Information Processing Letters最新文献

{"title":"Deterministic treasure hunt and rendezvous in arbitrary connected graphs","authors":"Debasish Pattanayak,&nbsp;Andrzej Pelc","doi":"10.1016/j.ipl.2023.106455","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106455","url":null,"abstract":"<div><p>Treasure hunt and rendezvous are fundamental tasks performed by mobile agents in graphs. In treasure hunt, an agent has to find an inert target (called treasure) situated at an unknown node of the graph. In rendezvous, two agents, initially located at distinct nodes of the graph, traverse its edges in synchronous rounds and have to meet at some node. We assume that the graph is connected (otherwise none of these tasks is feasible) and consider deterministic treasure hunt and rendezvous algorithms. The time of a treasure hunt algorithm is the worst-case number of edge traversals performed by the agent until the treasure is found. The time of a rendezvous algorithm is the worst-case number of rounds since the wakeup of the earlier agent until the meeting.</p><p>To the best of our knowledge, all known treasure hunt and rendezvous algorithms rely on the assumption that degrees of all nodes are finite, even when the graph itself may be infinite. In the present paper we remove this assumption for the first time, and consider both above tasks in arbitrary connected graphs whose nodes can have either finite or countably infinite degrees. Our main result is the first universal treasure hunt algorithm working for arbitrary connected graphs. We prove that the time of this algorithm has optimal order of magnitude among all possible treasure hunt algorithms working for arbitrary connected graphs. As a consequence of this result we obtain the first universal rendezvous algorithm working for arbitrary connected graphs. The time of this algorithm is polynomial in a lower bound holding in many graphs, in particular in the tree all of whose degrees are infinite.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"185 ","pages":"Article 106455"},"PeriodicalIF":0.5,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67739970","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 effect of iterativity on adversarial opinion forming","authors":"Konstantinos Panagiotou,&nbsp;Simon Reisser","doi":"10.1016/j.ipl.2023.106453","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106453","url":null,"abstract":"<div><p>Consider the following model to study adversarial effects on opinion forming. A set of initially selected experts form their binary opinion while being influenced by an adversary, who may convince some of them of the falsehood. All other participants in the network then take the opinion of the majority of their neighboring experts. Can the adversary influence the experts in such a way that the majority of the network believes the falsehood? Alon et al. <span>[2]</span> conjectured that in this context an iterative dissemination process will always be beneficial to the adversary. In this note we provide a counterexample to that conjecture.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"185 ","pages":"Article 106453"},"PeriodicalIF":0.5,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92027369","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":"Anti Tai mapping for unordered labeled trees","authors":"Mislav Blažević ,&nbsp;Stefan Canzar ,&nbsp;Khaled Elbassioni ,&nbsp;Domagoj Matijević","doi":"10.1016/j.ipl.2023.106454","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106454","url":null,"abstract":"&lt;div&gt;&lt;p&gt;The well-studied Tai mapping between two rooted labeled trees &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; defines a one-to-one mapping between nodes in &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; that preserves ancestor relationship &lt;span&gt;[1]&lt;/span&gt;. For unordered trees the problem of finding a maximum-weight Tai mapping is known to be NP-complete &lt;span&gt;[2]&lt;/span&gt;. In this work, we define an anti Tai mapping &lt;span&gt;&lt;math&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;⊆&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt; as a binary relation between two unordered labeled trees such that any two &lt;/span&gt;&lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; violate ancestor relationship and thus cannot be part of the same Tai mapping, i.e. &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;⇔&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;≰&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∨&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;⇔&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;≰&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, given an ancestor order &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; meaning that &lt;em&gt;x&lt;/em&gt; is an ancestor of &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;. Finding a maximum-weight anti Tai mapping arises in the cutting plane method for solving the maximum-weight Tai mapping problem via integer programming. We give an efficient polynomial-time algorithm for finding a maximum-weight anti Tai mapping for the case when one of the two trees is a path and further show how to extend this result in order to provide a polynomially