Information Processing Letters最新文献

{"title":"On conflict-free cuts: Algorithms and complexity","authors":"Johannes Rauch ,&nbsp;Dieter Rautenbach ,&nbsp;Uéverton S. Souza","doi":"10.1016/j.ipl.2024.106503","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106503","url":null,"abstract":"<div><p>One way to define the <span>Matching Cut</span> problem is: Given a graph <em>G</em>, is there an edge-cut <em>M</em> of <em>G</em> such that <em>M</em> is an independent set in the line graph of <em>G</em>? We propose the more general <span>Conflict-Free Cut</span> problem: Together with the graph <em>G</em>, we are given a so-called conflict graph <span><math><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> on the edges of <em>G</em>, and we ask for an edge-cutset <em>M</em> of <em>G</em> that is independent in <span><math><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span>. Since conflict-free settings are popular generalizations of classical optimization problems and <span>Conflict-Free Cut</span> was not considered in the literature so far, we start the study of the problem. We show that the problem is <span><math><mi>NP</mi></math></span>-complete even when the maximum degree of <em>G</em> is 5 and <span><math><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> is 1-regular. The same reduction implies an exponential lower bound on the solvability based on the Exponential Time Hypothesis. We also give parameterized complexity results: We show that the problem is fixed-parameter tractable with the vertex cover number of <em>G</em> as a parameter, and we show <span><math><mi>W</mi><mo>[</mo><mn>1</mn><mo>]</mo></math></span>-hardness even when <em>G</em> has a feedback vertex set of size one, and the clique cover number of <span><math><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> is the parameter. Since the clique cover number of <span><math><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> is an upper bound on the independence number of <span><math><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> and thus the solution size, this implies <span><math><mi>W</mi><mo>[</mo><mn>1</mn><mo>]</mo></math></span>-hardness when parameterized by the cut size. We list polynomial-time solvable cases and interesting open problems. At last, we draw a connection to a symmetric variant of <span>SAT</span>.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106503"},"PeriodicalIF":0.5,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000334/pdfft?md5=245b78d016a76de957fec713f0824a46&pid=1-s2.0-S0020019024000334-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140948679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Improved lower bound for differentially private facility location","authors":"Pasin Manurangsi","doi":"10.1016/j.ipl.2024.106502","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106502","url":null,"abstract":"<div><p>We consider the differentially private (DP) facility location problem in the so called <em>super-set output</em> setting proposed by Gupta et al. <span>[13]</span>. The current best known expected approximation ratio for an <em>ϵ</em>-DP algorithm is <span><math><mi>O</mi><mrow><mo>(</mo><mfrac><mrow><mi>log</mi><mo>⁡</mo><mi>n</mi></mrow><mrow><msqrt><mrow><mi>ϵ</mi></mrow></msqrt></mrow></mfrac><mo>)</mo></mrow></math></span> due to Cohen-Addad et al. <span>[3]</span> where <em>n</em> denote the size of the metric space, meanwhile the best known lower bound is <span><math><mi>Ω</mi><mo>(</mo><mn>1</mn><mo>/</mo><msqrt><mrow><mi>ϵ</mi></mrow></msqrt><mo>)</mo></math></span> <span>[8]</span>.</p><p>In this short note, we give a lower bound of <span><math><mover><mrow><mi>Ω</mi></mrow><mrow><mo>˜</mo></mrow></mover><mrow><mo>(</mo><mi>min</mi><mo>⁡</mo><mrow><mo>{</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>,</mo><msqrt><mrow><mfrac><mrow><mi>log</mi><mo>⁡</mo><mi>n</mi></mrow><mrow><mi>ϵ</mi></mrow></mfrac></mrow></msqrt><mo>}</mo></mrow><mo>)</mo></mrow></math></span> on the expected approximation ratio of any <em>ϵ</em>-DP algorithm, which is the first evidence that the approximation ratio has to grow with the size of the metric space.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106502"},"PeriodicalIF":0.5,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880174","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":"Is this network proper forest-based?","authors":"Katharina T. Huber ,&nbsp;Leo van Iersel ,&nbsp;Vincent Moulton ,&nbsp;Guillaume E. Scholz","doi":"10.1016/j.ipl.2024.106500","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106500","url":null,"abstract":"<div><p>In evolutionary biology, networks are becoming increasingly used to represent evolutionary histories for species that have undergone non-treelike or reticulate evolution. Such networks are essentially directed acyclic graphs with a leaf set that corresponds to a collection of species, and in which non-leaf vertices with indegree 1 correspond to speciation events and vertices with indegree greater than 1 correspond to reticulate events such as gene transfer. Recently forest-based networks have been introduced, which are essentially (multi-rooted) networks that can be formed by adding some arcs to a collection of phylogenetic trees (or phylogenetic forest), where each arc is added in