We study a generalization of the standard approval-based model of participatory budgeting (PB), in which voters are providing approval ballots over a set of predefined projects and—in addition to a global budget limit, there are several groupings of the projects, each group with its own budget limit. We study the computational complexity of identifying project bundles that maximize voter satisfaction while respecting all budget limits. We show that the problem is generally intractable and describe efficient exact algorithms for several special cases, including instances with only few groups and instances where the group structure is close to be hierarchical, as well as efficient approximation algorithms. Our results could allow, e.g., municipalities to hold richer PB processes that are thematically and geographically inclusive.
{"title":"Participatory budgeting with project groups","authors":"Pallavi Jain , Krzysztof Sornat , Nimrod Talmon , Meirav Zehavi","doi":"10.1016/j.jcss.2025.103702","DOIUrl":"10.1016/j.jcss.2025.103702","url":null,"abstract":"<div><div>We study a generalization of the standard approval-based model of participatory budgeting (PB), in which voters are providing approval ballots over a set of predefined projects and—in addition to a global budget limit, there are several groupings of the projects, each group with its own budget limit. We study the computational complexity of identifying project bundles that maximize voter satisfaction while respecting all budget limits. We show that the problem is generally intractable and describe efficient exact algorithms for several special cases, including instances with only few groups and instances where the group structure is close to be hierarchical, as well as efficient approximation algorithms. Our results could allow, e.g., municipalities to hold richer PB processes that are thematically and geographically inclusive.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"156 ","pages":"Article 103702"},"PeriodicalIF":0.9,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145060902","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 : 2025-08-12DOI: 10.1016/j.jcss.2025.103699
Shengyu Huang , Chih-Hung Liu , Daniel Rutschmann
Given n elements, an integer and a parameter , we study the problem of selecting an element with rank in using unreliable comparisons where the outcome of each comparison is incorrect independently with a constant error probability, and multiple comparisons between the same pair of elements are independent. We develop a randomized algorithm that performs expected comparisons to achieve success probability at least . We also prove that even in the absence of comparison faults, any randomized algorithm with success probability at least performs expected comparisons. In particular, our algorithm is optimal as long as n is large enough, i.e., when ; outside this parameter range, no algorithm performs a sublinear number of comparisons. Surprisingly, for constant Q, our algorithm performs expected comparisons with and without comparison faults, while for the exact selection problem, the expected number of comparisons is with faults versus without faults.
{"title":"Approximate selection with unreliable comparisons in sublinear time","authors":"Shengyu Huang , Chih-Hung Liu , Daniel Rutschmann","doi":"10.1016/j.jcss.2025.103699","DOIUrl":"10.1016/j.jcss.2025.103699","url":null,"abstract":"<div><div>Given <em>n</em> elements, an integer <span><math><mi>k</mi><mo>≤</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> and a parameter <span><math><mi>ε</mi><mo>≥</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac></math></span>, we study the problem of selecting an element with rank in <span><math><mo>(</mo><mi>k</mi><mo>−</mo><mi>n</mi><mi>ε</mi><mo>,</mo><mi>k</mi><mo>+</mo><mi>n</mi><mi>ε</mi><mo>]</mo></math></span> using <em>unreliable</em> comparisons where the outcome of each comparison is incorrect independently with a constant error probability, and multiple comparisons between the same pair of elements are independent. We develop a randomized algorithm that performs <em>expected</em> <span><math><mi>O</mi><mo>(</mo><mfrac><mrow><mi>k</mi></mrow><mrow><mi>n</mi></mrow></mfrac><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mi>log</mi><mo></mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>Q</mi></mrow></mfrac><mo>)</mo></math></span> comparisons to achieve success probability at least <span><math><mn>1</mn><mo>−</mo><mi>Q</mi></math></span>. We also prove that even in the absence of comparison faults, any randomized algorithm with success probability at least <span><math><mn>1</mn><mo>−</mo><mi>Q</mi></math></span> performs <em>expected</em> <span><math><mi>Ω</mi><mo>(</mo><mi>min</mi><mo></mo><mo>{</mo><mi>n</mi><mo>,</mo><mfrac><mrow><mi>k</mi></mrow><mrow><mi>n</mi></mrow></mfrac><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mi>log</mi><mo></mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>Q</mi></mrow></mfrac><mo>}</mo><mo>)</mo></math></span> comparisons. In particular, our algorithm is optimal as long