Information Processing Letters最新文献

{"title":"Recognizing LBFS trees of bipartite graphs","authors":"Robert Scheffler","doi":"10.1016/j.ipl.2024.106483","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106483","url":null,"abstract":"<div><p>The graph searches Breadth First Search (BFS) and Depth First Search (DFS) and the spanning trees constructed by them are some of the most basic concepts in algorithmic graph theory. BFS trees are first-in trees, i.e., every vertex is connected to its first visited neighbor. DFS trees are last-in trees, i.e., every vertex is connected to the last visited neighbor before it. The problem whether a given spanning tree can be the first-in tree or last-in tree of a graph search ordering was introduced in the 1980s and has been studied for several graph searches and graph classes. Here, we consider the problem of deciding whether a given spanning tree of a bipartite graph can be a first-in tree or a last-in tree of the Lexicographic Breadth First Search (LBFS), a special variant of BFS that is commonly used in graph algorithms. We show that the recognition of both first-in trees and last-in trees of LBFS is <span><math><mi>NP</mi></math></span>-hard even if the start vertex of the search ordering is fixed and the height of the tree is four. We prove that the bound on the height is tight (unless <span><math><mi>P</mi><mo>=</mo><mrow><mi>NP</mi></mrow></math></span>) by showing that for all spanning trees of bipartite graphs with height smaller than four we can solve both search tree recognition problems of LBFS in polynomial time. Finally, we give a linear-time algorithm that solves both problems for chordal bipartite graphs and fixed start vertices.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106483"},"PeriodicalIF":0.5,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000139/pdfft?md5=0a705320becd861a4100ad392710d19e&pid=1-s2.0-S0020019024000139-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139738315","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":"Skolem and positivity completeness of ergodic Markov chains","authors":"Mihir Vahanwala","doi":"10.1016/j.ipl.2024.106481","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106481","url":null,"abstract":"<div><p>We consider the following Markov Reachability decision problems that view Markov Chains as Linear Dynamical Systems: given a finite, rational Markov Chain, source and target states, and a rational threshold, does the probability of reaching the target from the source at the <span><math><msup><mrow><mi>n</mi></mrow><mrow><mi>t</mi><mi>h</mi></mrow></msup></math></span> step: (i) equal the threshold for some <em>n</em>? (ii) cross the threshold for some <em>n</em>? (iii) cross the threshold for infinitely many <em>n</em>? These problems are respectively known to be equivalent to the Skolem, Positivity, and Ultimate Positivity problems for Linear Recurrence Sequences (LRS), number-theoretic problems whose decidability has been open for decades. We present an elementary reduction from LRS Problems to Markov Reachability Problems that improves the state of the art as follows. (a) We map LRS to <em>ergodic</em> (irreducible and aperiodic) Markov Chains that are ubiquitous, not least by virtue of their spectral structure, and (b) our reduction maps LRS of order <em>k</em> to Markov Chains of order <span><math><mi>k</mi><mo>+</mo><mn>1</mn></math></span>: a substantial improvement over the previous reduction that mapped LRS of order <em>k</em> to reducible and periodic Markov chains of order <span><math><mn>4</mn><mi>k</mi><mo>+</mo><mn>5</mn></math></span>. This contribution is significant in view of the fact that the number-theoretic hardness of verifying Linear Dynamical Systems can often be mitigated by spectral assumptions and restrictions on order.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106481"},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000115/pdfft?md5=da39be99a4cd399e31f45e5c0e089132&pid=1-s2.0-S0020019024000115-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139738314","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":"On size-independent sample complexity of ReLU networks","authors":"Mark Sellke","doi":"10.1016/j.ipl.2024.106482","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106482","url":null,"abstract":"<div><p>We study the sample complexity of learning ReLU neural networks from the point of view of generalization. Given norm constraints on the weight matrices, a common approach is to estimate the Rademacher complexity of the associated function class. Previously <span>[9]</span> obtained a bound independent of the network size (scaling with a product of Frobenius norms) except for a factor of the square-root depth. We give a refinement which often has no explicit depth-dependence at all.