Journal of Combinatorial Optimization最新文献

{"title":"Recent advances in combinatorial optimization","authors":"Silvano Martello, Nikolaos Matsatsinis","doi":"10.1007/s10878-026-01420-9","DOIUrl":"https://doi.org/10.1007/s10878-026-01420-9","url":null,"abstract":"","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"54 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147739340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"IoT botnet attack detection using ensemble classifiers with optimal training","authors":"Shankar Vuppu, V. Chandra Shekhar Rao, M. Sujatha, Shaik Munawar, S. Nagaraju, N. Gayatri","doi":"10.1007/s10878-025-01388-y","DOIUrl":"https://doi.org/10.1007/s10878-025-01388-y","url":null,"abstract":"","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"5 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147733415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Information-theoretic coordinate subset and partition selection of multivariate Markov chains via submodular optimization","authors":"Zheyuan Lai, Michael C. H. Choi","doi":"10.1007/s10878-026-01417-4","DOIUrl":"https://doi.org/10.1007/s10878-026-01417-4","url":null,"abstract":"","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"71 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147708612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Genus of Cartesian products of complete graph K12t+7documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$K_{12t+7}$$end{document} with cycles and paths","authors":"Jyoti Anant Pulgam, Prashant Malavadkar","doi":"10.1007/s10878-026-01416-5","DOIUrl":"https://doi.org/10.1007/s10878-026-01416-5","url":null,"abstract":"The genus of a graph is the minimum genus (number of \"handles\") of an orientable surface in which the graph can be embedded without any edges crossing. A fundamental optimization problem in network topology research is to determine genus of a graph, which is a quantitative measure of a graph’s deviation from planarity. In this study, we determine the genus of the Cartesian products <inline-formula><alternatives><mml:math><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:mn>12</mml:mn><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>7</mml:mn></mml:mrow></mml:msub><mml:mo>□</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$K_{12t+7} Box C_{2s}$$end{document}</tex-math></alternatives></inline-formula> and <inline-formula><alternatives><mml:math><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:mn>12</mml:mn><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>7</mml:mn></mml:mrow></mml:msub><mml:mo>□</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$K_{12t+7} Box P_{s}$$end{document}</tex-math></alternatives></inline-formula>, where <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>t</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msup><mml:mo>∪</mml:mo><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$t in mathbb {Z}^+ cup {0}$$end{document}</tex-math></alternatives></inline-formula> and <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>s</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$s ge 2$$end{document}</tex-math></alternatives></inline-formula>.","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"51 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147702351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"DP color functions of hypergraphs","authors":"Ruiyi Cui, Liangxia Wan, Fengming Dong","doi":"10.1007/s10878-026-01414-7","DOIUrl":"https://doi.org/10.1007/s10878-026-01414-7","url":null,"abstract":"The DP color function &lt;inline-formula&gt;&lt;alternatives&gt;&lt;mml:math&gt;&lt;mml:mrow&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;P&lt;/mml:mi&gt;&lt;mml:mrow&gt;&lt;mml:mi mathvariant=\"italic\"&gt;DP&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;&lt;mml:mi mathvariant=\"script\"&gt;H&lt;/mml:mi&gt;&lt;mml:mo&gt;,&lt;/mml:mo&gt;&lt;mml:mi&gt;k&lt;/mml:mi&gt;&lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;/mml:mrow&gt;&lt;/mml:math&gt;&lt;tex-math&gt;documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$P_{DP}({mathcal {H}},k)$$end{document}&lt;/tex-math&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; of a hypergraph &lt;inline-formula&gt;&lt;alternatives&gt;&lt;mml:math&gt;&lt;mml:mi mathvariant=\"script\"&gt;H&lt;/mml:mi&gt;&lt;/mml:math&gt;&lt;tex-math&gt;documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${mathcal {H}}$$end{document}&lt;/tex-math&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; for &lt;inline-formula&gt;&lt;alternatives&gt;&lt;mml:math&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;k&lt;/mml:mi&gt;&lt;mml:mo&gt;∈&lt;/mml:mo&gt;&lt;mml:mi