Journal of Combinatorial Optimization最新文献

{"title":"Algorithms with competitive analysis for online traveling salesman problem on a semi-line","authors":"Kai Wang, Qian Liu, An Zhang, Yong Chen, Guangting Chen","doi":"10.1007/s10878-026-01457-w","DOIUrl":"https://doi.org/10.1007/s10878-026-01457-w","url":null,"abstract":"We study the online traveling salesman problem on a semi-line, where a server (salesman) starts from the origin point of the semi-line and moves either at unit speed or ‘waits’ (with zero speed) at somewhere, so as to serve the requests that are released online along the semi-line. The objective is to minimize the time for serving all requests. We distinguish the homing version and the nomadic version by whether the server is required to return to the origin point or not. When no information of the requests is disclosed, the best online algorithms for two versions are <inline-formula><alternatives><mml:math><mml:mfrac><mml:mn>3</mml:mn><mml:mn>2</mml:mn></mml:mfrac></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}$$frac{3}{2}$$end{document}</tex-math></alternatives></inline-formula>- and 2-competitive respectively. When the locations of all requests are known in advance, the online algorithm for the homing version could be 1-competitive. We present a <inline-formula><alternatives><mml:math><mml:mfrac><mml:mn>10</mml:mn><mml:mn>7</mml:mn></mml:mfrac></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}$$frac{10}{7}$$end{document}</tex-math></alternatives></inline-formula>-competitive algorithm for the nomadic version, improving the previous <inline-formula><alternatives><mml:math><mml:mfrac><mml:mn>13</mml:mn><mml:mn>9</mml:mn></mml:mfrac></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}$$frac{13}{9}$$end{document}</tex-math></alternatives></inline-formula>-competitive algorithm. We also improve the lower bound of this version from <inline-formula><alternatives><mml:math><mml:mfrac><mml:mn>4</mml:mn><mml:mn>3</mml:mn></mml:mfrac></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}$$frac{4}{3}$$end{document}</tex-math></alternatives></inline-formula> to 1.356. If machine-learned predictions are adopted for the locations, then we introduce learning-augmented algorithms that have competitive ratios of <inline-formula><alternatives><mml:math><mml:mrow><mml:mo movablelimits=\"true\">min</mml:mo><mml:mo stretchy=\"false\">{</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>η</mml:mi><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepacka","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"5 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148612829","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":"Approximation algorithms for k-submodular maximization under fairness constraints and size constraints","authors":"Bin Liu, Weijia Hu","doi":"10.1007/s10878-026-01440-5","DOIUrl":"https://doi.org/10.1007/s10878-026-01440-5","url":null,"abstract":"Submodular optimization is an important part of combinatorial optimization, and meanwhile, it has been widely used in the fields of economy, computer science, etc. In recent years, many generalizations of the submodular maximization problem have been proposed, such as the <italic>k</italic>-submodular maximization problem, which considers not only whether the elements of the ground set are selected, but also which set of <italic>k</italic>-set they are selected into. Many machine learning problems, including influence maximization with <italic>k</italic> kinds of topics and sensor placement with <italic>k</italic> kinds of sensors, can be modeled as <italic>k</italic>-submodular maximization models. In practical applications, elements usually have certain attributes, such as gender, age, race, and so on. Based on these attributes we can group elements in the ground set. For fairness, we want the number of elements in each group to be relatively balanced, which introduces group fairness. Group fairness can be conceptualized in various ways, but typically falls into two primary categories: equity-fairness and equality-fairness. At present, the existing algorithms on <italic>k</italic>-submodular do not consider group fairness constraints, which can result in the number of elements in some groups being too high or too low. This motivates us to study <italic>k</italic>-submodular maximization under group fairness constraints. In this paper, we consider intersection constraints of two different categories of group fairness constraints and total size constraint, respectively. For the <italic>k</italic>-submodular maximization problem under equity-fairness constraints and total size constraint, we design an offline approximation algorithm with an