Journal of Combinatorial Optimization最新文献

{"title":"A divide-and-conquer based preprocessing for routing in a simple polygon","authors":"Siddharth Gaur, R. Inkulu","doi":"10.1007/s10878-025-01345-9","DOIUrl":"https://doi.org/10.1007/s10878-025-01345-9","url":null,"abstract":"<p>Given a simple polygon <i>P</i> defined with <i>n</i> vertices in the plane, we preprocess <i>P</i> and compute routing tables at every vertex of <i>P</i>. In the routing phase, a packet originating at any source vertex of <i>P</i> is routed to its destination vertex belonging to <i>P</i>. At every vertex <i>v</i> of <i>P</i> along the routing path, until the packet reaches its destination, the next hop is determined using the routing tables at <i>v</i> and the additional information (including the packet’s destination vertex label) in the packet. We show our routing scheme constructs routing tables in <span><span style=\"\"></span><span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mstyle scriptlevel=\"0\"&gt;&lt;mrow&gt;&lt;mo maxsize=\"1.2em\" minsize=\"1.2em\"&gt;(&lt;/mo&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mstyle scriptlevel=\"0\"&gt;&lt;mrow&gt;&lt;mo maxsize=\"1.2em\" minsize=\"1.2em\"&gt;(&lt;/mo&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;/mfrac&gt;&lt;mstyle scriptlevel=\"0\"&gt;&lt;mrow&gt;&lt;mo maxsize=\"1.2em\" minsize=\"1.2em\"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;mstyle scriptlevel=\"0\"&gt;&lt;mrow&gt;&lt;mo maxsize=\"1.2em\" minsize=\"1.2em\"&gt;(&lt;/mo&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;mi&gt;lg&lt;/mi&gt;&lt;mo&gt;&amp;#x2061;&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;msup&gt;&lt;mstyle scriptlevel=\"0\"&gt;&lt;mrow&gt;&lt;mo maxsize=\"1.2em\" minsize=\"1.2em\"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mstyle scriptlevel=\"0\"&gt;&lt;mrow&gt;&lt;mo maxsize=\"1.2em\" minsize=\"1.2em\"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"3.615ex\" role=\"img\" style=\"vertical-align: -1.006ex;\" viewbox=\"0 -1123.3 8719.1 1556.6\" width=\"20.251ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-4F\" y=\"0\"></use><use x=\"763\" xlink:href=\"#MJSZ1-28\" y=\"-1\"></use><use x=\"1222\" xlink:href=\"#MJMATHI-6E\" y=\"0\"></use><use x=\"1822\" xlink:href=\"#MJSZ1-28\" y=\"-1\"></use><use x=\"2281\" xlink:href=\"#MJMAIN-31\" y=\"0\"></use><use x=\"3003\" xlink:href=\"#MJMAIN-2B\" y=\"0\"></use><g transform=\"translate(3782,0)\"><g transform=\"translate(342,0)\"><rect height=\"60\" stroke=\"none\" width=\"473\" x=\"0\" y=\"220\"></rect><use transform=\"scale(0.707)\" x=\"84\" xlink:href=\"#MJMAIN-31\" y=\"556\"></use><use transform=\"scale(0.707)\" x=\"131\" xlink:href=\"#MJMATHI-3F5\" y=\"-488\"></use></g></g><use x=\"4718\" xlink:href=\"#MJSZ1-29\" y=\"-1\"></use><use x=\"5176\" xlink:href=\"#MJSZ1-28\" y=\"-1\"></use><g transform=\"translate(5802,0)\"><use xlink:href=\"#MJMAIN-6C\"></use><use x=\"278\" xlink:href=\"#MJMAIN-67\" y=\"0\"></use></g><","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"128 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003501","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":"Moving horizon capacitated arc routing problem","authors":"Somnath Buriuly, Leena Vachhani, Arpita Sinha, Sivapragasam Ravitharan, Sunita Chauhan","doi":"10.1007/s10878-025-01344-w","DOIUrl":"https://doi.org/10.1007/s10878-025-01344-w","url":null,"abstract":"<p>In transportation networks, routing problems are cursed with arbitrary changes occurring in the dataset due to unpredictable events like agent breakdown (sensor or vehicle failure), network connectivity changes, resource/demand fluctuations, etc. Moreover, capacity restriction on the agents may require multi-trip solutions for meeting large demands over networks. For example, a battery-powered inspection wagon can only service a limited number of track sections in a single trip. We investigate a moving horizon approach for the multi-trip dynamic capacitated arc routing problem with limited duration to mitigate the limitations of CARP variants in the literature. The proposed approach addresses arbitrary changes in the underlying network, agent unavailability scenarios, and simultaneously satisfies the time limit on meeting all demands. The moving horizon approach subdivides the planning horizon to determine the current trip (single-trip) for all agents, hence coined as Moving Horizon Capacitated Arc Routing Problem (MH-CARP). The proposed MH-CARP is formulated as a set covering problem that considers both partial and full trips (trips may not start at the depot), making it suitable for tackling arbitrary events by re-planning. Theoretical results for the computation of dual variables are derived and then implemented in the column generation algorithm to obtain lower bounds. The algorithm is validated on a widely available dataset for CARP, having instances of up to 147 tasks that require servicing by up to 20 agents. Using this benchmark data, the partial-trip based re-planning strategy is also validated. Lastly, a simulation study is presented to demonstrate the re-planning strategy and compare an MH-CARP solution to two CARP based solutions - one with no arbitrary events and the other with known arbitrary events. The results also convey that greedy solutions are avoided to satisfy the limited duration restriction, and automatic re-ordering of the trips is achieved to compensate for arbitrary events.