Journal of Computer and System Sciences最新文献

{"title":"Labeled sample compression schemes for complexes of oriented matroids","authors":"Victor Chepoi ,&nbsp;Kolja Knauer ,&nbsp;Manon Philibert","doi":"10.1016/j.jcss.2024.103543","DOIUrl":"https://doi.org/10.1016/j.jcss.2024.103543","url":null,"abstract":"<div><p>We show that the topes of a complex of oriented matroids (abbreviated COM) of VC-dimension <em>d</em> admit a proper labeled sample compression scheme of size <em>d</em>. This considerably extends results of Moran and Warmuth on ample classes, of Ben-David and Litman on affine arrangements of hyperplanes, and of the authors on complexes of uniform oriented matroids, and is a step towards the sample compression conjecture – one of the oldest open problems in computational learning theory. On the one hand, our approach exploits the rich combinatorial cell structure of COMs via oriented matroid theory. On the other hand, viewing tope graphs of COMs as partial cubes creates a fruitful link to metric graph theory.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"144 ","pages":"Article 103543"},"PeriodicalIF":1.1,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140605005","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}

{"title":"On the parameterized complexity of interval scheduling with eligible machine sets","authors":"Danny Hermelin ,&nbsp;Yuval Itzhaki ,&nbsp;Hendrik Molter ,&nbsp;Dvir Shabtay","doi":"10.1016/j.jcss.2024.103533","DOIUrl":"10.1016/j.jcss.2024.103533","url":null,"abstract":"<div><p>We provide new parameterized complexity results for <span>Interval Scheduling on Eligible Machines</span>. In this problem, a set of <em>n</em> jobs is given to be processed non-preemptively on a set of <em>m</em> machines. Each job has a <em>processing time</em>, a <em>deadline</em>, a <em>weight</em>, and a set of <em>eligible machines</em> that can process it. The goal is to find a maximum weight subset of jobs that can each be processed on one of its eligible machines such that it completes exactly at its deadline. We focus on two parameters: The number <em>m</em> of machines, and the largest processing time <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>max</mi></mrow></msub></math></span>. Our main contribution is showing <span>W[1]</span>-hardness when parameterized by <em>m</em>. This answers Open Problem 8 of Mnich and van Bevern's list of 15 open problems in parameterized complexity of scheduling problems [Computers &amp; Operations Research, 2018]. Furthermore, we show <span>NP</span>-hardness even when <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>max</mi></mrow></msub><mo>=</mo><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span> and present an <span>FPT</span>-algorithm with for the combined parameter <span><math><mi>m</mi><mo>+</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>max</mi></mrow></msub></math></span>.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"144 ","pages":"Article 103533"},"PeriodicalIF":1.1,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140402533","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}