approximate ratio of <inline-formula><alternatives><mml:math><mml:mrow><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>2</mml:mn><mml:mo>-</mml:mo><mml:mi>ϵ</mml:mi></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}$$1/2-epsilon $$end{document}</tex-math></alternatives></inline-formula> for the case of monotone, and an approximate ratio of <inline-formula><alternatives><mml:math><mml:mrow><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>3</mml:mn><mml:mo>-</mml:mo><mml:mi>ϵ</mml:mi></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}$$1/3-epsilon $$end{document}</tex-math></alternatives></inline-formula> for non-monotone. For the <italic>k</italic>-submodular maximization problem under equality-fairness constraints and total size constraint, we get an approximate ratio of 1/2 for the case of monoto","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"458 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148552121","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":"New integer linear programming formulations for the maximally diverse grouping problem","authors":"Kevin Fu Yuan Lam, Jiang Qian","doi":"10.1007/s10878-026-01427-2","DOIUrl":"https://doi.org/10.1007/s10878-026-01427-2","url":null,"abstract":"The Maximally Diverse Grouping Problem (MDGP) is the problem of assigning a set of elements to mutually disjoint groups in order to maximise the overall diversity between the elements. The MDGP is often formulated as an Integer Quadratic Programme (IQP). Because the MDGP is NP-complete, most studies have focused on heuristic solution approaches, as compared to exact solution approaches, to the problem. Although heuristic solution approaches are often used in practice, these approaches do not guarantee a global optimal solution. Conversely, although exact solution approaches are not often used in practice, these approaches guarantee a global optimal solution, and therefore serve as useful benchmarks for the performance of heuristics. As such, a few studies have formulated the MDGP as an Integer Linear Programme (ILP), which can be solved using exact solution approaches. The present paper proposes two new ILP formulations, and compares their performances against existing formulations. The proposed formulations can be used to establish useful benchmarks for the performance of heuristics in a broader range of applications moving forward.","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"39 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148552123","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":"HABROA: Elevating wireless sensor networks through heterogeneous learning and advanced optimization strategies","authors":"A. Swaminathan, R. Saravanan, Baskar Kasi, S. Ramaraju","doi":"10.1007/s10878-026-01437-0","DOIUrl":"https://doi.org/10.1007/s10878-026-01437-0","url":null,"abstract":"In the realm of wireless sensor networks (WSN), clustering schemes stand out as effective approaches to optimize resource utilization, particularly in minimizing overhead and enhancing energy efficiency to extend network lifespan. Clustering optimisation that takes energy considerations into account is a difficult NP optimisation issue. In light of this difficulty, meta-heuristic optimisation algorithms stand out as a possible solution; they may greatly enhance energy efficiency, which would lead to the sustainability of the network. This article introduces a novel solution, the Hybrid African Buffalo and Remora Optimization Algorithm (HABROA), designed to achieve energy stability and prolong network lifetime through the judicious selection of cluster heads (CH) during the clustering process. HABROA is specifically tailored to navigate the intricate trade-off between exploitation and exploration rates, thereby facilitating the efficient identification of Cluster Head Candidates (CHS). This strategic balance contributes to the sustained longevity and energy stability of the network. The proposed HABROA model exhibits notable performance metrics, surpassing alternative methods. With a Mean Packet Delivery of 96%, a Mean Residual Energy of 0.130, and an End-to-End Delay of 0.76, the results demonstrate the efficacy of HABROA in achieving superior outcomes. This research significantly contributes to the field by presenting a robust approach for optimizing energy consumption and ensuring the prolonged functionality of WSN.","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"21 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148552126","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":"The characterizations and complexity of Roman {2}-domination number and 2-domination number in graphs","authors":"Cai-Xia