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"84 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003503","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":"Semistrong edge colorings of planar graphs","authors":"Yuquan Lin, Wensong Lin","doi":"10.1007/s10878-025-01346-8","DOIUrl":"https://doi.org/10.1007/s10878-025-01346-8","url":null,"abstract":"&lt;p&gt;Strengthened notions of a matching &lt;i&gt;M&lt;/i&gt; of a graph &lt;i&gt;G&lt;/i&gt; have been considered, requiring that the matching &lt;i&gt;M&lt;/i&gt; has some properties with respect to the subgraph &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msub&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"2.313ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -778.3 1630 995.9\" width=\"3.786ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-47\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"1112\" xlink:href=\"#MJMATHI-4D\" y=\"-213\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span role=\"presentation\"&gt;&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msub&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;G_M&lt;/script&gt;&lt;/span&gt; of &lt;i&gt;G&lt;/i&gt; induced by the vertices covered by &lt;i&gt;M&lt;/i&gt;: If &lt;i&gt;M&lt;/i&gt; is the unique perfect matching of &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msub&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"2.409ex\" role=\"img\" style=\"vertical-align: -0.605ex;\" viewbox=\"0 -777 1908.5 1037.3\" width=\"4.433ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-47\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"1112\" xlink:href=\"#MJMATHI-4D\" y=\"-213\"&gt;&lt;/use&gt;&lt;use x=\"1630\" xlink:href=\"#MJMAIN-2C\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span role=\"presentation\"&gt;&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msub&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;G_M,&lt;/script&gt;&lt;/span&gt; then &lt;i&gt;M&lt;/i&gt; is a &lt;i&gt;uniquely restricted matching&lt;/i&gt; of &lt;i&gt;G&lt;/i&gt;; if all the edges of &lt;i&gt;M&lt;/i&gt; are pendant edges of &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msub&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"2.413ex\" role=\"img\" style=\"vertical-align: -0.606ex;\" viewbox=\"0 -778.3 1908.5 1039.1\" width=\"4.433ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-47\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"1112\" xlink:href=\"#MJMATHI-4D\" y=\"-213\"&gt;&lt;/use&gt;&lt;use x=\"1630\" xlink:hre","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"135 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003460","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":"Maximum expert consensus models with both type- $$alpha $$ and type- $$varepsilon $$ constraints","authors":"Dong Cheng, Huina Zhang, Yong Wu","doi":"10.1007/s10878-025-01342-y","DOIUrl":"https://doi.org/10.1007/s10878-025-01342-y","url":null,"abstract":"&lt;p&gt;The maximum expert consensus model (MECM) aims to maximize the number of consensual decision-makers (DMs) within a limited budget. However, it may fail to achieve high group satisfaction or even cannot reach an acceptable consensus due to its neglect of the group consensus level, resulting in type-&lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;&amp;#x03B1;&lt;/mi&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"1.412ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -519.5 640.5 607.8\" width=\"1.488ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-3B1\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span role=\"presentation\"&gt;&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;alpha &lt;/script&gt;&lt;/span&gt; constraints not being satisfied. To address this issue, we extend the existing MECM by considering both type-&lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;&amp;#x03B1;&lt;/mi&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"1.412ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -519.5 