Pub Date : 2025-08-01DOI: 10.1016/j.disopt.2025.100903
Ashim Khanal, Hadi Charkhgard
We study a class of nonlinear optimization problems with diverse practical applications, particularly in cooperative game theory. These problems are referred to as Maximum Multiplicative Programs (MMPs), and can be conceived as instances of “Optimization Over the Frontier” in multi-objective optimization. To solve MMPs, we introduce a feasibility pump-based heuristic that is specifically designed to search the criterion space of their multi-objective optimization counterparts. Through a computational study, we show the efficacy of the proposed method.
{"title":"A criterion space search feasibility pump heuristic for solving maximum multiplicative programs","authors":"Ashim Khanal, Hadi Charkhgard","doi":"10.1016/j.disopt.2025.100903","DOIUrl":"10.1016/j.disopt.2025.100903","url":null,"abstract":"<div><div>We study a class of nonlinear optimization problems with diverse practical applications, particularly in cooperative game theory. These problems are referred to as Maximum Multiplicative Programs (MMPs), and can be conceived as instances of “Optimization Over the Frontier” in multi-objective optimization. To solve MMPs, we introduce a feasibility pump-based heuristic that is specifically designed to search the criterion space of their multi-objective optimization counterparts. Through a computational study, we show the efficacy of the proposed method.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"57 ","pages":"Article 100903"},"PeriodicalIF":1.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144738317","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}
Pub Date : 2025-07-24DOI: 10.1016/j.disopt.2025.100902
Soumyashree Rana , Sounaka Mishra , Bhawani Sankar Panda
<div><div>A set <span><math><mrow><mi>D</mi><mo>⊆</mo><mi>V</mi></mrow></math></span> 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 a dominating set of <span><math><mi>G</mi></math></span> if each vertex <span><math><mrow><mi>v</mi><mo>∈</mo><mi>V</mi><mo>∖</mo><mi>D</mi></mrow></math></span> is adjacent to at least one vertex in <span><math><mrow><mi>D</mi><mo>,</mo></mrow></math></span> whereas a set <span><math><mrow><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⊆</mo><mi>V</mi></mrow></math></span> is a 2-dominating (double dominating) set of <span><math><mi>G</mi></math></span> if each vertex <span><math><mrow><mi>v</mi><mo>∈</mo><mi>V</mi><mo>∖</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> is adjacent to at least two vertices in <span><math><mrow><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>.</mo></mrow></math></span> A graph <span><math><mi>G</mi></math></span> is a <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>-graph if there exists a pair (<span><math><mrow><mi>D</mi><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>) of dominating set and 2-dominating set of <span><math><mi>G</mi></math></span> which are disjoint. In this paper, we give approximation algorithms for the problem of determining a minimal spanning <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>-graph of minimum size (<span>Min-</span> <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>) with an approximation ratio of 3; a minimal spanning <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>-graph of maximum size (<span>Max-</span> <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>) with an approximation ratio of 3; and for the problem of adding minimum number of edges to a graph <span><math><mi>G</mi></math></span> to make it a <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>-graph (<span>Min-to-</span> <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>) with an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mo>log</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> approximation ratio. The above three results answer the open problems mentioned in the paper, Miotk et al. (2020). Furthermore, we prove that <span>Min-</span> <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> and <s
{"title":"Disjoint dominating and 2-dominating sets in graphs: Hardness and approximation results","authors":"Soumyashree Rana , Sounaka Mishra , Bhawani Sankar Panda","doi":"10.1016/j.disopt.2025.100902","DOIUrl":"10.1016/j.disopt.2025.100902","url":null,"abstract":"<div><div>A set <span><math><mrow><mi>D</mi><mo>⊆</mo><mi>V</mi></mrow></math></span> 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 a dominating set of <span><math><mi>G</mi></math></span> if each vertex <span><math><mrow><mi>v</mi><mo>∈</mo><mi>V</mi><mo>∖</mo><mi>D</mi></mrow></math></span> is adjacent to at least one vertex in <span><math><mrow><mi>D</mi><mo>,</mo></mrow></math></span> whereas a set <span><math><mrow><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⊆</mo><mi>V</mi></mrow></math></span> is a 2-dominating (double dominating) set of <span><math><mi>G</mi></math></span> if each vertex <span><math><mrow><mi>v</mi><mo>∈</mo><mi>V</mi><mo>∖</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> is adjacent to at least two vertices in <span><math><mrow><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>.</mo></mrow></math></span> A graph <span><math><mi>G</mi></math></span> is a <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>-graph if there exists a pair (<span><math><mrow><mi>D</mi><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>) of dominating set and 2-dominating set of <span><math><mi>G</mi></math></span> which are disjoint. In this paper, we give approximation algorithms for the problem of determining a minimal spanning <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>-graph of minimum size (<span>Min-</span> <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>) with an approximation ratio of 3; a minimal spanning <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>-graph of maximum size (<span>Max-</span> <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>) with an approximation ratio of 3; and for the problem of adding minimum number of edges to a graph <span><math><mi>G</mi></math></span> to make it a <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>-graph (<span>Min-to-</span> <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>) with an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mo>log</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> approximation ratio. The above three results answer the open problems mentioned in the paper, Miotk et al. (2020). Furthermore, we prove that <span>Min-</span> <span><math><mrow><mi>D</mi><mspace></mspace><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> and <s","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"57 ","pages":"Article 100902"},"PeriodicalIF":0.9,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144696742","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}
In this paper, we investigate the integrality gap of the Asymmetric Traveling Salesman Problem (ATSP) with respect to the linear relaxation given by the Asymmetric Subtour Elimination Problem (ASEP) for instances with nodes, where is small. In particular, we focus on the geometric properties and symmetries of the ASEP polytope () and its vertices. The polytope’s symmetries are exploited to design a heuristic pivoting algorithm to search vertices where the integrality gap is maximized. Furthermore, a general procedure for the extension of vertices from to is defined. The generated vertices improve the known lower bounds of the integrality gap for and, provide small hard-to-solve ATSP instances.