{"title":"Preprocessing to reduce the search space: Antler structures for feedback vertex set","authors":"Huib Donkers,&nbsp;Bart M.P. Jansen","doi":"10.1016/j.jcss.2024.103532","DOIUrl":"https://doi.org/10.1016/j.jcss.2024.103532","url":null,"abstract":"<div><p>The goal of this paper is to open up a new research direction aimed at understanding the power of preprocessing in speeding up algorithms that solve NP-hard problems exactly. We explore this direction for the classic <span>Feedback Vertex Set</span> problem on undirected graphs, leading to a new type of graph structure called <em>antler decomposition</em>, which identifies vertices that belong to an optimal solution. It is an analogue of the celebrated <em>crown decomposition</em> which has been used for <span>Vertex Cover</span>. We develop the graph structure theory around such decompositions and develop fixed-parameter tractable algorithms to find them, parameterized by the number of vertices for which they witness presence in an optimal solution. This reduces the search space of fixed-parameter tractable algorithms parameterized by the solution size that solve <span>Feedback Vertex Set</span>.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"144 ","pages":"Article 103532"},"PeriodicalIF":1.1,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022000024000278/pdfft?md5=2d8e7a91708f0a0fee2cda8d00eb9d75&pid=1-s2.0-S0022000024000278-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140543243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"A cop and robber game on edge-periodic temporal graphs","authors":"Thomas Erlebach ,&nbsp;Nils Morawietz ,&nbsp;Jakob T. Spooner ,&nbsp;Petra Wolf","doi":"10.1016/j.jcss.2024.103534","DOIUrl":"10.1016/j.jcss.2024.103534","url":null,"abstract":"<div><p>We introduce a cops and robbers game with one cop and one robber on a special type of time-varying graphs (TVGs), namely edge-periodic graphs. These are TVGs in which, for each edge <em>e</em>, a binary string <span><math><mi>τ</mi><mo>(</mo><mi>e</mi><mo>)</mo></math></span> is given such that the edge <em>e</em> is present in time step <em>t</em> if and only if <span><math><mi>τ</mi><mo>(</mo><mi>e</mi><mo>)</mo></math></span> contains a 1 at position <span><math><mi>t</mi><mspace></mspace><mrow><mi>mod</mi></mrow><mspace></mspace><mo>|</mo><mi>τ</mi><mo>(</mo><mi>e</mi><mo>)</mo><mo>|</mo></math></span>. This periodicity allows for a compact representation of infinite TVGs. We prove that even for very simple underlying graphs, i.e., directed and undirected cycles, the problem of deciding whether a cop-winning strategy exists is NP-hard and <span><math><mi>W</mi><mo>[</mo><mn>1</mn><mo>]</mo></math></span>-hard parameterized by the number of vertices. Furthermore, we show that this decision problem can be solved on general edge-periodic graphs in PSPACE. Finally, we present tight bounds on the minimum length of a directed or undirected cycle that guarantees the cycle to be robber-winning.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"144 ","pages":"Article 103534"},"PeriodicalIF":1.1,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022000024000291/pdfft?md5=b5026eb7f4f00c8742c1bca27d3f8d40&pid=1-s2.0-S0022000024000291-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140403344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"On kernels for d-path vertex cover","authors":"Radovan Červený,&nbsp;Pratibha Choudhary,&nbsp;Ondřej Suchý","doi":"10.1016/j.jcss.2024.103531","DOIUrl":"10.1016/j.jcss.2024.103531","url":null,"abstract":"<div><p>In this paper we study the kernelization of the <em>d</em>-<span>Path Vertex Cover</span> (<em>d</em>-PVC) problem. Given a graph <em>G</em>, the problem requires finding whether there exists a set of at most <em>k</em> vertices whose removal from <em>G</em> results in a graph that does not contain a path (not necessarily induced) with <em>d</em> vertices. It is known that <em>d</em>-PVC is <span>NP</span>-complete for <span><math><mi>d</mi><mo>≥</mo><mn>2</mn></math></span>. Since the problem generalizes to <em>d</em>-<span>Hitting Set</span>, it is known to admit a kernel with <span><math><mi>O</mi><mo>(</mo><mi>d</mi><msup><mrow><mi>k</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span> edges. We improve on this by giving better kernels. Specifically, we give kernels with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> vertices and edges for the cases when <span><math><mi>d</mi><mo>=</mo><mn>4</mn></math></span> and <span><math><mi>d</mi><mo>=</mo><mn>5</mn></math></span>. Further, we give a kernel with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>4</mn></mrow></msup><msup><mrow><mi>d</mi></mrow><mrow><mn>2</mn><mi>d</mi><mo>+</mo><mn>9</mn></mrow></msup><mo>)</mo></math></span> vertices and edges for general <em>d</em>.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"144 ","pages":"Article 103531"},"PeriodicalIF":1.1,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140323105","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}

{"title":"Decidable problems in substitution shifts","authors":"Marie-Pierre Béal ,&nbsp;Dominique Perrin ,&nbsp;Antonio Restivo","doi":"10.1016/j.jcss.2024.103529","DOIUrl":"10.1016/j.jcss.2024.103529","url":null,"abstract":"<div><p>In this paper, we investigate the structure of the most general kind of substitution shifts, including non-minimal ones, and allowing erasing morphisms. We prove the decidability of many properties of these morphisms with respect to the shift space generated by iteration, such as aperiodicity, recognizability and (under an additional assumption) irreducibility, or minimality.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"143 ","pages":"Article 103529"},"PeriodicalIF":1.1,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201967","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}

{"title":"Packing arc-disjoint cycles in oriented graphs","authors":"Jasine Babu ,&nbsp;Ajay Saju Jacob ,&nbsp;R. Krithika ,&nbsp;Deepak Rajendraprasad","doi":"10.1016/j.jcss.2024.103530","DOIUrl":"10.1016/j.jcss.2024.103530","url":null,"abstract":"<div><p><span>Arc-Disjoint Cycle Packing</span> is a classical <span>NP</span>-complete problem and we study it from two perspectives: (1) by restricting the cycles in the packing to be of a fixed length, and (2) by restricting the inputs to bipartite tournaments. Focusing first on <span>Arc-Disjoint</span> <em>r</em><span>-Cycle Packing</span> (where the cycles in the packing are required to be of length <em>r</em>), we show <span>NP</span>-completeness in oriented graphs with girth <em>r</em> for each <span><math><mi>r</mi><mo>≥</mo><mn>3</mn></math></span> and study the parameterized complexity of the problem with respect to two parameterizations (solution size and vertex cover size) for <span><math><mi>r</mi><mo>=</mo><mn>4</mn></math></span> in oriented graphs. Moving on to <span>Arc-Disjoint Cycle Packing</span> in bipartite tournaments, we show that every bipartite tournament either contains <em>k</em> arc-disjoint cycles or has a feedback arc set of size at most <span><math><mn>7</mn><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>. This result adds to the set of Erdös-Pósa-type results known in the combinatorics literature for packing and covering problems.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"143 ","pages":"Article 103530"},"PeriodicalIF":1.1,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201944","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}