640.5 607.8\" width=\"1.488ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-3B1\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span role=\"presentation\"&gt;&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;alpha &lt;/script&gt;&lt;/span&gt; and type-&lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mrow&gt;&lt;mtext&gt;&amp;#x03B5;&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"1.412ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -519.5 466.5 607.8\" width=\"1.083ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-3B5\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span role=\"presentation\"&gt;&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mrow&gt;&lt;mtext&gt;ε&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;varepsilon &lt;/script&gt;&lt;/span&gt; consensus constraints to enable the group consensus level and the number of consensual DMs as large as possible. Firstly, we construct a dual-MECM that considers the above two constraints. Secondly, we further develop a dual-MECM considering compromise limits (dual-MEC","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"46 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003462","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":"Strategy-proof mechanisms for maximizing social satisfaction in the facility location game","authors":"Xiaowei Li, Xiwen Lu","doi":"10.1007/s10878-025-01341-z","DOIUrl":"https://doi.org/10.1007/s10878-025-01341-z","url":null,"abstract":"&lt;p&gt;The facility location game, where the agents’ locations are on a line, is considered in this paper. The input consists of the reported locations of agents, which are collected as part of the game setup. We introduce the concept of a fairness baseline and define a function to characterize each agent’s satisfaction with the facility location. Our objective is to establish a mechanism that obtains the true information of agents and outputs a single facility location so that the sum of all agents’ satisfaction with the location is maximized. For the game with two agents, we propose a &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mfrac&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"3.215ex\" role=\"img\" style=\"vertical-align: -1.006ex;\" viewbox=\"0 -950.8 713.9 1384.1\" width=\"1.658ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;g transform=\"translate(120,0)\"&gt;&lt;rect height=\"60\" stroke=\"none\" width=\"473\" x=\"0\" y=\"220\"&gt;&lt;/rect&gt;&lt;use transform=\"scale(0.707)\" x=\"84\" xlink:href=\"#MJMAIN-35\" y=\"575\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"84\" xlink:href=\"#MJMAIN-34\" y=\"-524\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span role=\"presentation\"&gt;&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mfrac&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;frac{5}{4}&lt;/script&gt;&lt;/span&gt;-approximate strategy-proof mechanism, which is the best possible. In the general case, we demonstrate that the median mechanism achieves an approximation ratio of &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mfrac&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"3.215ex\" role=\"img\" style=\"vertical-align: -1.006ex;\" viewbox=\"0 -950.8 713.9 1384.1\" width=\"1.658ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;g transform=\"translate(120,0)\"&gt;&lt;rect height=\"60\" stroke=\"none\" width=\"473\" x=\"0\" y=\"220\"&gt;&lt;/rect&gt;&lt;use transform=\"scale(0.707)\" x=\"84\" xlink:href=\"#MJMAIN-33\" y=\"575\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"84\" xlink:href=\"#MJMAIN-32\" y=\"-513\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span role=\"presentation\"&gt;&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mfrac&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;frac{3}{2}&lt;/script&gt;&lt;/span&gt;. In particular, the median mechanism is an optimal group strategy-proof mechanism for the game with three agents. Additionally, we devise a &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"3 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003446","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 improvement on the Louvain algorithm using random walks","authors":"Duy Hieu Do, Thi Ha Duong Phan","doi":"10.1007/s10878-025-01337-9","DOIUrl":"https://doi.org/10.1007/s10878-025-01337-9","url":null,"abstract":"<p>We present improvements to famous algorithms for community detection, namely Newman’s spectral method algorithm and the Louvain algorithm. The Newman algorithm begins by treating the original graph as a single cluster, then repeats the process to split each cluster into two, based on the signs of the eigenvector corresponding to the second-largest