Discrete Optimization最新文献

{"title":"Corrigendum to “A polyhedral study of lifted multicuts” [Discrete Optim. 47 (2023) 100757]","authors":"Bjoern Andres , Silvia Di Gregorio , Jannik Irmai , Jan-Hendrik Lange","doi":"10.1016/j.disopt.2024.100876","DOIUrl":"10.1016/j.disopt.2024.100876","url":null,"abstract":"","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"55 ","pages":"Article 100876"},"PeriodicalIF":0.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143177281","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":"Uniform capacitated facility location with outliers/penalties","authors":"Rajni Dabas,&nbsp;Neelima Gupta","doi":"10.1016/j.disopt.2025.100878","DOIUrl":"10.1016/j.disopt.2025.100878","url":null,"abstract":"<div><div>In this paper, we present a framework to design approximation algorithms for capacitated facility location problems with penalties/outliers. We apply our framework to obtain first approximations for capacitated <span><math><mi>k</mi></math></span>-facility location problem with penalties (C<span><math><mi>k</mi></math></span>FLwP) and capacitated facility location problem with outliers (CFLwO), for hard uniform capacities. Our solutions incur slight violations in capacities, (<span><math><mrow><mn>1</mn><mo>+</mo><mi>ϵ</mi></mrow></math></span>) for the problems without cardinality(<span><math><mi>k</mi></math></span>) constraint and (<span><math><mrow><mn>2</mn><mo>+</mo><mi>ϵ</mi></mrow></math></span>) for the problems with the cardinality constraint. For the outlier variant, we also incur a small loss (<span><math><mrow><mn>1</mn><mo>+</mo><mi>ϵ</mi></mrow></math></span>) in outliers. To the best of our knowledge, no results are known for CFLwO and C<span><math><mi>k</mi></math></span>FLwP in the literature. For uniform facility opening cost, we get rid of violation in capacities for CFLwO. Our approach is based on LP rounding technique.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"55 ","pages":"Article 100878"},"PeriodicalIF":0.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143177068","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":"A polynomial-time algorithm for conformable coloring on regular bipartite and subcubic graphs","authors":"Luerbio Faria,&nbsp;Mauro Nigro,&nbsp;Diana Sasaki","doi":"10.1016/j.disopt.2024.100865","DOIUrl":"10.1016/j.disopt.2024.100865","url":null,"abstract":"<div><div>In 1988, Chetwynd and Hilton observed that a <span><math><mrow><mo>(</mo><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-total coloring induces a vertex coloring in the graph, they called it conformable. A <span><math><mrow><mo>(</mo><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-vertex coloring of a graph <span><math><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span> is called <em>conformable</em> if the number of color classes of parity different from that of <span><math><mrow><mo>|</mo><mi>V</mi><mo>|</mo></mrow></math></span> is at most the deficiency <span><math><mrow><mo>def</mo><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mo>∑</mo></mrow><mrow><mi>v</mi><mo>∈</mo><mi>V</mi></mrow></msub><mrow><mo>(</mo><mi>Δ</mi><mo>−</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>G</mi></mrow></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> of <span><math><mi>G</mi></math></span>, where <span><math><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>G</mi></mrow></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></math></span> is the degree of a vertex <span><math><mi>v</mi></math></span> of <span><math><mi>V</mi></math></span>. In 1994, McDiarmid and Sánchez-Arroyo proved that deciding whether a graph <span><math><mi>G</mi></math></span> has <span><math><mrow><mo>(</mo><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-total coloring is NP-complete even when <span><math><mi>G</mi></math></span> is <span><math><mi>k</mi></math></span>-regular bipartite with <span><math><mrow><mi>k</mi><mo>≥</mo><mn>3</mn></mrow></math></span>. However, the time-complexity of the problem of determining whether a graph admits a conformable coloring (<span>Conformability</span> problem) remains unknown. In this paper, we prove that <span>Conformability</span> problem is polynomial solvable for the class of <span><math><mi>k</mi></math></span>-regular bipartite and for the class of subcubic graphs.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"55 ","pages":"Article 100865"},"PeriodicalIF":0.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142745017","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 pure fixed charge transportation problem","authors":"Pengfei Zhu ,&nbsp;Guangting Chen ,&nbsp;Yong Chen ,&nbsp;An Zhang","doi":"10.1016/j.disopt.2024.100875","DOIUrl":"10.1016/j.disopt.2024.100875","url":null,"abstract":"<div><div>The <em>pure fixed charge transportation problem</em> is a well-known variant of the classic transportation problem where the cost of sending goods from a source to a destination only equals a fixed charge, regardless of the flow quantity. The objective is to minimize the total cost of shipping available goods to meet the required demands. Hence, we first demonstrate that this problem is NP-hard even when there are only two destinations, and it is Strong NP-hard when the number of destinations is input. These two new complexity results are an important supplement to the previous complexity results of this problem. Then, we propose two simple but novel approximation algorithms with a constant worst-case ratio, which is proved using an integer convex optimization model. Although our approximation algorithm applies to a few destinations, to our knowledge, it is the first approximation algorithm to handle the pure fixed-charge transportation problem.