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106482"},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139907353","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":"Expressive completeness by separation for discrete time interval temporal logic with expanding modalities","authors":"Dimitar P. Guelev ,&nbsp;Ben Moszkowski","doi":"10.1016/j.ipl.2024.106480","DOIUrl":"10.1016/j.ipl.2024.106480","url":null,"abstract":"<div><p>Recently we established an analog of Gabbay's separation theorem about linear temporal logic (LTL) for the extension of Moszkowski's discrete time propositional Interval Temporal Logic (ITL) by two sets of expanding modalities, namely the unary neighbourhood modalities and the binary weak inverses of ITL's <em>chop</em> operator. One of the many useful applications of separation in LTL is the concise proof of LTL's expressive completeness wrt the monadic first-order theory of <span><math><mo>〈</mo><mi>ω</mi><mo>,</mo><mo>&lt;</mo><mo>〉</mo></math></span> it enables. In this paper we show how our separation theorem about ITL facilitates a similar proof of the expressive completeness of ITL with expanding modalities wrt the monadic first- and second-order theories of <span><math><mo>〈</mo><mi>Z</mi><mo>,</mo><mo>&lt;</mo><mo>〉</mo></math></span>.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106480"},"PeriodicalIF":0.5,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000103/pdfft?md5=587945e657c3449e305fda69d4d98cbd&pid=1-s2.0-S0020019024000103-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139690178","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":"Robust scheduling for minimizing maximum lateness on a serial-batch processing machine","authors":"Wei Wu ,&nbsp;Liang Tang ,&nbsp;Andrea Pizzuti","doi":"10.1016/j.ipl.2024.106473","DOIUrl":"10.1016/j.ipl.2024.106473","url":null,"abstract":"<div><p>We study a robust single-machine scheduling problem with uncertain processing times on a serial-batch processing machine to minimize maximum lateness. The problem can model many practical production and logistics applications which involve uncertain factors such as defect rates. A solution to a batch scheduling problem can be represented as a combination of a job-processing sequence and a partition of this sequence (batch sizing). To solve the problem, we prove that the job ordering rule for the earliest due date is optimal for any uncertainty set. For the batch sizing problem, we propose an exact algorithm based on dynamic programming with the same time complexity as solving the nominal problem.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106473"},"PeriodicalIF":0.5,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139585590","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":"Splitting NP-complete sets infinitely","authors":"Liyu Zhang,&nbsp;Mahmoud Quweider,&nbsp;Fitra Khan,&nbsp;Hansheng Lei","doi":"10.1016/j.ipl.2024.106472","DOIUrl":"10.1016/j.ipl.2024.106472","url":null,"abstract":"<div><p>Glaßer et al. (SIAMJCOMP 2009 and TCS 2009) proved that NP-complete languages are polynomial-time mitotic for the many-one reduction, meaning that each NP-complete language <em>L</em> can be split into two NP-complete languages <span><math><mi>L</mi><mo>∩</mo><mi>S</mi></math></span> and <span><math><mi>L</mi><mo>∩</mo><mover><mrow><mi>S</mi></mrow><mo>‾</mo></mover></math></span>, where <em>S</em> is a language in P. It follows that every NP-complete language can be partitioned into an arbitrary <em>finite</em> number of NP-complete languages. We strengthen and generalize this result by showing that every NP-complete language can be partitioned into <em>infinitely</em> many NP-complete languages. Furthermore those NP-complete languages resulting from such partitioning can be <em>effectively presented</em>.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106472"},"PeriodicalIF":0.5,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139518105","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":"FPT approximation and subexponential algorithms for covering few or many edges","authors":"Fedor V. Fomin ,&nbsp;Petr A. Golovach ,&nbsp;Tanmay Inamdar ,&nbsp;Tomohiro Koana","doi":"10.1016/j.ipl.2024.106471","DOIUrl":"10.1016/j.ipl.2024.106471","url":null,"abstract":"<div><p>We study the <em>α</em><span>-Fixed Cardinality Graph Partitioning (</span><em>α</em><span>-FCGP)</span> problem, the generic local graph partitioning problem introduced by Bonnet et al. [Algorithmica 2015]. In this problem, we are given a graph <em>G</em>, two numbers <span><math><mi>k</mi><mo>,</mo><mi>p</mi></math></span> and <span><math><mn>0</mn><mo>≤</mo><mi>α</mi><mo>≤</mo><mn>1</mn></math></span>, the question is whether there is a set <span><math><mi>S</mi><mo>⊆</mo><mi>V</mi></math></span> of size <em>k</em> with a specified coverage function <span><math><msub><mrow><mi>cov</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>(</mo><mi>S</mi><mo>)</mo></math></span> at least <em>p</em> (or at most <em>p</em> for the minimization version). The coverage function <span><math><msub><mrow><mi>cov</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>(</mo><mo>⋅</mo><mo>)</mo></math></span> counts edges with exactly one endpoint in <em>S</em> with weight <em>α</em> and edges with both endpoints in <em>S</em> with weight <span><math><mn>1</mn><mo>−</mo><mi>α</mi></math></span>. <em>α</em>-FCGP generalizes a number of fundamental graph problems such as <span>Densest</span> <em>k</em><span>-Subgraph</span>, <span>Max</span> <em>k</em><span>-Vertex Cover</span>, and <span>Max</span> <span><math><mo>(</mo><mi>k</mi><mo>,</mo><mi>n</mi><mo>−</mo><mi>k</mi><mo>)</mo></math></span><span>-Cut</span>.</p><p>A natural question in the study of <em>α</em>-FCGP is whether the algorithmic results known for its special cases, like <span>Max</span> <em>k</em><span>-Vertex Cover</span>, could be extended to more general settings. One of the simple but powerful methods for obtaining parameterized approximation [Manurangsi, SOSA 2019] and subexponential algorithms [Fomin et al. IPL 2011] for <span>Max</span> <em>k</em><span>-Vertex Cover</span> is based on the greedy vertex degree orderings. The main insight of our work is that the idea of greedy vertex degree ordering could be used to design fixed-parameter approximation schemes (FPT-AS) for <span><math><mi>α</mi><mo>&gt;</mo><mn>0</mn></math></span> and subexponential-time algorithms for the problem on apex-minor free graphs for maximization with <span><math><mi>α</mi><mo>&gt;</mo><mn>1</mn><mo>/</mo><mn>3</mn></math></span> and minimization with <span><math><mi>α</mi><mo>&lt;</mo><mn>1</mn><mo>/</mo><mn>3</mn></math></span>.<span>⁴</span></p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"185 ","pages":"Article 106471"},"PeriodicalIF":0.5,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000012/pdfft?md5=dbf0e44d15c4aa0bfc53c54ec0a43a71&pid=1-s2.0-S0020019024000012-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139408753","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":"On-line exploration of rectangular cellular environments with a rectangular hole","authors":"Qi Wei ,&nbsp;Xiaolin Yao ,&nbsp;Wenxin Zhang ,&nbsp;Ruiyue Zhang ,&nbsp;Yonggong Ren","doi":"10.1016/j.ipl.2023.106470","DOIUrl":"10.1016/j.ipl.2023.106470","url":null,"abstract":"<div><p>This paper considers the problem of exploring an unknown rectangular cellular environment with a rectangular hole using a mobile robot. The robot's task is to visit each cell at least once and return to the start. The robot has limited visibility that can only detect four cells adjacent to it. And it has large amount of memory that can store a map of discovered cells. The goal of this work is to find the shortest exploration tour, that is, minimizing the total number of multiple visited cells. We consider the environment in four possible scenarios: rectangular, <em>L</em>-shaped, <em>C</em>-shaped or <em>O</em>-shaped grid polygon. An on-line strategy has been proposed for these scenarios. We prove that it is optimal for rectangular, <em>L</em>-shaped, <em>C</em>-shaped grid polygon, and is 4/3-competitive for <em>O</em>-shaped grid polygon.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"185 ","pages":"Article 106470"},"PeriodicalIF":0.5,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139409511","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":"On the hull number on cycle convexity of graphs","authors":"J. Araújo, Victor A. Campos, D. Girão, J. Nogueira, António Salgueiro, Ana Silva","doi":"10.1016/j.ipl.2023.106420","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106420","url":null,"abstract":"","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"61 1","pages":"106420"},"PeriodicalIF":0.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"54535832","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 new key recovery attack on a code-based signature from the Lyubashevsky framework","authors":"C. H. Tan, Theo Fanuela Prabowo","doi":"10.1016/j.ipl.2023.106422","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106422","url":null,"abstract":"","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"183 1","pages":"106422"},"PeriodicalIF":0.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"54535916","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}