eigenvalue. Our improvement involves replacing the time-consuming computation of eigenvalues with a random walk during the splitting process. The Louvain algorithm iteratively performs the following steps until no increase in modularity can be achieved anymore: each step consists of two phases–phase 1 for partitioning the graph into clusters, and phase 2 for constructing a new graph where each vertex represents one cluster obtained from phase 1. We propose an improvement to this algorithm by adding our random walk algorithm as an additional phase for refining clusters obtained from phase 1. It maintains a complexity comparable to the Louvain algorithm while exhibiting superior efficiency. To validate the robustness and effectiveness of our proposed algorithms, we conducted experiments using randomly generated graphs and real-world data.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"38 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003447","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":"Bivalent quadratic optimization with sum-of-square of quadratic penalties","authors":"Tongli Zhang, Yong Xia","doi":"10.1007/s10878-025-01339-7","DOIUrl":"https://doi.org/10.1007/s10878-025-01339-7","url":null,"abstract":"&lt;p&gt;The problem of maximizing the sum-of-square of quadratic functions with bivalent variables, denoted by (P), arises from bivalent quadratic optimization with &lt;i&gt;K&lt;/i&gt; quadratic disjunctive penalties. Though NP-hard in general, (P) is polynomially solvable when the input matrices can concatenate to a fixed-rank matrix. We present a nonconvex quadratic semidefinite programming (SDP) relaxation, which provides a 0.4-approximate solution for (P). We show that the quadratic SDP relaxation can be approximately and globally solved to a precision &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"1.412ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -519.5 406.5 607.8\" width=\"0.944ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-3F5\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span role=\"presentation\"&gt;&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;epsilon &lt;/script&gt;&lt;/span&gt; via solving at most &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;msup&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;/mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"2.914ex\" role=\"img\" style=\"vertical-align: -0.706ex;\" viewbox=\"0 -950.8 6609.2 1254.7\" width=\"15.35ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-4F\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"763\" xlink:href=\"#MJMAIN-28\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1153\" xlink:href=\"#MJMAIN-28\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1542\" xlink:href=\"#MJMATHI-4B\" y=\"0\"&gt;&lt;/use&gt;&lt;g transform=\"translate(2432,0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-6E\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"849\" xlink:href=\"#MJMAIN-33\" y=\"513\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;use x=\"3486\" xlink:href=\"#MJMAIN-2F\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"3986\" xlink:href=\"#MJMATHI-3F5\" y=\"0\"&gt;&lt;/use&gt;&lt;g transform=\"translate(4393,0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMAIN-29\" y=\"0\"&gt;&lt;/use&gt;&lt;g transform=\"translate(389,362)\"&gt;&lt;use transform=\"scale(0.707)\" x=\"0\" xlink:href=\"#MJMATHI-4B\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"142 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003469","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":"Hybrid quantum-enhanced reinforcement learning for energy-efficient resource allocation in fog-edge computing","authors":"S. Sureka Nithila Princy, Paulraj Ranjith kumar","doi":"10.1007/s10878-025-01336-w","DOIUrl":"https://doi.org/10.1007/s10878-025-01336-w","url":null,"abstract":"<p>The proliferation of Internet of Things (IoT) devices has intensified the need for intelligent, adaptive, and energy-efficient resource management across mobile edge–fog–cloud infrastructures. Conventional optimization approaches often fail to manage the dynamic interplay among fluctuating workloads, energy constraints, and real-time scheduling. To address this, a Hybrid Quantum-Enhanced Reinforcement Learning (HQERL) framework is introduced, unifying quantum-inspired heuristics, swarm intelligence, and reinforcement learning into a co-adaptive sched uling system. HQERL employs a feedback-driven architecture to synchronize exploration, optimization, and policy refinement for enhanced task scheduling and resource control. The Maximum Likelihood Swarm Whale Optimization (MLSWO) module encodes dynamic task and system states using swarm intelligence