as <em>n</em> is large enough, i.e., when <span><math><mi>n</mi><mo>=</mo><mi>Ω</mi><mrow><mo>(</mo><mfrac><mrow><mi>k</mi></mrow><mrow><mi>n</mi></mrow></mfrac><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mi>log</mi><mo></mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>Q</mi></mrow></mfrac><mo>)</mo></mrow></math></span>; outside this parameter range, no algorithm performs a sublinear number of comparisons. Surprisingly, for constant <em>Q</em>, our algorithm performs expected <span><math><mi>O</mi><mo>(</mo><mfrac><mrow><mi>k</mi></mrow><mrow><mi>n</mi></mrow></mfrac><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>)</mo></math></span> comparisons with and without comparison faults, while for the exact selection problem, the expected number of comparisons is <span><math><mi>Θ</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo></mo><mi>k</mi><mo>)</mo></math></span> with faults versus <span><math><mi>Θ</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> without faults.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"155 ","pages":"Article 103699"},"PeriodicalIF":0.9,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886722","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 : 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.
{"title":"How to tamper with a Parliament: Strategic campaigns in apportionment elections","authors":"Robert Bredereck , Piotr Faliszewski , Michał Furdyna , Andrzej Kaczmarczyk , Joanna Kaczmarek , Martin Lackner , Christian Laußmann , Jörg Rothe , Tessa Seeger","doi":"10.1016/j.jcss.2025.103700","DOIUrl":"10.1016/j.jcss.2025.103700","url":null,"abstract":"<div><div>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 <em>strategic campaigns</em> 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.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"155 ","pages":"Article 103700"},"PeriodicalIF":0.9,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864523","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 : 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":"2025-08-05","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 : 2025-07-31DOI: 10.1016/j.jcss.2025.103695
Konstantinos Georgiou , Woojin Jang
The input to the Triangle Evacuation problem is a non-obtuse triangle ABC. A feasible solution is two unit-speed trajectories of mobile agents that start at some point on the perimeter and eventually visit every point on the perimeter of ABC. The goal is to find trajectories that minimize the evacuation cost, defined as the supremum, over all points T, of the time when T is first visited by one agent plus the distance from T to the other agent at that time. We introduce 4 different algorithmic problems arising by letting the starting edge and/or the starting point S on that edge to be chosen either by the algorithm or the adversary. To that end, we provide a tight analysis for the algorithm that has been proved to be optimal for the previously studied search domains, as well as we provide lower bounds for each of the problems.
{"title":"Triangle evacuation of 2 agents in the wireless model & the power of choosing a starting point","authors":"Konstantinos Georgiou , Woojin Jang","doi":"10.1016/j.jcss.2025.103695","DOIUrl":"10.1016/j.jcss.2025.103695","url":null,"abstract":"<div><div>The input to the <em>Triangle Evacuation</em> problem is a non-obtuse triangle <em>ABC</em>. A feasible solution is two unit-speed trajectories of mobile agents that start at some point on the perimeter and eventually visit every point on the perimeter of <em>ABC</em>. The goal is to find trajectories that minimize the evacuation cost, defined as the supremum, over all points <em>T</em>, of the time when <em>T</em> is first visited by one agent plus the distance from <em>T</em> to the other agent at that time. We introduce 4 different algorithmic problems arising by letting the starting edge and/or the starting point <em>S</em> on that edge to be chosen either by the algorithm or the adversary. To that end, we provide a tight analysis for the algorithm that has been proved to be optimal for the previously studied search domains, as well as we provide lower bounds for each of the problems.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"155 ","pages":"Article 103695"},"PeriodicalIF":0.9,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766445","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 : 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":"2025-07-30","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 : 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":"2025-07-22","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 : 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":"2025-07-21","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}
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":"2025-07-17","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 : 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":"2025-07-03","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}
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