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"55 ","pages":"Article 100875"},"PeriodicalIF":0.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178626","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":"Two-set inequalities for the binary knapsack polyhedra","authors":"Todd Easton ,&nbsp;Jennifer Tryon ,&nbsp;Fabio Vitor","doi":"10.1016/j.disopt.2024.100859","DOIUrl":"10.1016/j.disopt.2024.100859","url":null,"abstract":"<div><p>This paper presents two-set inequalities, a class of valid inequalities for knapsack and multiple knapsack problems. Two-set inequalities are generated from two arbitrary sets of variables from a knapsack constraint. This class of cutting planes is not a traditional type of lifting since a valid inequality over a restricted space is not required to start. Furthermore, they cannot be derived using any existing lifting technique. The paper presents a quadratic algorithm to efficiently generate many two-set inequalities. Conditions for facet-defining two-set inequalities are also derived. Computational experiments tested these inequalities as pre-processing cuts versus CPLEX, a high-performance mathematical programming solver, at default settings. Overall, two-set inequalities reduced the time to solve some benchmark multiple knapsack instances to up to 80%. Computational results also showed the potential of this new class of cutting planes to solve computationally challenging binary integer programs.</p></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"54 ","pages":"Article 100859"},"PeriodicalIF":0.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142172518","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":"Mostar index and bounded maximum degree","authors":"Michael A. Henning ,&nbsp;Johannes Pardey ,&nbsp;Dieter Rautenbach ,&nbsp;Florian Werner","doi":"10.1016/j.disopt.2024.100861","DOIUrl":"10.1016/j.disopt.2024.100861","url":null,"abstract":"&lt;div&gt;&lt;p&gt;Došlić et al. defined the Mostar index of a graph &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; as &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munder&gt;&lt;mrow&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, where, for an edge &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; of &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, the term &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; denotes the number of vertices of &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; that have a smaller distance in &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; to &lt;span&gt;&lt;math&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; than to &lt;span&gt;&lt;math&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. For a graph &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of order &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and maximum degree at most &lt;span&gt;&lt;math&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, we show &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;log&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;log&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; only depends on &lt;span&gt;&lt;math&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and the &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; term only depends on &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. Furthermore, for integers &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; at least 3, we show the existence of a &lt;span&gt;&lt;math&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-regular graph of order &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; at least &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;log&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; where &lt;span&gt;&lt;mat","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"54 ","pages":"Article 100861"},"PeriodicalIF":0.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1572528624000409/pdfft?md5=e34071dea61722ee4baab21c7039f3bf&pid=1-s2.0-S1572528624000409-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142228672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On non-superperfection of edge intersection graphs of paths","authors":"Victoria Kaial,&nbsp;Hervé Kerivin ,&nbsp;Annegret K. Wagler","doi":"10.1016/j.disopt.2024.100857","DOIUrl":"10.1016/j.disopt.2024.100857","url":null,"abstract":"<div><p>The routing and spectrum assignment problem in modern flexgrid elastic optical networks asks for assigning to given demands a route in an optical network and a channel within an optical frequency spectrum so that the channels of two demands are disjoint whenever their routes share a link in the optical network. This problem can be modeled in two phases: firstly, a selection of paths in the network and, secondly, an interval coloring problem in the edge intersection graph of these paths. The interval chromatic number equals the smallest size of a spectrum such that a proper