such a way that its ends always lie in two different trees in the forest. In this paper, we consider the complexity of deciding whether a given network is proper forest-based, that is, whether it can be formed by adding arcs to some underlying phylogenetic forest which contains the same number of trees as there are roots in the network. More specifically, we show that it is NP-complete to decide whether a tree-child network with <em>m</em> roots is proper forest-based, for each <span><math><mi>m</mi><mo>≥</mo><mn>2</mn></math></span>. Moreover, for binary networks the problem remains NP-complete when <span><math><mi>m</mi><mo>≥</mo><mn>3</mn></math></span> but becomes polynomial-time solvable for <span><math><mi>m</mi><mo>=</mo><mn>2</mn></math></span>. We also give a fixed parameter tractable (FPT) algorithm, with parameters the maximum outdegree of a vertex, the number of roots, and the number of indegree 2 vertices, for deciding if a semi-binary network is proper forest-based. A key element in proving our results is a new characterization for when a network with <em>m</em> roots is proper forest-based in terms of certain <em>m</em>-colorings.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106500"},"PeriodicalIF":0.5,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000309/pdfft?md5=6bb24ac246fe9301af0f20ad64b94c09&pid=1-s2.0-S0020019024000309-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140924528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Top-down complementation of automata on finite trees","authors":"Laurent Doyen","doi":"10.1016/j.ipl.2024.106499","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106499","url":null,"abstract":"<div><p>We present a new complementation construction for nondeterministic automata on finite trees. The traditional complementation involves determinization of the corresponding bottom-up automaton (recall that top-down deterministic automata are less powerful than nondeterministic automata, whereas bottom-up deterministic automata are equally powerful).</p><p>The construction works directly in a top-down fashion, therefore without determinization. The main advantages of this construction are: (<em>i</em>) in the special case of finite words it boils down to the standard subset construction (which is not the case of the traditional bottom-up complementation construction), and <span><math><mo>(</mo><mi>i</mi><mi>i</mi><mo>)</mo></math></span> it illustrates the core argument of the complementation lemma for infinite trees, central in the proof of Rabin's tree theorem, in a simpler setting where issues related to acceptance conditions over infinite words and determinacy of infinite games are not present.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106499"},"PeriodicalIF":0.5,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000292/pdfft?md5=c514386574ffd52c0851a3a48a6c2db9&pid=1-s2.0-S0020019024000292-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140825394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dispersion problem on a convex polygon","authors":"Pawan K. Mishra ,&nbsp;S.V. Rao ,&nbsp;Gautam K. Das","doi":"10.1016/j.ipl.2024.106498","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106498","url":null,"abstract":"<div><p>Given a set <span><math><mi>P</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></math></span> of <em>n</em> points in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and a positive integer <em>k</em> <span><math><mo>(</mo><mo>≤</mo><mi>n</mi><mo>)</mo></math></span>, we wish to find a subset <em>S</em> of <em>P</em> of size <em>k</em> such that the cost of a subset <em>S</em>, <span><math><mi>c</mi><mi>o</mi><mi>s</mi><mi>t</mi><mo>(</mo><mi>S</mi><mo>)</mo><mo>=</mo><mi>min</mi><mo>⁡</mo><mo>{</mo><mi>d</mi><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo><mo>|</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>∈</mo><mi>S</mi><mo>}</mo></math></span>, is maximized, where <span><math><mi>d</mi><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> is the Euclidean distance between two points <em>p</em> and <em>q</em>. The problem is called the <em>max-min k-dispersion problem</em>. In this article, we consider the max-min <em>k</em>-dispersion problem, where a given set <em>P</em> of <em>n</em> points are vertices of a convex polygon. We refer to this variant of the problem as the <em>convex k-dispersion</em> problem.</p><p>We propose an 1.733-factor approximation algorithm for the convex <em>k</em>-dispersion problem. In addition, we study the convex <em>k</em>-dispersion problem for <span><math><mi>k</mi><mo>=</mo><mn>4</mn></math></span>. We propose an iterative algorithm that returns an optimal solution of size 4 in <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> time.