Pub Date : 2026-03-01Epub Date: 2025-09-05DOI: 10.1016/j.jcss.2025.103703
Joshua A. Grochow , Michael Levet
We leverage the Weisfeiler–Leman algorithm for groups (Brachter & Schweitzer, LICS 2020) to improve parallel complexity upper bounds on isomorphism testing for several families of groups. We first show that groups with an Abelian normal Hall subgroup whose complement is -generated are identified by constant-dimensional Weisfeiler–Leman using -rounds. This places isomorphism testing for this family of groups into ; the previous upper bound for isomorphism testing was (Qiao, Sarma, & Tang, STACS 2011). We next use the individualize-and-refine paradigm to obtain an isomorphism test for groups without Abelian normal subgroups by circuits of depth and size , previously only known to be in (Babai, Codenotti, & Qiao, ICALP 2012) and (Chattopadhyay, Torán, & Wagner, ACM Trans. Comput. Theory, 2013). We next extend a result of Brachter & Schweitzer (ESA, 2022) on direct products of groups to the parallel setting. Namely, we how that Weisfeiler–Leman can identify direct products in parallel, provided it can identify each of the indecomposable direct factors in parallel. They previously showed the analogous result for . We finally consider the count-free Weisfeiler–Leman algorithm, where we show that count-free WL is unable to even distinguish Abelian groups in polynomial-time. Nonetheless, we use count-free WL in tandem with bounded non-determinism and limited counting to obtain a new upper bound of for isomorphism testing of Abelian groups. This improves upon the previous upper bound due to Chattopadhyay, Torán, & Wagner (ACM Trans. Comput. Theory, 2013).
{"title":"On the parallel complexity of group isomorphism via Weisfeiler–Leman","authors":"Joshua A. Grochow , Michael Levet","doi":"10.1016/j.jcss.2025.103703","DOIUrl":"10.1016/j.jcss.2025.103703","url":null,"abstract":"<div><div>We leverage the Weisfeiler–Leman algorithm for groups (Brachter & Schweitzer, LICS 2020) to improve parallel complexity upper bounds on isomorphism testing for several families of groups. We first show that groups with an Abelian normal Hall subgroup whose complement is <span><math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span>-generated are identified by constant-dimensional Weisfeiler–Leman using <span><math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span>-rounds. This places isomorphism testing for this family of groups into <span><math><mtext>L</mtext></math></span>; the previous upper bound for isomorphism testing was <span><math><mi>P</mi></math></span> (Qiao, Sarma, & Tang, STACS 2011). We next use the individualize-and-refine paradigm to obtain an isomorphism test for groups without Abelian normal subgroups by <span><math><mi>SAC</mi></math></span> circuits of depth <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span> and size <span><math><msup><mrow><mi>n</mi></mrow><mrow><mi>O</mi><mo>(</mo><mi>log</mi><mo></mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></mrow></msup></math></span>, previously only known to be in <span><math><mi>P</mi></math></span> (Babai, Codenotti, & Qiao, ICALP 2012) and <span><math><msup><mrow><mi>quasiSAC</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> (Chattopadhyay, Torán, & Wagner, <em>ACM Trans. Comput. Theory</em>, 2013). We next extend a result of Brachter & Schweitzer (ESA, 2022) on direct products of groups to the parallel setting. Namely, we how that Weisfeiler–Leman can identify direct products in parallel, provided it can identify each of the indecomposable direct factors in parallel. They previously showed the analogous result for <span><math><mi>P</mi></math></span>. We finally consider the count-free Weisfeiler–Leman algorithm, where we show that count-free WL is unable to even distinguish Abelian groups in polynomial-time. Nonetheless, we use count-free WL in tandem with bounded non-determinism and limited counting to obtain a new upper bound of <span><math><msub><mrow><mi>β</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mtext>MAC</mtext></mrow><mrow><mn>0</mn></mrow></msup><mo>(</mo><mtext>FOLL</mtext><mo>)</mo></math></span> for isomorphism testing of Abelian groups. This improves upon the previous <span><math><msup><mrow><mtext>TC</mtext></mrow><mrow><mn>0</mn></mrow></msup><mo>(</mo><mtext>FOLL</mtext><mo>)</mo></math></span> upper bound due to Chattopadhyay, Torán, & Wagner (<em>ACM Trans. Comput. Theory</em>, 2013).</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"156 ","pages":"Article 103703"},"PeriodicalIF":0.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-10-30DOI: 10.1016/j.jcss.2025.103729
Maximilien Gadouleau , Loïc Paulevé , Sara Riva
Boolean networks are extensively applied as models of complex dynamical systems, aiming at capturing essential features related to causality and synchronicity of the state changes of components along time. Dynamics of Boolean networks result from the application of their Boolean map according to a so-called update mode, specifying the possible transitions between network configurations. In this paper, we explore update modes that possess a memory on past configurations, and provide a generic framework to define them. We show that recently introduced modes such as the most permissive and interval modes can be naturally expressed in this framework, and we propose novel update modes, the history-based, trapping, and subcube-based modes. Building on the unified definitions, we provide a comprehensive comparison of memory-based update modes, resulting in their hierarchy by simulation and weak simulation. Finally, we highlight consequences of introducing memory on the notions of trajectory and attractors.