Wang, Yu Yang, Ze-Peng Li, Shou-Jun Xu","doi":"10.1007/s10878-026-01441-4","DOIUrl":"https://doi.org/10.1007/s10878-026-01441-4","url":null,"abstract":"Given a graph <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>V</mml:mi><mml:mo>,</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></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}$$G=(V,E)$$end{document}</tex-math></alternatives></inline-formula> and a function <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>b</mml:mi><mml:mo>:</mml:mo><mml:mi>V</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mo stretchy=\"false\">{</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy=\"false\">}</mml:mo></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}$$b: Vrightarrow {0, 1, 2}$$end{document}</tex-math></alternatives></inline-formula>. If <italic>b</italic> satisfies <inline-formula><alternatives><mml:math><mml:mrow><mml:msub><mml:mo>∑</mml:mo><mml:mrow><mml:mi>z</mml:mi><mml:mo>∈</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>G</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>w</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>z</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><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}$$sum _{zin N_G(w)}b(z)ge 2$$end{document}</tex-math></alternatives></inline-formula> for every vertex <italic>w</italic> with <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>b</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>w</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>=</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}$$b(w)=0$$end{document}</tex-math></alternatives></inline-formula>, where <inline-formula><alternatives><mml:math><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>G</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>w</mml:mi><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{upg","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"25 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148552198","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":"An improved two-stage approximation algorithm for the k-supplier problem with parameterized triangle inequality","authors":"Wei Ding, Yu Zhou, Guangting Chen, Ke Qiu","doi":"10.1007/s10878-026-01434-3","DOIUrl":"https://doi.org/10.1007/s10878-026-01434-3","url":null,"abstract":"Given an edge-weighted undirected connected graph <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>V</mml:mi><mml:mo>,</mml:mo><mml:mi>E</mml:mi><mml:mo>,</mml:mo><mml:mi>ρ</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"script\">X</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"script\">Y</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></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}$$G = (V, E, rho , mathcal {X}, mathcal {Y})$$end{document}</tex-math></alternatives></inline-formula>, where <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>ρ</mml:mi><mml:mo>:</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:msup><mml:mtext>R</mml:mtext><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}$$rho : E rightarrow textrm{R}^{+} cup { 0 }$$end{document}</tex-math></alternatives></inline-formula> is an edge-weight function, <inline-formula><alternatives><mml:math><mml:mrow><mml:mi mathvariant=\"script\">X</mml:mi><mml:mo>⊂</mml:mo><mml:mi>V</mml:mi></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}$$mathcal {X} subset V$$end{document}</tex-math></alternatives></inline-formula> is a subset of clients, and <inline-formula><alternatives><mml:math><mml:mrow><mml:mi mathvariant=\"script\">Y</mml:mi><mml:mo>⊂</mml:mo><mml:mi>V</mml:mi></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}$$mathcal {Y} subset V$$end{document}</tex-math></alternatives></inline-formula> is a subset of candidates, and a positive integer <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>k</mml:mi><mml:mo><</mml:mo><mml:mo stretchy=\"false\">|</mml:mo><mml:mi mathvariant=\"script\">Y</mml:mi><mml:mo stretchy=\"false\">|</mml:mo></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}$$k < |mathcal {Y}|$$end{document}</tex-math></alternatives></inline-formula>, the <","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"156 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148552122","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 Detecting Some Defective Items in Group Testing","authors":"Nader H. Bshouty, Catherine A. Haddad-Zaknoon","doi":"10.1007/s10878-026-01394-8","DOIUrl":"https://doi.org/10.1007/s10878-026-01394-8","url":null,"abstract":"Group testing is an approach aimed at identifying up to <italic>d</italic> defective items among a total of <italic>n</italic> elements. This