interval coloring is possible, the weighted clique number is a natural lower bound. Graphs where both parameters coincide for all possible non-negative integral weights are called superperfect. Therefore, the occurrence of non-superperfect edge intersection graphs of routing paths can provoke the need of larger spectral resources. In this work, we examine the question which minimal non-superperfect graphs can occur in the edge intersection graphs of routing paths in different underlying networks: when the network is a path, a tree, a cycle, or a sparse planar graph with small maximum degree. We show that for any possible network (even if it is restricted to a path) the resulting edge intersection graphs are not necessarily superperfect. We close with a discussion of possible consequences and of some lines of future research.</p></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"54 ","pages":"Article 100857"},"PeriodicalIF":0.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141979335","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":"Corrigendum to “Bilevel time minimizing transportation problem” [Discrete Optim.] 5 (4) (2008) 714–723","authors":"Sonia ,&nbsp;Ankit Khandelwal","doi":"10.1016/j.disopt.2024.100863","DOIUrl":"10.1016/j.disopt.2024.100863","url":null,"abstract":"<div><div>This is a corrigendum to our research paper titled “Bilevel time minimizing transportation problem” published in 2008. We deeply regret a minor error in the formulation of an intermediate problem solved as part of the algorithm. The intermediate problem, <span><math><msubsup><mrow><mrow><mo>(</mo><mi>T</mi><mi>P</mi><mo>)</mo></mrow></mrow><mrow><mi>t</mi></mrow><mrow><mi>T</mi></mrow></msubsup></math></span>, used to iteratively generate the prospective solution pairs, was initially modeled as a linear programming problem. But the correct formulation of its objective function now involves a binary function, thus making it an NP-hard problem. The algorithm is no longer polynomially bound as it involves solving a finite number of mixed 0-1 programming problems. The manuscript’s original contribution stands correct and there is no change to the structure or the accuracy of the algorithm. The changes required to the original paper, due to this error, are presented in this corrigendum.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"54 ","pages":"Article 100863"},"PeriodicalIF":0.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697348","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":"Circuit and Graver walks and linear and integer programming","authors":"Shmuel Onn","doi":"10.1016/j.disopt.2024.100862","DOIUrl":"10.1016/j.disopt.2024.100862","url":null,"abstract":"<div><div>We show that a circuit walk from a given feasible point of a given linear program to an optimal point can be computed in polynomial time using only linear algebra operations and the solution of the single given linear program. We also show that a Graver walk from a given feasible point of a given integer program to an optimal point is polynomial time computable using an integer programming oracle, but without such an oracle, it is hard to compute such a walk even if an optimal solution to the given program is given as well. Combining our oracle algorithm with recent results on sparse integer programming, we also show that Graver walks from any point are polynomial time computable over matrices of bounded tree-depth and subdeterminants.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"54 ","pages":"Article 100862"},"PeriodicalIF":0.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425831","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":"Easy and hard separation of sparse and dense odd-set constraints in matching","authors":"Brady Hunsaker,&nbsp;Craig Tovey","doi":"10.1016/j.disopt.2024.100849","DOIUrl":"10.1016/j.disopt.2024.100849","url":null,"abstract":"<div><p>We investigate polytopes intermediate between the fractional matching and the perfect matching polytopes, by imposing a strict subset of the odd-set (blossom) constraints. For sparse constraints, we give a polynomial time separation algorithm if only constraints on all odd sets bounded by a given size (e.g. <span><math><mrow><mo>≤</mo><mn>9</mn><mo>+</mo><mrow><mo>|</mo><mi>V</mi><mo>|</mo></mrow><mo>/</mo><mn>6</mn></mrow></math></span>) are present. Our algorithm also solves the more general problem of finding a T-cut subject to upper bounds on the cardinality of its defining node set and on its cost. In contrast, regarding dense constraints, we prove that for every <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>≤</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>, it is NP-complete to separate over the class of constraints on odd sets of size <span><math><mrow><mn>2</mn><mrow><mo>⌊</mo><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>α</mi><mrow><mo>|</mo><mi>V</mi><mo>|</mo></mrow><mo>)</mo></mrow><mo>/</mo><mn>2</mn><mo>⌋</mo></mrow><mo>−</mo><mn>1</mn></mrow></math></span> or <span><math><mrow><mo>≥</mo><mi>α</mi><mrow><mo>|</mo><mi>V</mi><mo>|</mo></mrow></mrow></math></span>.</p></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"54 ","pages":"Article 100849"},"PeriodicalIF":0.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142228671","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}