mathvariant=\"double-struck\"&gt;N&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:math&gt;&lt;tex-math&gt;documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$kin mathbb N$$end{document}&lt;/tex-math&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; is introduced, based on the DP coloring introduced by Bernshteyn and Kostochka, which is the minimum value of &lt;inline-formula&gt;&lt;alternatives&gt;&lt;mml:math&gt;&lt;mml:mrow&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;P&lt;/mml:mi&gt;&lt;mml:mrow&gt;&lt;mml:mi mathvariant=\"italic\"&gt;DP&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;&lt;mml:mi mathvariant=\"script\"&gt;H&lt;/mml:mi&gt;&lt;mml:mo&gt;,&lt;/mml:mo&gt;&lt;mml:mi mathvariant=\"script\"&gt;F&lt;/mml:mi&gt;&lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;/mml:mrow&gt;&lt;/mml:math&gt;&lt;tex-math&gt;documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$P_{DP}(mathcal {H},mathcal {F})$$end{document}&lt;/tex-math&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; over all &lt;italic&gt;k&lt;/italic&gt;-fold covers &lt;inline-formula&gt;&lt;alternatives&gt;&lt;mml:math&gt;&lt;mml:mi mathvariant=\"script\"&gt;F&lt;/mml:mi&gt;&lt;/mml:math&gt;&lt;tex-math&gt;documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathcal {F}$$end{document}&lt;/tex-math&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; of &lt;inline-formula&gt;&lt;alternatives&gt;&lt;mml:math&gt;&lt;mml:mi mathvariant=\"script\"&gt;H&lt;/mml:mi&gt;&lt;/mml:math&gt;&lt;tex-math&gt;documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{math","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"13 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147702352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Improving order with queues","authors":"Andreas Karrenbauer, Kurt Mehlhorn, Pranabendu Misra, Paolo Luigi Rinaldi, Anna Twelsiek, Alireza Haqi, Siavash Rahimi Shateranloo","doi":"10.1007/s10878-026-01419-2","DOIUrl":"https://doi.org/10.1007/s10878-026-01419-2","url":null,"abstract":"Given a sequence of <italic>n</italic> numbers and <italic>k</italic> parallel First-in-First-Out (FIFO) queues, how close can one bring the sequence to sorted order? It is known that <italic>k</italic> queues suffice to sort the sequence if the <italic>Longest Decreasing Subsequence (LDS)</italic> of the input sequence is at most <italic>k</italic>. But, what if the number of queues is too small for sorting completely? <list list-type=\"order\"><list-item>We give a simple algorithm, based on Patience Sort, that reduces the LDS by <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$k - 1$$end{document}</tex-math></alternatives></inline-formula>. We also show, that the algorithm is optimal, i.e., for any <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>L</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$L &gt; 0$$end{document}</tex-math></alternatives></inline-formula> there exists a sequence of LDS <italic>L</italic> such that the LDS cannot be reduced below <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>L</mml:mi><mml:mo>-</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$L - k + 1$$end{document}</tex-math></alternatives></inline-formula> with <italic>k</italic> queues.</list-item><list-item>Merging two sorted queues is at the core of Merge Sort. In contrast, two sequences of LDS two cannot always be merged into a sequence of LDS two. We characterize when it is possible and give an algorithm to decide whether it is possible. Merging into a sequence of LDS three is always possible.</list-item><list-item>A <italic>down-step</italic> in a sequence is an item immediately followed by a smaller item. We give an optimal algorithm for reducing the number of down-steps. The algorithm is online.</list-item></list> Our research was inspired by an application in car manufacturing.","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"14 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147702350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Homological invariants of edge ideals of Wollastonite graphs","authors":"Bilal Ahmad Rather","doi":"10.1007/s10878-025-01389-x","DOIUrl":"https://doi.org/10.1007/s10878-025-01389-x","url":null,"abstract":"We investigate homological invariants arising from the linear strand of Wollastonite graphs. In particular, we derive combinatorial formulas for the Castelnuovo-Mumford regularity, the projective dimension, and the initial graded Betti numbers of the edge ideals of these graphs. Furthermore, we express the remaining Betti numbers of these edge ideals in terms of the Hilbert series associated with the <italic>i</italic>-dimensional faces of their corresponding simplicial complexes. Finally, we show that the edge ring of a Wollastonite graph is not Cohen-Macaulay.","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"9 