{"title":"Bringing memory to Boolean networks: A unifying framework","authors":"Maximilien Gadouleau , Loïc Paulevé , Sara Riva","doi":"10.1016/j.jcss.2025.103729","DOIUrl":"10.1016/j.jcss.2025.103729","url":null,"abstract":"<div><div>Boolean networks are extensively applied as models of complex dynamical systems, aiming at capturing essential features related to causality and synchronicity of the state changes of components along time. Dynamics of Boolean networks result from the application of their Boolean map according to a so-called update mode, specifying the possible transitions between network configurations. In this paper, we explore update modes that possess a memory on past configurations, and provide a generic framework to define them. We show that recently introduced modes such as the most permissive and interval modes can be naturally expressed in this framework, and we propose novel update modes, the history-based, trapping, and subcube-based modes. Building on the unified definitions, we provide a comprehensive comparison of memory-based update modes, resulting in their hierarchy by simulation and weak simulation. Finally, we highlight consequences of introducing memory on the notions of trajectory and attractors.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"156 ","pages":"Article 103729"},"PeriodicalIF":0.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145473539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study Sequential Token Swapping, which can be seen as a variant of the generalized 15 puzzle. Given a graph and two token placements on the vertices, the problem asks to find a walk of the minimum length (if any exists) such that the sequence of token swappings along the walk obtains one of the given token placements from the other one. This problem was introduced by Yamanaka et al. [JGAA 2019], who showed that the problem is intractable in general but polynomial-time solvable for trees, complete graphs, and cycles. In this paper, we present a polynomial-time algorithm for block-cactus graphs, which include all previously known cases. We also present general tools for showing the hardness of the problem on restricted graph classes such as chordal graphs and chordal bipartite graphs. We also show that the problem is hard on grids and king's graphs, which are the graphs corresponding to the 15 puzzle and its variant with relaxed moves.
{"title":"Sequentially swapping tokens: Further on graph classes","authors":"Hironori Kiya , Yuto Okada , Hirotaka Ono , Yota Otachi","doi":"10.1016/j.jcss.2025.103691","DOIUrl":"10.1016/j.jcss.2025.103691","url":null,"abstract":"<div><div>In this paper, we study <span>Sequential Token Swapping</span>, which can be seen as a variant of the generalized 15 puzzle. Given a graph and two token placements on the vertices, the problem asks to find a walk of the minimum length (if any exists) such that the sequence of token swappings along the walk obtains one of the given token placements from the other one. This problem was introduced by Yamanaka et al. [JGAA 2019], who showed that the problem is intractable in general but polynomial-time solvable for trees, complete graphs, and cycles. In this paper, we present a polynomial-time algorithm for block-cactus graphs, which include all previously known cases. We also present general tools for showing the hardness of the problem on restricted graph classes such as chordal graphs and chordal bipartite graphs. We also show that the problem is hard on grids and king's graphs, which are the graphs corresponding to the 15 puzzle and its variant with relaxed moves.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"155 ","pages":"Article 103691"},"PeriodicalIF":0.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-07-22DOI: 10.1016/j.jcss.2025.103693
Ru Wang, Yufei Tao
This article studies two problems related to sampling from the results of database queries. The first one is to uniformly sample a tuple from the result of a join obeying an acyclic set of degree constraints (the join itself need not be acyclic). The second is to uniformly sample a given subgraph pattern's occurrence (the pattern may contain cycles) in a directed data graph. It is shown that, after a linear expected-time preprocessing, both problems admit an algorithm drawing a sample in expected time, where OUT and polymat are the “full result size” and “polymatroid bound” of the underlying problem, respectively (assuming data complexity). These results are derived with a new sampling algorithm for the former problem and a new graph-theoretic theorem for the latter.