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106498"},"PeriodicalIF":0.5,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140843117","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":"Regular D-length: A tool for improved prefix-stable forward Ramsey factorisations","authors":"Théodore Lopez,&nbsp;Benjamin Monmege,&nbsp;Jean-Marc Talbot","doi":"10.1016/j.ipl.2024.106497","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106497","url":null,"abstract":"<div><p>Recently, Jecker has introduced and studied the regular <span><math><mi>D</mi></math></span>-length of a monoid, as the length of its longest chain of regular <span><math><mi>D</mi></math></span>-classes. We use this parameter in order to improve the construction, originally proposed by Colcombet, of a deterministic automaton that allows to map a word to one of its forward Ramsey splits: these are a relaxation of factorisation forests that enjoy prefix stability, thus allowing a compositional construction. For certain monoids that have a small regular <span><math><mi>D</mi></math></span>-length, our construction produces an exponentially more succinct deterministic automaton. Finally, we apply it to obtain better complexity result for the problem of fast infix evaluation.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106497"},"PeriodicalIF":0.5,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140647631","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":"Correcting matrix products over the ring of integers","authors":"Yu-Lun Wu,&nbsp;Hung-Lung Wang","doi":"10.1016/j.ipl.2024.106496","DOIUrl":"10.1016/j.ipl.2024.106496","url":null,"abstract":"<div><p>Let <em>A</em>, <em>B</em>, and <em>C</em> be three <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> matrices. We investigate the problem of verifying whether <span><math><mi>A</mi><mi>B</mi><mo>=</mo><mi>C</mi></math></span> over the ring of integers and finding the correct product <em>AB</em>. Given that <em>C</em> is different from <em>AB</em> by at most <em>k</em> entries, we propose an algorithm that uses <span><math><mi>O</mi><mo>(</mo><msqrt><mrow><mi>k</mi></mrow></msqrt><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>n</mi><mo>)</mo></math></span> operations. Let <em>α</em> be the largest absolute value of an entry in <em>A</em>, <em>B</em>, and <em>C</em>. The integers involved in the computation are of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><msup><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106496"},"PeriodicalIF":0.5,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140616211","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":"A linear-time algorithm for the center problem in weighted cycle graphs","authors":"Taekang Eom ,&nbsp;Hee-Kap Ahn","doi":"10.1016/j.ipl.2024.106495","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106495","url":null,"abstract":"<div><p>We study the problem of computing the center of cycle graphs whose vertices are weighted. The distance from a vertex to a point of the graph is defined as the weight of the vertex times the length of the shortest path between the vertex and the point. The weighted center of the graph is a point of the graph such that the maximum distance of the vertices of the graph to the point is minimum among all points of the graph. We present an <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-time algorithm for the discrete and continuous weighted center problem on cycle graphs with <em>n</em> vertices. Our algorithm improves upon the best known algorithm that takes <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> time. Moreover, it is optimal for the weighted center problem of cycle graphs.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106495"},"PeriodicalIF":0.5,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140540027","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":"The autocorrelation of a class of quaternary sequences of length pq with high complexity","authors":"Feifei Yan ,&nbsp;Pinhui Ke ,&nbsp;Zuling Chang","doi":"10.1016/j.ipl.2024.106494","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106494","url":null,"abstract":"<div><p>Recently, a class of quaternary sequences with period <em>pq</em>, where <em>p</em> and <em>q</em> are two distinct odd primes introduced by Zhang et al. were proved to possess high linear complexity and 4-adic complexity. In this paper, we determine the autocorrelation distribution of this class of quaternary sequence. Our results indicate that the studied quaternary sequence are weak with respect to the correlation property.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106494"},"PeriodicalIF":0.5,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140321256","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":"Branching bisimulation semantics for quantum processes","authors":"Hao Wu ,&nbsp;Qizhe Yang ,&nbsp;Huan Long","doi":"10.1016/j.ipl.2024.106492","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106492","url":null,"abstract":"<div><p>The qCCS model proposed by Feng et al. provides a powerful framework to describe and reason about quantum communication systems that could be entangled with the environment. However, they only studied weak bisimulation semantics. In this paper we propose a new branching bisimilarity for qCCS and show that it is a congruence. The new bisimilarity is based on the concept of <em>ϵ</em>-tree and preserves the branching structure of concurrent processes where both quantum and classical components are allowed. Furthermore, we present a polynomial time equivalence checking algorithm for the ground version of our branching bisimilarity.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106492"},"PeriodicalIF":0.5,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140163830","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}