{"title":"On the integrality gap of small Asymmetric Traveling Salesman Problems: A polyhedral and computational approach","authors":"Eleonora Vercesi , Janos Barta , Luca Maria Gambardella , Stefano Gualandi , Monaldo Mastrolilli","doi":"10.1016/j.disopt.2025.100901","DOIUrl":"10.1016/j.disopt.2025.100901","url":null,"abstract":"<div><div>In this paper, we investigate the integrality gap of the Asymmetric Traveling Salesman Problem (ATSP) with respect to the linear relaxation given by the Asymmetric Subtour Elimination Problem (ASEP) for instances with <span><math><mi>n</mi></math></span> nodes, where <span><math><mi>n</mi></math></span> is small. In particular, we focus on the geometric properties and symmetries of the ASEP polytope (<span><math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ASEP</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>) and its vertices. The polytope’s symmetries are exploited to design a heuristic pivoting algorithm to search vertices where the integrality gap is maximized. Furthermore, a general procedure for the extension of vertices from <span><math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ASEP</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> to <span><math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ASEP</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msubsup></math></span> is defined. The generated vertices improve the known lower bounds of the integrality gap for <span><math><mrow><mn>16</mn><mo>≤</mo><mi>n</mi><mo>≤</mo><mn>22</mn></mrow></math></span> and, provide small hard-to-solve ATSP instances.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"57 ","pages":"Article 100901"},"PeriodicalIF":0.9,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144549222","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}
Pub Date : 2025-06-13DOI: 10.1016/j.disopt.2025.100900
Alexander Kononov , Victor Il’ev
Clustering is the task of dividing objects into groups (called clusters) so that objects in the same group are similar to each other. The Cluster Editing problem is one of the most natural ways to model clustering on graphs. In this problem, the similarity relation between objects is given by an undirected graph whose vertices correspond to the objects, edges connect couples of similar objects, and it is required to partition the set of vertices into disjoint subsets minimizing the number of edges between clusters and the number of missing edges within clusters. We present new approximation algorithms with better worst-case performance guarantees when cluster sizes are upper bounded by three or four vertices.
{"title":"Approximation algorithms for the cluster editing problem with small clusters","authors":"Alexander Kononov , Victor Il’ev","doi":"10.1016/j.disopt.2025.100900","DOIUrl":"10.1016/j.disopt.2025.100900","url":null,"abstract":"<div><div>Clustering is the task of dividing objects into groups (called clusters) so that objects in the same group are similar to each other. The Cluster Editing problem is one of the most natural ways to model clustering on graphs. In this problem, the similarity relation between objects is given by an undirected graph whose vertices correspond to the objects, edges connect couples of similar objects, and it is required to partition the set of vertices into disjoint subsets minimizing the number of edges between clusters and the number of missing edges within clusters. We present new approximation algorithms with better worst-case performance guarantees when cluster sizes are upper bounded by three or four vertices.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"57 ","pages":"Article 100900"},"PeriodicalIF":0.9,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144279680","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}
Pub Date : 2025-06-11DOI: 10.1016/j.disopt.2025.100891
Michaela Borzechowski , Simon Weber
Klaus showed that the Oriented Matroid Complementarity Problem (OMCP) can be solved by a reduction to the problem of sink-finding in a unique sink orientation (USO) if the input is promised to be given by a non-degenerate extension of a P-matroid. In this paper, we investigate the effect of degeneracy on this reduction. On the one hand, this understanding of degeneracies allows us to prove a linear lower bound on the number of vertex evaluations required for sink-finding in P-matroid USOs, the set of USOs obtainable through Klaus’ reduction. On the other hand, it allows us to adjust Klaus’ reduction to also work with degenerate instances. Furthermore, we introduce a total search version of the P-Matroid Oriented Matroid Complementarity Problem (P-OMCP). Given any extension of any oriented matroid , by reduction to a total search version of USO sink-finding we can either solve the OMCP, or provide a polynomial-time verifiable certificate that is not a P-matroid. This places the total search version of the P-OMCP in the complexity class Unique End of Potential Line (UEOPL).