{"title":"Join and subgraph sampling under degree constraints","authors":"Ru Wang, Yufei Tao","doi":"10.1016/j.jcss.2025.103693","DOIUrl":"10.1016/j.jcss.2025.103693","url":null,"abstract":"<div><div>This article studies two problems related to sampling from the results of database queries. The first one is to uniformly sample a tuple from the result of a join obeying an acyclic set of degree constraints (the join itself need not be acyclic). The second is to uniformly sample a given subgraph pattern's occurrence (the pattern may contain cycles) in a directed data graph. It is shown that, after a linear expected-time preprocessing, both problems admit an algorithm drawing a sample in <span><math><mi>O</mi><mo>(</mo><mrow><mi>polymat</mi></mrow><mo>/</mo><mi>max</mi><mo></mo><mo>{</mo><mn>1</mn><mo>,</mo><mrow><mi>OUT</mi></mrow><mo>}</mo><mo>)</mo></math></span> expected time, where OUT and <em>polymat</em> are the “full result size” and “polymatroid bound” of the underlying problem, respectively (assuming data complexity). These results are derived with a new sampling algorithm for the former problem and a new graph-theoretic theorem for the latter.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"155 ","pages":"Article 103693"},"PeriodicalIF":1.1,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-08-05DOI: 10.1016/j.jcss.2025.103694
Pablo Barceló , Gaëlle Fontaine , Sylvain Salvati , Sophie Tison
Applications of graph databases are prone to inconsistency due to interoperability issues. This raises the need for studying query answering over inconsistent graph databases in a simple but general framework. We follow the approach of consistent query answering (CQA), and study its data complexity over graph databases for conjunctive regular-path queries (CRPQs) and conjunctive regular-path constraints (CRPCs). We deal with subset, superset and symmetric-difference repairs. Without restrictions, CQA is undecidable for the semantics of superset- and symmetric-difference repairs, and -complete for subset-repairs. However, we identify restrictions on CRPCs and databases that lead to decidability, and even tractability of CQA.
{"title":"Corrections to “On the data complexity of consistent query answering over graph databases [Journal of Computer and System Sciences 88 (2017) 164–194]”","authors":"Pablo Barceló , Gaëlle Fontaine , Sylvain Salvati , Sophie Tison","doi":"10.1016/j.jcss.2025.103694","DOIUrl":"10.1016/j.jcss.2025.103694","url":null,"abstract":"<div><div>Applications of graph databases are prone to inconsistency due to interoperability issues. This raises the need for studying query answering over inconsistent graph databases in a simple but general framework. We follow the approach of consistent query answering (CQA), and study its data complexity over graph databases for conjunctive regular-path queries (CRPQs) and conjunctive regular-path constraints (CRPCs). We deal with subset, superset and symmetric-difference repairs. Without restrictions, CQA is undecidable for the semantics of superset- and symmetric-difference repairs, and <span><math><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>2</mn></mrow><mrow><mtext>P</mtext></mrow></msubsup></math></span>-complete for subset-repairs. However, we identify restrictions on CRPCs and databases that lead to decidability, and even tractability of CQA.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"155 ","pages":"Article 103694"},"PeriodicalIF":0.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144772499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-07-03DOI: 10.1016/j.jcss.2025.103683
Jakob Dyrseth , Paloma T. de Lima
Given a graph and a colouring of its vertices, a rainbow path is a path such that all its internal nodes are coloured distinctly. A graph is rainbow vertex-connected if between every pair of vertices there exists a rainbow path. We study the problem of deciding whether a graph can be coloured using k colours such that it is rainbow vertex-connected. Heggernes et al. (MFCS, 2018) conjectured that if every induced subgraph in G has a dominating diametral path, then G can always be rainbow coloured with colours. We confirm their conjecture for chordal, bipartite and claw-free diametral path graphs. We complement these results by showing the conjecture does not hold without the condition on every induced subgraph. In this case, even though colours are enough, it is NP-complete to determine whether a graph with a dominating diametral path of length three can be rainbow coloured with two colours.
