in common, and (iii) whether they have the same set of cycles, remain <strong>PSPACE</strong>-complete even in the inhibitorless and reactantless classes, as well as the problem of deciding if a global cycle attractor exists in a reactantless reaction system. Interestingly, however, we demonstrate that no global cycle attractor of length at least 2 can exist in inhibitorless reaction systems; and no global cycle attractor of length greater than 2 can exist in reactantless reaction systems. Furthermore, we show that the problems of deciding whether a given state is a global attractor and whether a global fixed point attractor exists become polynomially solvable when restricted to inhibitorless and reactantless reaction systems.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1045 ","pages":"Article 115300"},"PeriodicalIF":0.9,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936274","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":"Telephone Broadcast on graphs of treewidth two","authors":"Prafullkumar Tale","doi":"10.1016/j.tcs.2025.115282","DOIUrl":"10.1016/j.tcs.2025.115282","url":null,"abstract":"<div><div>Consider the <span>Telephone Broadcast</span> problem in which an input is a connected graph <em>G</em> on <em>n</em> vertices, a source vertex <span><math><mi>s</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, and a positive integer <em>t</em>. The objective is to decide whether there is a broadcast protocol from <em>s</em> that ensures that all the vertices of <em>G</em> get the message in at most <em>t</em> rounds. We consider the broadcast protocol where, in a round, any node aware of the message can forward it to at most one of its neighbors. Fomin, Fraigniaud, and Golovach [WG 2023; TCS 2024] asked whether the problem is <figure><img></figure> when parameterized by the feedback vertex set number of the graph. We answer this question in the negative.<ul><li><span>•</span><span><div><span>Telephone Broadcast</span>, when restricted to graphs of the feedback vertex number one, and hence treewidth of two, is <figure><img></figure>-<span>complete</span>.</div></span></li></ul> We find this a relatively rare example of problems that admit a polynomial-time algorithm on trees but is <figure><img></figure>-<span>complete</span> on graphs of treewidth two.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1045 ","pages":"Article 115282"},"PeriodicalIF":0.9,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143923489","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}