{"title":"On degeneracy in the P-matroid oriented matroid complementarity problem","authors":"Michaela Borzechowski , Simon Weber","doi":"10.1016/j.disopt.2025.100891","DOIUrl":"10.1016/j.disopt.2025.100891","url":null,"abstract":"<div><div>Klaus showed that the <span>Oriented Matroid Complementarity Problem</span> (<span>OMCP</span>) can be solved by a reduction to the problem of sink-finding in a <em>unique sink orientation (USO)</em> if the input is promised to be given by a <em>non-degenerate</em> extension of a <em>P-matroid</em>. In this paper, we investigate the effect of degeneracy on this reduction. On the one hand, this understanding of degeneracies allows us to prove a linear lower bound on the number of vertex evaluations required for sink-finding in <em>P-matroid USOs</em>, the set of USOs obtainable through Klaus’ reduction. On the other hand, it allows us to adjust Klaus’ reduction to also work with degenerate instances. Furthermore, we introduce a total search version of the <span>P-Matroid Oriented Matroid Complementarity Problem</span> (<span>P-OMCP</span>). Given <em>any</em> extension of <em>any</em> oriented matroid <span><math><mi>M</mi></math></span>, by reduction to a total search version of USO sink-finding we can either solve the <span>OMCP</span>, or provide a polynomial-time verifiable certificate that <span><math><mi>M</mi></math></span> is <em>not</em> a P-matroid. This places the total search version of the <span>P-OMCP</span> in the complexity class <span>Unique End of Potential Line</span> (<span>UEOPL</span>).</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"57 ","pages":"Article 100891"},"PeriodicalIF":0.9,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144253723","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}
Pub Date : 2025-05-22DOI: 10.1016/j.disopt.2025.100890
D.S. Protasov , A.D. Tolmachev , V.A. Voronov
We consider the problem of partitioning a two-dimensional flat torus into sets in order to minimize the maximum diameter of a part. For we give numerical estimates for the maximum diameter at which the partition exists. Several approaches are proposed to obtain such estimates. In particular, we use the search for mesh partitions via the SAT solver, the global optimization approach for polygonal partitions, and the optimization of periodic hexagonal tilings. For , the exact estimate is proved using elementary topological reasoning.
{"title":"Optimal partitions of the flat torus into parts of smaller diameter","authors":"D.S. Protasov , A.D. Tolmachev , V.A. Voronov","doi":"10.1016/j.disopt.2025.100890","DOIUrl":"10.1016/j.disopt.2025.100890","url":null,"abstract":"<div><div>We consider the problem of partitioning a two-dimensional flat torus <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> into <span><math><mi>m</mi></math></span> sets in order to minimize the maximum diameter of a part. For <span><math><mrow><mi>m</mi><mo>⩽</mo><mn>25</mn></mrow></math></span> we give numerical estimates for the maximum diameter <span><math><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>m</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> at which the partition exists. Several approaches are proposed to obtain such estimates. In particular, we use the search for mesh partitions via the SAT solver, the global optimization approach for polygonal partitions, and the optimization of periodic hexagonal tilings. For <span><math><mrow><mi>m</mi><mo>=</mo><mn>3</mn></mrow></math></span>, the exact estimate is proved using elementary topological reasoning.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"57 ","pages":"Article 100890"},"PeriodicalIF":0.9,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116524","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}
Pub Date : 2025-05-01DOI: 10.1016/j.disopt.2025.100889
Mohammed Lalou , Hamamache Kheddouci
We consider the k-way vertex cut problem that consists in finding a subset of vertices of a given cardinality, in a graph, whose removal partitions the graph into the maximum connected components. This problem has been proven to be NP-complete on general graphs, split and planar graphs. In this paper, we consider it on bipartite graphs and we show that it remains NP-complete even restricted on this class of graphs. However, for the subclass of bipartite-permutation graphs, we develop a polynomial-time algorithm using the dynamic programming approach for solving the problem. The algorithm runs in time and space, where is the graph order, and is the number of deleted vertices. We also extend our attention by considering vertex deletion costs, and we adapt the proposed dynamic program to the case where non-negative costs are associated to vertex deletion. The obtained algorithm is of time and space complexity and , respectively.