{"title":"On the complexity of rainbow vertex colouring diametral path graphs","authors":"Jakob Dyrseth , Paloma T. de Lima","doi":"10.1016/j.jcss.2025.103683","DOIUrl":"10.1016/j.jcss.2025.103683","url":null,"abstract":"<div><div>Given a graph and a colouring of its vertices, a rainbow path is a path such that all its internal nodes are coloured distinctly. A graph is rainbow vertex-connected if between every pair of vertices there exists a rainbow path. We study the problem of deciding whether a graph can be coloured using <em>k</em> colours such that it is rainbow vertex-connected. Heggernes et al. (MFCS, 2018) conjectured that if every induced subgraph in <em>G</em> has a dominating diametral path, then <em>G</em> can always be rainbow coloured with <span><math><mrow><mi>diam</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>−</mo><mn>1</mn></math></span> colours. We confirm their conjecture for chordal, bipartite and claw-free diametral path graphs. We complement these results by showing the conjecture does not hold without the condition on <em>every</em> induced subgraph. In this case, even though <span><math><mrow><mi>diam</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math></span> colours are enough, it is NP-complete to determine whether a graph with a dominating diametral path of length three can be rainbow coloured with two colours.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"155 ","pages":"Article 103683"},"PeriodicalIF":1.1,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144572748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-07-30DOI: 10.1016/j.jcss.2025.103697
Hans-Joachim Böckenhauer , Ralf Klasing , Tobias Mömke , Peter Rossmanith , Moritz Stocker , David Wehner
We analyze the competitive ratio of the proportional online knapsack problem with removal and limited recourse. In contrast to the classical online knapsack problem, packed items can be removed and a limited number of removed items can be re-inserted to the knapsack. The variant with removal only was analyzed by Iwama and Taketomi (ICALP, 2002). We show that even a single use of recourse can improve the performance of an algorithm. We give lower bounds for a constant number of uses of recourse in total, matching upper bounds for , and a general upper bound for any value of k. For a variant where a constant number of uses of recourse can be used per step, we give tight bounds for all . We further look at a scenario where an algorithm is informed when the instance ends and give improved upper bounds in both variants for this case.
{"title":"Online knapsack with removal and recourse","authors":"Hans-Joachim Böckenhauer , Ralf Klasing , Tobias Mömke , Peter Rossmanith , Moritz Stocker , David Wehner","doi":"10.1016/j.jcss.2025.103697","DOIUrl":"10.1016/j.jcss.2025.103697","url":null,"abstract":"<div><div>We analyze the competitive ratio of the proportional online knapsack problem with removal and limited recourse. In contrast to the classical online knapsack problem, packed items can be removed and a limited number of removed items can be re-inserted to the knapsack. The variant with removal only was analyzed by Iwama and Taketomi (ICALP, 2002). We show that even a single use of recourse can improve the performance of an algorithm. We give lower bounds for a constant number of <span><math><mi>k</mi><mo>≥</mo><mn>1</mn></math></span> uses of recourse in total, matching upper bounds for <span><math><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>3</mn></math></span>, and a general upper bound for any value of <em>k</em>. For a variant where a constant number of <span><math><mi>k</mi><mo>≥</mo><mn>1</mn></math></span> uses of recourse can be used per step, we give tight bounds for all <span><math><mi>k</mi><mo>≥</mo><mn>1</mn></math></span>. We further look at a scenario where an algorithm is informed when the instance ends and give improved upper bounds in both variants for this case.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"155 ","pages":"Article 103697"},"PeriodicalIF":0.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-08-28DOI: 10.1016/j.jcss.2025.103701
David C. Kutner , Laura Larios-Jones
Given a population with dynamic pairwise connections, we ask if the entire population could be (indirectly) infected by a small group of k initially infected individuals. We formalise this problem as the Temporal Reachability Dominating Set (TaRDiS) problem on temporal graphs. We provide positive and negative parameterized complexity results in four different parameters: the number k of initially infected, the lifetime τ of the graph, the number of locally earliest edges in the graph, and the treewidth of the footprint graph . We additionally introduce and study the MaxMinTaRDiS problem, where the aim is to schedule connections between individuals so that at least k individuals must be infected for the entire population to become fully infected. We classify three variants of the problem: Strict, Nonstrict, and Happy. We show these to be coNP-complete, NP-hard, and -complete, respectively. Interestingly, we obtain hardness of the Nonstrict variant by showing that a natural restriction is exactly the well-studied Distance-3 Independent Set problem on static graphs.