is accomplished by examining subsets to determine if at least one defective item is present. We focus on the problem of identifying a subset of <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>ℓ</mml:mi><mml:mo><</mml:mo><mml:mi>d</mml:mi></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}$$ell < d$$end{document}</tex-math></alternatives></inline-formula> defective items. We develop upper and lower bounds on the number of tests required to detect <inline-formula><alternatives><mml:math><mml:mi>ℓ</mml:mi></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}$$ell $$end{document}</tex-math></alternatives></inline-formula> defective items in both the adaptive and non-adaptive settings while considering scenarios where no prior knowledge of <italic>d</italic> is available, and situations where some non-trivial estimate of <italic>d</italic> is at hand. When <italic>d</italic> is unknown, we prove a lower bound of <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>Ω</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mfrac><mml:mrow><mml:mi>ℓ</mml:mi><mml:msup><mml:mo>log</mml:mo><mml:mn>2</mml:mn></mml:msup><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mo>log</mml:mo><mml:mi>ℓ</mml:mi><mml:mo>+</mml:mo><mml:mo>log</mml:mo><mml:mo>log</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:mfrac><mml:mo stretchy=\"false\">)</mml:mo></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}$$ varOmega (frac{ell log ^2n}{log ell +log log n})$$end{document}</tex-math></alternatives></inline-formula> tests in the randomized non-adaptive settings and an upper bound of <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>ℓ</mml:mi><mml:msup><mml:mo>log</mml:mo><mml:mn>2</mml:mn></mml:msup><mml:mi>n</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></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}$$O(ell log ^2 n)$$end{document}</tex-math></alternatives></inline-formula> for the same settings. Furthermore, we demonstrate that any non-adaptive deterministic algorithm must make <inline-formula><alternatives><mml","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"70 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148287965","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":"Submodular Optimization for Heterogeneous UAV Deployment","authors":"Yang Lv, Fengmin Wang, Xiankun Yu, Xin Li, Dachuan Xu, Ruiqi Yang","doi":"10.1007/s10878-026-01435-2","DOIUrl":"https://doi.org/10.1007/s10878-026-01435-2","url":null,"abstract":"Unmanned Aerial Vehicles (UAVs) are widely used in environmental monitoring tasks such as forest surveillance, agricultural mapping, and disaster assessment, where their ability to collect dense and high-resolution observations is particularly advantageous. However, many existing approaches implicitly assume that UAV platforms and onboard sensors are homogeneous. This assumption can introduce significant estimation errors in real-world deployments. This work studies the deployment of heterogeneous UAVs equipped with sensors of different accuracies for fire-scene assessment, using a point-of-interest–based model. Research on heterogeneous UAV measurements remains relatively limited. We introduce a weighted frame potential (WFP) that captures the orthogonality structure of sensing matrices under heterogeneous noise. By reformulating the problem as a submodular maximization task, we develop a Random Greedy Algorithm that guarantees a <inline-formula><alternatives><mml:math><mml:mrow><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>c</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></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}$$1/(1+c)$$end{document}</tex-math></alternatives></inline-formula> approximation of the optimal solution, where <italic>c</italic> denotes the curvature of the submodular function. A theoretical upper bound on the reconstruction error induced by the selected UAV configuration is also established. Experiments on both small- and large-scale fire monitoring tasks show that the proposed method achieves higher reconstruction accuracy and better computational efficiency than existing algorithms.","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"36 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148355774","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":"The location-routing problem in the pallet pooling system with demand uncertainty","authors":"Xiaoting Shang, Bowen Miao, Qingguo Bai, Yongguang Zhong","doi":"10.1007/s10878-026-01430-7","DOIUrl":"https://doi.org/10.1007/s10878-026-01430-7","url":null,"abstract":"This study investigates the location-routing problem in the pallet pooling system, which is an extended combinatorial