{"title":"The k-way vertex cut problem on bipartite graphs: Complexity results and algorithms","authors":"Mohammed Lalou , Hamamache Kheddouci","doi":"10.1016/j.disopt.2025.100889","DOIUrl":"10.1016/j.disopt.2025.100889","url":null,"abstract":"<div><div>We consider the <em>k-way vertex cut problem</em> that consists in finding a subset of vertices of a given cardinality, in a graph, whose removal partitions the graph into the maximum connected components. This problem has been proven to be NP-complete on general graphs, split and planar graphs. In this paper, we consider it on bipartite graphs and we show that it remains NP-complete even restricted on this class of graphs. However, for the subclass of bipartite-permutation graphs, we develop a polynomial-time algorithm using the dynamic programming approach for solving the problem. The algorithm runs in <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>n</mi><msup><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> time and <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>n</mi><mi>K</mi><mo>)</mo></mrow></mrow></math></span> space, where <span><math><mi>n</mi></math></span> is the graph order, and <span><math><mi>K</mi></math></span> is the number of deleted vertices. We also extend our attention by considering vertex deletion costs, and we adapt the proposed dynamic program to the case where non-negative costs are associated to vertex deletion. The obtained algorithm is of time and space complexity <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>, respectively.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"56 ","pages":"Article 100889"},"PeriodicalIF":0.9,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937847","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}
Pub Date : 2025-04-10DOI: 10.1016/j.disopt.2025.100887
Gerold Jäger , Marcel Turkensteen
This paper considers the computation of lower tolerances of combinatorial optimization problems with an objective of type bottleneck, in which the objective is to minimize the element with maximum cost of a feasible solution. A lower tolerance can be defined as the supremum decrease such that the objective value remains the same. We develop a computational approach for generic problems with objective of type bottleneck and two specific approaches for the Linear Bottleneck Assignment Problem and the Bottleneck Shortest Path Problem, which have a similar complexity as solution approaches for these two problems. Finally, we present some experimental results on random instances for these problems.
{"title":"Computation of lower tolerances of combinatorial bottleneck problems","authors":"Gerold Jäger , Marcel Turkensteen","doi":"10.1016/j.disopt.2025.100887","DOIUrl":"10.1016/j.disopt.2025.100887","url":null,"abstract":"<div><div>This paper considers the computation of lower tolerances of combinatorial optimization problems with an objective of type bottleneck, in which the objective is to minimize the element with maximum cost of a feasible solution. A lower tolerance can be defined as the supremum decrease such that the objective value remains the same. We develop a computational approach for generic problems with objective of type bottleneck and two specific approaches for the Linear Bottleneck Assignment Problem and the Bottleneck Shortest Path Problem, which have a similar complexity as solution approaches for these two problems. Finally, we present some experimental results on random instances for these problems.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"56 ","pages":"Article 100887"},"PeriodicalIF":0.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143816640","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}
Pub Date : 2025-04-02DOI: 10.1016/j.disopt.2025.100888
İmdat Kara, Gözde Önder Uzun
In this paper, we show that, the formulation given in a recent paper [1] for the travelling salesman problem with time windows (TSPTW), may not find the optimal solution and then we recommend to add a new constraint to the model.
{"title":"A remark on the formulation given in “A note on the lifted Miller-Tucker-Zemlin subtour elimination constraints for routing problems with time windows”","authors":"İmdat Kara, Gözde Önder Uzun","doi":"10.1016/j.disopt.2025.100888","DOIUrl":"10.1016/j.disopt.2025.100888","url":null,"abstract":"<div><div>In this paper, we show that, the formulation given in a recent paper [1] for the travelling salesman problem with time windows (TSPTW), may not find the optimal solution and then we recommend to add a new constraint to the model.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"56 ","pages":"Article 100888"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143748273","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}
Pub Date : 2025-03-01DOI: 10.1016/j.disopt.2025.100880
Gökçe Çakmak , Ali Deniz , Şahin Koçak
V. Turaev defined recently an operation of “Trimming” for pseudo-metric spaces and analyzed the tight span of (pseudo-)metric spaces via this process. In this work we investigate the trimming of finite subspaces of the Manhattan plane. We show that this operation amounts for them to taking the metric center set and we give an algorithm to construct the tight spans via trimming.
V. Turaev最近定义了伪度量空间的“修剪”操作，并通过此过程分析了（伪）度量空间的紧跨度。在这项工作中，我们研究了曼哈顿平面的有限子空间的修剪。我们证明了这种操作相当于取度量中心集，并给出了一种通过切边构造紧跨的算法。
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