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147702353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the enumeration of resolute majority rules","authors":"Josep Freixas, Dani Samaniego","doi":"10.1007/s10878-026-01412-9","DOIUrl":"https://doi.org/10.1007/s10878-026-01412-9","url":null,"abstract":"This paper considers resolute decision rules in which each voter may vote “yes\", “abstain\" or vote “no\", and the outcome is “yes\" or “no\". The model we consider is more general than that of simple games since the input admits abstention or indecision, but it is more specialized since it assumes the properties of monotonicity and anonymity. Many subclasses of these resolute decision rules have been studied in the literature from an axiomatic point of view. The purpose of this work is to enumerate these subclasses as a function of the number of voters.","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"126 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147461815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Binary jumbled indexing: suffix tree histogram","authors":"Luís Cunha, Mário Medina","doi":"10.1007/s10878-026-01407-6","DOIUrl":"https://doi.org/10.1007/s10878-026-01407-6","url":null,"abstract":"Given a binary string &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$$omega $$&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;ω&lt;/mml:mi&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; over the alphabet &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$${0, 1}$$&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;{&lt;/mml:mo&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;mml:mo&gt;}&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; , a vector ( &lt;jats:italic&gt;a&lt;/jats:italic&gt; , &lt;jats:italic&gt;b&lt;/jats:italic&gt; ) is a Parikh vector if and only if a factor of &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$$omega $$&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;ω&lt;/mml:mi&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; contains exactly &lt;jats:italic&gt;a&lt;/jats:italic&gt; occurrences of 0 and &lt;jats:italic&gt;b&lt;/jats:italic&gt; occurrences of 1. Answering whether a vector is a Parikh vector of &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$$omega $$&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;ω&lt;/mml:mi&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; is known as the Binary Jumbled Indexing Problem ( &lt;jats:sc&gt;BJIP&lt;/jats:sc&gt; ) or the Histogram Indexing Problem. Most solutions to this problem rely on an &lt;jats:italic&gt;O&lt;/jats:italic&gt; ( &lt;jats:italic&gt;n&lt;/jats:italic&gt; ) word-space index to answer queries in constant time, encoding the Parikh set of &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$$omega $$&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;ω&lt;/mml:mi&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; , i.e., all its Parikh vectors. Cunha et al. ( &lt;jats:italic&gt;Combinatorial Pattern Matching&lt;/jats:italic&gt; , 2017) introduced an algorithm ( &lt;jats:italic&gt;JBM2017&lt;/jats:italic&gt; ), which computes the index table in &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$$O(n+rho ^2)$$&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;O&lt;/mml:mi&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;mml:mo&gt;+&lt;/mml:mo&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;ρ&lt;/mml:mi&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;/mml:msup&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; time, where &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$$rho $$&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;ρ&lt;/mml:mi&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; is the number of runs of identical digits in &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$$omega $$&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;ω&lt;/mml:mi&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; , leading to &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$$O(n^2)$$&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mm","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"130 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147462160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Online dispatching and routing for automated guided vehicles in pickup and delivery systems on loop-based graphs","authors":"Louis Stubbe, Jens Goemaere, Jan Goedgebeur","doi":"10.1007/s10878-026-01410-x","DOIUrl":"https://doi.org/10.1007/s10878-026-01410-x","url":null,"abstract":"","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"3 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147373856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}