computable lower bound on the optimal anti Tai mapping for two unordered labeled trees. The latter result stems from the special class of anti Tai mappings defined by the more restricted condition &lt;/span&gt;&lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∼&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;⇔&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;≁&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"185 ","pages":"Article 106454"},"PeriodicalIF":0.5,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92027370","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":"Discrete and mixed two-center problems for line segments","authors":"Sukanya Maji,&nbsp;Sanjib Sadhu","doi":"10.1016/j.ipl.2023.106451","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106451","url":null,"abstract":"<div><p>Given a set of <em>n</em> non-intersecting line segments <span><math><mi>L</mi></math></span> and a set <em>Q</em> of <em>m</em> points in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>; we present algorithms of the discrete two-center problem for (i) covering, (ii) stabbing and (iii) hitting the set <span><math><mi>L</mi></math></span> in (i) <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mo>(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo>)</mo><msup><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span>, (ii) <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> and (iii) <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mo>(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo>)</mo><msup><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> time respectively, where the two disks are centered at two points of <em>Q</em> and radius of the larger disk is minimized. We also study the mixed two-center problems for (i) covering, (ii) stabbing and (iii) hitting the set <span><math><mi>L</mi></math></span>, where only one of the disks is centered at a point <span><math><msub><mrow><mi>q</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><mi>Q</mi></math></span> and the other disk is centered at any point in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, and these three problems are solved in (i) <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span>, (ii) <span><math><mi>O</mi><mo>(</mo><mi>m</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> and (iii) <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>n</mi><msup><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> time, respectively. The space complexities for all these algorithms are linear.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106451"},"PeriodicalIF":0.5,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192084","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":"Ranking and unranking bordered and unbordered words","authors":"Daniel Gabric","doi":"10.1016/j.ipl.2023.106452","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106452","url":null,"abstract":"<div><p>A <em>border</em> of a word <em>w</em> is a word that is both a non-empty proper prefix and suffix of <em>w</em>. If <em>w</em> has a border, then it is said to be <em>bordered</em>; otherwise, it is said to be <em>unbordered</em>. The main results of this paper are the first algorithms to rank and unrank length-<em>n</em> bordered and unbordered words over a <em>k</em>-letter alphabet. We show that, under the unit-cost RAM model, ranking bordered and unbordered words can be done in <span><math><mi>O</mi><mo>(</mo><mi>k</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> time using <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> space, and unranking them can be done in <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>4</mn></mrow></msup><mi>k</mi><mi>log</mi><mo>⁡</mo><mi>k</mi><mo>)</mo></math></span> time using <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> space.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106452"},"PeriodicalIF":0.5,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192085","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":"Vertex-connectivity for node failure identification in Boolean Network Tomography","authors":"Nicola Galesi ,&nbsp;Fariba Ranjbar ,&nbsp;Michele Zito","doi":"10.1016/j.ipl.2023.106450","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106450","url":null,"abstract":"<div><p>We study the node failure identification problem in undirected graphs by means of Boolean Network Tomography. We argue that vertex-connectivity plays a central role. We prove bounds on the maximum number of simultaneous node failures that can be identified in arbitrary networks. We argue that (augmented) grids are a class of networks with large failure identifiability, and provide very tight results in this context.