{"title":"Monitoring the edges of a graph using distances with given girth","authors":"Chenxu Yang ,&nbsp;Gang Yang ,&nbsp;Sun-Yuan Hsieh ,&nbsp;Yaping Mao ,&nbsp;Ralf Klasing","doi":"10.1016/j.jcss.2024.103528","DOIUrl":"10.1016/j.jcss.2024.103528","url":null,"abstract":"<div><p>A set <em>M</em> of vertices of a graph <em>G</em> is a <em>distance-edge-monitoring set</em> if for every edge <span><math><mi>e</mi><mo>∈</mo><mi>G</mi></math></span>, there is a vertex <span><math><mi>x</mi><mo>∈</mo><mi>M</mi></math></span> and a vertex <span><math><mi>y</mi><mo>∈</mo><mi>G</mi></math></span> such that <em>e</em> belongs to all shortest paths between <em>x</em> and <em>y</em>. We denote by <span><math><mrow><mi>dem</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math></span> the smallest size of such a set in <em>G</em>. In this paper, we prove that <span><math><mi>dem</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mi>n</mi><mo>−</mo><mo>⌊</mo><mi>g</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>/</mo><mn>2</mn><mo>⌋</mo></math></span> for any connected graph <em>G</em>, which is not a tree, of order <em>n</em>, where <span><math><mi>g</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is the length of a shortest cycle in <em>G</em>, and give the graphs with <span><math><mi>dem</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>n</mi><mo>−</mo><mo>⌊</mo><mi>g</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>/</mo><mn>2</mn><mo>⌋</mo></math></span>. We also obtain that <span><math><mo>|</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mo>≥</mo><mi>k</mi><mo>+</mo><mo>⌊</mo><mi>g</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>/</mo><mn>2</mn><mo>⌋</mo></math></span> for every connected graph <em>G</em> with <span><math><mrow><mi>dem</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>k</mi></math></span> and <span><math><mi>g</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>g</mi></math></span>. Furthermore, the lower bound holds if and only if <span><math><mi>g</mi><mo>=</mo><mn>3</mn></math></span> and <span><math><mi>k</mi><mo>=</mo><mi>n</mi><mo>−</mo><mn>1</mn></math></span> or <span><math><mi>g</mi><mo>=</mo><mn>4</mn></math></span> and <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span>. We prove that <span><math><mrow><mi>dem</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mn>2</mn><mi>n</mi><mo>/</mo><mn>5</mn></math></span> for <span><math><mi>g</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≥</mo><mn>5</mn></math></span>.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"143 ","pages":"Article 103528"},"PeriodicalIF":1.1,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140053823","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}

{"title":"Deep kernelization for the Tree Bisection and Reconnection (TBR) distance in phylogenetics","authors":"Steven Kelk ,&nbsp;Simone Linz ,&nbsp;Ruben Meuwese","doi":"10.1016/j.jcss.2024.103519","DOIUrl":"10.1016/j.jcss.2024.103519","url":null,"abstract":"<div><p>We describe a kernel of size <span><math><mn>9</mn><mi>k</mi><mo>−</mo><mn>8</mn></math></span> for the NP-hard problem of computing the Tree Bisection and Reconnection (TBR) distance <em>k</em> between two unrooted binary phylogenetic trees. To achieve this, we extend the existing portfolio of reduction rules with three new reduction rules. Two of these are based on the idea of topologically transforming the trees in a distance-preserving way in order to guarantee execution of earlier reduction rules. The third rule extends the local neighborhood approach introduced in <span>[20]</span> to more global structures, allowing new situations to be identified when the deletion of a leaf definitely reduces the TBR distance by one. The bound on the kernel size is tight up to an additive term. Our results also apply to the equivalent problem of computing a maximum agreement forest between two unrooted binary phylogenetic trees. We anticipate that our results are widely applicable for computing agreement-forest based dissimilarity measures.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"142 ","pages":"Article 103519"},"PeriodicalIF":1.1,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002200002400014X/pdfft?md5=d95807a5290b9b72c4034f27a39f9776&pid=1-s2.0-S002200002400014X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139587066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"SAT backdoors: Depth beats size","authors":"Jan Dreier ,&nbsp;Sebastian Ordyniak ,&nbsp;Stefan Szeider","doi":"10.1016/j.jcss.2024.103520","DOIUrl":"10.1016/j.jcss.2024.103520","url":null,"abstract":"<div><p>For several decades, much effort has been put into identifying classes of CNF formulas whose satisfiability can be decided in polynomial time. Classic results are the linear-time tractability of Horn formulas (Aspvall, Plass, and Tarjan, 1979) and Krom (i.e., 2CNF) formulas (Dowling and Gallier, 1984). Backdoors, introduced by Williams, Gomes and Selman (2003), gradually extend such a tractable class to all formulas of bounded distance to the class. Backdoor size provides a natural but rather crude distance measure between a formula and a tractable class. Backdoor depth, introduced by Mählmann, Siebertz, and Vigny (2021), is a more refined distance measure, which admits the utilization of different backdoor variables in parallel. We propose FPT approximation algorithms to compute backdoor depth into the classes Horn and Krom. This leads to a linear-time algorithm for deciding the satisfiability of formulas of bounded backdoor depth into these classes.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"142 ","pages":"Article 103520"},"PeriodicalIF":1.1,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022000024000151/pdfft?md5=aa98f57a25f01ddf20d9eccf4811314c&pid=1-s2.0-S0022000024000151-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139501386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}