guided by statistical likelihood, generating information-rich inputs for the learning controller. To prevent premature convergence and expand the scheduling search space, the Quantum Brainstorm Optimization (QBO) component incorporates probabilistic memory and collective learning to diversify scheduling solutions. These enhanced representations and exploratory strategies feed into the Proximal Policy Optimization (PPO) controller, which dynamically adapts resource allocation policies in real time based on system feedback, ensuring resilience to workload shifts. Furthermore, Dynamic Voltage Scaling (DVS) is integrated to improve energy efficiency by adjusting processor voltages and frequencies according to workload demands. This seamless coordination enables HQERL to balance task latency, resource use, and power consumption. Evaluation on the LSApp dataset reveals HQERL yields a 15% energy efficiency gain, 12% makespan reduction, and a 23.3% boost in peak system utility, validating its effectiveness for sustainable IoT resource management.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"13 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003449","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":"Mutually dependent, balanced contributions, and the priority value","authors":"Songtao He, Erfang Shan, Yuxin Sun","doi":"10.1007/s10878-025-01340-0","DOIUrl":"https://doi.org/10.1007/s10878-025-01340-0","url":null,"abstract":"<p>The Priority value (Béal et al. in Int J Game Theory 51:431–450, 2022) is an allocation rule for TU-games with a priority structure, which distributes the Harsanyi dividend of each coalition among the set of its priority players. In this paper we propose two variants of the differential marginality of mutually dependent players axiom for TU-games with a priority structure, and extend the classical axiom of balanced contributions to TU-games with a priority structure. We provide several new characterizations of the Priority value which invoke these modified axioms and the standard axioms: efficiency, the null player property, the priority player out and the null player out.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"123 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003450","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 integrated operating room and physician scheduling problem solved by a hybrid variable neighborhood search-based algorithm","authors":"Yuli Wang, Wenjuan Fan, Shaowen Lan, Shuwan Zhu, Jianmei Du","doi":"10.1007/s10878-025-01335-x","DOIUrl":"https://doi.org/10.1007/s10878-025-01335-x","url":null,"abstract":"<p>This paper addresses an integrated operating room (OR) and physician scheduling problem driven by the real-world needs in the surgical department. The OR scheduling problem involves determining the number of ORs to be opened each day, the operation date of each surgery, and the schedule of surgeries in each OR. The physician scheduling problem considers two primary work for physicians: surgery service and consultation service, aiming to assign physicians to shifts and determine their responsibilities for either performing surgeries or providing consultation services in the outpatient department. The integration of these two scheduling problems improves coordination between OR availability and physician schedules, which can directly reduce operational costs and enhance resource utilization in the surgical department. The objective of the integrated problem is to minimize the total costs of the hospital and the patients, including the total waiting cost of patients, the total working cost of physicians, the total opening cost of ORs, and the total overtime cost of ORs. To solve the problem, a hybrid approach DP-H-VNS is proposed, which incorporates dynamic programming (DP), heuristics, and a variable neighborhood search (VNS) algorithm. The DP algorithm is used to assign surgeries to specific ORs, while the proposed heuristic rules are presented to determine the number of ORs to open each day and the scheduling of physicians. The presented VNS algorithm can search for high-quality solutions for the proposed problem and serves as a framework to integrate the DP, heuristics, local search, and shaking procedures. Experimental results demonstrate that the proposed DP-H-VNS is superior to the other compared algorithms on the quality of the found solutions and the performance. These results confirm the effectiveness of the proposed approach in optimizing the resource allocation in the surgical department and improving patient care.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"12 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003452","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}