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106450"},"PeriodicalIF":0.5,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192157","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":"Checking in polynomial time whether or not a regular tree language is deterministic top-down","authors":"Sebastian Maneth ,&nbsp;Helmut Seidl","doi":"10.1016/j.ipl.2023.106449","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106449","url":null,"abstract":"<div><p><span>It is well known that for a given bottom-up tree automaton it can be decided whether or not an equivalent deterministic top-down tree automaton exists. Recently it was claimed that such a decision can be carried out in </span>polynomial time<span> (Leupold and Maneth, FCT'2021); but their procedure and corresponding property is wrong. Here we address this mistake and present a correct property which allows to determine in polynomial time whether or not a given tree language can be recognized by a deterministic top-down tree automaton. Furthermore, our new property is stated for arbitrary deterministic bottom-up tree automata, and not only for minimal such automata (as before).</span></p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106449"},"PeriodicalIF":0.5,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192082","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":"Inapproximability of counting independent sets in linear hypergraphs","authors":"Guoliang Qiu ,&nbsp;Jiaheng Wang","doi":"10.1016/j.ipl.2023.106448","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106448","url":null,"abstract":"<div><p>It is shown in this note that approximating the number of independent sets in a <em>k</em>-uniform linear hypergraph with maximum degree at most Δ is <strong>NP</strong>-hard if <span><math><mi>Δ</mi><mo>≥</mo><mn>5</mn><mo>⋅</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><mn>1</mn></math></span>. This confirms that for the relevant sampling and approximate counting problems, the regimes on the maximum degree where the state-of-the-art algorithms work are tight, up to some small factors. These algorithms include: the approximate sampler and randomised approximation scheme by Hermon et al. (2019) <span>[5]</span>, the perfect sampler by Qiu et al. (2022) <span>[6]</span>, and the deterministic approximation scheme by Feng et al. (2023) <span>[7]</span>.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106448"},"PeriodicalIF":0.5,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192083","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 facility location problem with maximum distance constraint","authors":"Xiaowei Li,&nbsp;Xiwen Lu","doi":"10.1016/j.ipl.2023.106447","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106447","url":null,"abstract":"<div><p>Motivated by practical problems, we investigate the facility location problem with maximum distance constraint, which requires that the distance from each customer to open facilities must not exceed a given threshold value of <em>L</em>. The goal is to minimise the sum of the opening costs of the facilities. We show that this problem is NP-hard and analyse its lower bound. As no <span><math><mo>(</mo><mi>α</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-approximation algorithm with <span><math><mi>α</mi><mo>&lt;</mo><mn>3</mn></math></span> exists, we provide a (3,1)-approximation algorithm that violates the maximum distance constraint. Based on this algorithm, we propose a 3-approximation algorithm for the <em>k</em>-supplier problem. The difference between this algorithm and the previous one in <span>[12]</span> is that the proposed algorithm avoids the construction of many bottleneck graphs, making the proposed algorithm less demanding in terms of memory and more suitable for large-scale problems.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106447"},"PeriodicalIF":0.5,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192081","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":"Relating planar graph drawings to planar satisfiability problems","authors":"Md. Manzurul Hasan ,&nbsp;Debajyoti Mondal ,&nbsp;Md. Saidur Rahman","doi":"10.1016/j.ipl.2023.106446","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106446","url":null,"abstract":"<div><p>A SAT graph <span><math><mi>G</mi><mo>(</mo><mi>Φ</mi><mo>)</mo></math></span><span> of a satisfiability instance Φ consists of a vertex for each clause and a vertex for each variable, where there exists an edge between a clause vertex and a variable vertex if and only if the variable or its negation appears in that clause. Many satisfiability problems<span>, which are NP-hard, become polynomial-time solvable when the SAT graph is restricted to satisfy some graph properties. A rich body of research attempts to narrow down the boundary between the NP-hardness and polynomial-time solvability of various satisfiability problems. In this paper, we examine planar satisfiability problems and leverage planar graph drawing algorithms to improve our understanding of these problems. A rich body of graph drawing algorithms exists to check whether a planar graph admits a drawing that satisfies certain drawing aesthetics. We show how the existing graph drawing knowledge could be used to establish sufficient conditions for a SAT instance to always be satisfiable and give algorithms to efficiently find a satisfying truth assignment. In some cases, our algorithm can find a truth assignment by setting a small number of variables to true, which relates to the satisfiability variants that seek to minimize the number of ones.</span></span></p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106446"},"PeriodicalIF":0.5,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192079","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}