{"title":"Temporal Reachability Dominating Sets: Contagion in temporal graphs","authors":"David C. Kutner , Laura Larios-Jones","doi":"10.1016/j.jcss.2025.103701","DOIUrl":"10.1016/j.jcss.2025.103701","url":null,"abstract":"<div><div>Given a population with dynamic pairwise connections, we ask if the entire population could be (indirectly) infected by a small group of <em>k</em> initially infected individuals. We formalise this problem as the <span>Temporal Reachability Dominating Set</span> (<span>TaRDiS</span>) problem on temporal graphs. We provide positive and negative parameterized complexity results in four different parameters: the number <em>k</em> of initially infected, the lifetime <em>τ</em> of the graph, the number of locally earliest edges in the graph, and the treewidth of the footprint graph <span><math><msub><mrow><mi>G</mi></mrow><mrow><mo>↓</mo></mrow></msub></math></span>. We additionally introduce and study the <span>MaxMinTaRDiS</span> problem, where the aim is to schedule connections between individuals so that at least <em>k</em> individuals must be infected for the entire population to become fully infected. We classify three variants of the problem: Strict, Nonstrict, and Happy. We show these to be coNP-complete, NP-hard, and <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>P</mi></mrow></msubsup></math></span>-complete, respectively. Interestingly, we obtain hardness of the Nonstrict variant by showing that a natural restriction is exactly the well-studied <span>Distance-3 Independent Set</span> problem on static graphs.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"155 ","pages":"Article 103701"},"PeriodicalIF":0.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-07-21DOI: 10.1016/j.jcss.2025.103692
Walter Didimo , Siddharth Gupta , Philipp Kindermann , Giuseppe Liotta , Alexander Wolff , Meirav Zehavi
Orthogonal graph drawings are used in applications such as UML diagrams, VLSI layout, cable plans, and metro maps. We focus on drawing planar graphs and assume that we are given an orthogonal representation that describes the desired shape, but not the exact coordinates of a drawing. Our aim is to compute an orthogonal drawing on the grid that has the minimum area among all grid drawings that adhere to the given orthogonal representation. This problem is called orthogonal compaction (OC) and is known to be NP-hard, even for orthogonal representations of cycles [Evans et al. 2022]. We investigate the complexity of OC with respect to several parameters. Among others, we show that OC is fixed-parameter tractable with respect to the most natural of these parameters, namely, the number of kitty corners of the orthogonal representation: the presence of pairs of kitty corners in an orthogonal representation makes the OC problem hard. Informally speaking, a pair of kitty corners is a pair of reflex corners of a face that point at each other. Accordingly, the number of kitty corners is the number of corners that are involved in some pair of kitty corners.
{"title":"Parameterized approaches to orthogonal compaction","authors":"Walter Didimo , Siddharth Gupta , Philipp Kindermann , Giuseppe Liotta , Alexander Wolff , Meirav Zehavi","doi":"10.1016/j.jcss.2025.103692","DOIUrl":"10.1016/j.jcss.2025.103692","url":null,"abstract":"<div><div>Orthogonal graph drawings are used in applications such as UML diagrams, VLSI layout, cable plans, and metro maps. We focus on drawing planar graphs and assume that we are given an <em>orthogonal representation</em> that describes the desired shape, but not the exact coordinates of a drawing. Our aim is to compute an orthogonal drawing on the grid that has the minimum area among all grid drawings that adhere to the given orthogonal representation. This problem is called orthogonal compaction (<span>OC</span>) and is known to be NP-hard, even for orthogonal representations of cycles [Evans et al. 2022]. We investigate the complexity of <span>OC</span> with respect to several parameters. Among others, we show that <span>OC</span> is fixed-parameter tractable with respect to the most natural of these parameters, namely, the number of <em>kitty corners</em> of the orthogonal representation: the presence of pairs of kitty corners in an orthogonal representation makes the <span>OC</span> problem hard. Informally speaking, a pair of kitty corners is a pair of reflex corners of a face that point at each other. Accordingly, the number of kitty corners is the number of corners that are involved in some pair of kitty corners.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"155 ","pages":"Article 103692"},"PeriodicalIF":0.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-08-08DOI: 10.1016/j.jcss.2025.103700
Robert Bredereck , Piotr Faliszewski , Michał Furdyna , Andrzej Kaczmarczyk , Joanna Kaczmarek , Martin Lackner , Christian Laußmann , Jörg Rothe , Tessa Seeger
In parliamentary elections, parties compete for a limited, typically fixed number of seats. Most parliaments are assembled using apportionment methods that distribute the seats based on the parties' vote counts. Common apportionment methods include divisor sequence methods (like D'Hondt or Sainte-Laguë), the largest-remainder method, and first-past-the-post. In many countries, an electoral threshold is implemented to prevent very small parties from entering the parliament. Further, several countries have apportionment systems that incorporate multiple districts. We study how computationally hard it is to change the election outcome (i.e., to increase or limit the influence of a distinguished party) by convincing a limited number of voters to change their vote. We refer to these bribery-style attacks as strategic campaigns and study the corresponding problems in terms of their computational (both classical and parameterized) complexity. We also run extensive experiments on real-world election data and study the effectiveness of optimal campaigns, in particular as opposed to using heuristic bribing strategies and with respect to the influence of the threshold and the influence of the number of districts. For apportionment elections with threshold, finally, we propose—as an alternative to the standard top-choice mode—the second-chance mode where voters of parties below the threshold receive a second chance to vote for another party, and we establish computational complexity results also in this setting.
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