optimization problem in the field of logistics management. A mixed-integer linear programming model is formulated for the location-routing problem, incorporating simultaneous pickup and delivery, and the limitations on carbon emissions and transportation time. To address the demand uncertainty, this study extends the model using a robust optimization approach to enhance solution reliability. Due to the NP-hard nature and high computational complexity of the problem, a heuristic algorithm integrating genetic algorithm and ant colony optimization is developed to obtain efficient solutions. Numerical experiments are conducted on classical benchmark instances to validate the model feasibility, demonstrate that the integrated optimization model outperforms the two-stage model, and highlight the superior performance of the heuristic algorithm in terms of solution quality and computational efficiency. Furthermore, the study provides valuable insights for logistics managers in the pallet pooling system.","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"61 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148355775","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":"Strong edge chromatic index of subquartic graphs","authors":"Junlei Zhu, Hongguo Zhu, Yuehua Bu","doi":"10.1007/s10878-026-01390-y","DOIUrl":"https://doi.org/10.1007/s10878-026-01390-y","url":null,"abstract":"A strong &lt;italic&gt;k&lt;/italic&gt;-edge coloring of a graph &lt;italic&gt;G&lt;/italic&gt; is an assignment of &lt;italic&gt;k&lt;/italic&gt; colors to the edges of &lt;italic&gt;G&lt;/italic&gt; such that for any two edges &lt;italic&gt;e&lt;/italic&gt; and &lt;italic&gt;f&lt;/italic&gt; with distance at most two receive different colors. The minimum number of &lt;italic&gt;k&lt;/italic&gt; such that &lt;italic&gt;G&lt;/italic&gt; has a strong &lt;italic&gt;k&lt;/italic&gt;-edge coloring is called the strong chromatic index of &lt;italic&gt;G&lt;/italic&gt;, denoted as &lt;inline-formula&gt;&lt;alternatives&gt;&lt;mml:math&gt;&lt;mml:mrow&gt;&lt;mml:msubsup&gt;&lt;mml:mi&gt;χ&lt;/mml:mi&gt;&lt;mml:mi&gt;s&lt;/mml:mi&gt;&lt;mml:mo&gt;′&lt;/mml:mo&gt;&lt;/mml:msubsup&gt;&lt;mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;G&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}$$chi '_s(G)$$end{document}&lt;/tex-math&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;. In this paper, we proved that for a subquartic graph &lt;italic&gt;G&lt;/italic&gt;, &lt;inline-formula&gt;&lt;alternatives&gt;&lt;mml:math&gt;&lt;mml:mrow&gt;&lt;mml:msubsup&gt;&lt;mml:mi&gt;χ&lt;/mml:mi&gt;&lt;mml:mi&gt;s&lt;/mml:mi&gt;&lt;mml:mo&gt;′&lt;/mml:mo&gt;&lt;/mml:msubsup&gt;&lt;mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;G&lt;/mml:mi&gt;&lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mo&gt;≤&lt;/mml:mo&gt;&lt;mml:mn&gt;12&lt;/mml:mn&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}$$chi _s'(G)le 12$$end{document}&lt;/tex-math&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; if &lt;inline-formula&gt;&lt;alternatives&gt;&lt;mml:math&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;m&lt;/mml:mi&gt;&lt;mml:mi&gt;a&lt;/mml:mi&gt;&lt;mml:mi&gt;d&lt;/mml:mi&gt;&lt;mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;G&lt;/mml:mi&gt;&lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mo&gt;&lt;&lt;/mml:mo&gt;&lt;mml:mfrac&gt;&lt;mml:mn&gt;14&lt;/mml:mn&gt;&lt;mml:mn&gt;5&lt;/mml:mn&gt;&lt;/mml:mfrac&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}$$mad(G)&lt;frac{14}{5}$$end{document}&lt;/tex-math&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, where &lt;inline-formula&gt;&lt;alternatives&gt;&lt;mml:math&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;m&lt;/mml:mi&gt;&lt;mml:mi&gt;a&lt;/mml:mi&gt;&lt;mml:mi&gt;d&lt;/mml:mi&gt;&lt;mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;G&lt;/mml:mi&gt;&lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mo&gt;=&lt;/mml:mo&gt;&lt;mml:mo movablelimits=\"true\"&gt;max&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;{&lt;/mml:mo&gt;&lt;mml:mfrac&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;2&lt;/mml:mn&gt;&lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt;&lt;mml:mi&gt;E&lt;/mml:mi&gt;&lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;H&lt;/mml:mi&gt;&lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt;&lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt;&lt;mml:mi&gt;V&lt;/mml:mi&gt;&lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;H&lt;/mml:mi&gt;&lt;mml:mo ","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"112 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148355665","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}