Networks最新文献

{"title":"Algorithms and complexity for the almost equal maximum flow problem","authors":"Rebekka Haese, Till Heller, Sven O. Krumke","doi":"10.1002/net.22209","DOIUrl":"https://doi.org/10.1002/net.22209","url":null,"abstract":"In the equal maximum flow problem (EMFP), we aim for a maximum flow where we require the same flow value on all arcs in some given subsets of the arc set, so called homologous arc sets. In this article, we study the closely related almost equal maximum flow problems (AEMFP) where the flow values on arcs of one homologous arc set differ at most by the valuation of a so called deviation function <mjx-container aria-label=\"normal upper Delta\" ctxtmenu_counter=\"0\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/net22209-math-0001.png\"><mjx-semantics><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"normal upper Delta\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml aria-hidden=\"true\" display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:net:media:net22209:net22209-math-0001\" display=\"inline\" location=\"graphic/net22209-math-0001.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-role=\"greekletter\" data-semantic-speech=\"normal upper Delta\" data-semantic-type=\"identifier\" mathvariant=\"normal\">Δ</mi></mrow>$$ Delta $$</annotation></semantics></math></mjx-assistive-mml></mjx-container>. We prove that the integer AEMFP is in general <mjx-container aria-label=\"script upper N script upper P\" ctxtmenu_counter=\"1\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/net22209-math-0002.png\"><mjx-mrow data-semantic-annotation=\"clearspeak:simple;clearspeak:unit\" data-semantic-children=\"0,1\" data-semantic-content=\"2\" data-semantic- data-semantic-role=\"implicit\" data-semantic-speech=\"script upper N script upper P\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"script\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"3\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"script\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-math><mjx-assistive-mml aria-hidden=\"true\" display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:net:media:net22209:net22209-math-0002\" display=\"inline\" location=\"graphic/net22209-","PeriodicalId":54734,"journal":{"name":"Networks","volume":"205 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139554307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the complexity of the upgrading version of the maximal covering location problem","authors":"Marta Baldomero-Naranjo, Jörg Kalcsics, Antonio M. Rodríguez-Chía","doi":"10.1002/net.22207","DOIUrl":"https://doi.org/10.1002/net.22207","url":null,"abstract":"In this article, we study the complexity of the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem is NP-hard on general networks. However, in some particular cases, we prove that this problem is solvable in polynomial time. The cases of star and path networks combined with different assumptions for the model parameters are analysed. In particular, we obtain that the problem on star networks is solvable in <math altimg=\"urn:x-wiley:net:media:net22207:net22207-math-0001\" display=\"inline\" location=\"graphic/net22207-math-0001.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mi>O</mi>\u0000<mo stretchy=\"false\">(</mo>\u0000<mi>n</mi>\u0000<mi>log</mi>\u0000<mi>n</mi>\u0000<mo stretchy=\"false\">)</mo>\u0000</mrow>\u0000$$ Oleft(nlog nright) $$</annotation>\u0000</semantics></math> time for uniform weights and NP-hard for non-uniform weights. On paths, the single facility problem is solvable in <math altimg=\"urn:x-wiley:net:media:net22207:net22207-math-0002\" display=\"inline\" location=\"graphic/net22207-math-0002.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mi>O</mi>\u0000<mo stretchy=\"false\">(</mo>\u0000<msup>\u0000<mrow>\u0000<mi>n</mi>\u0000</mrow>\u0000<mrow>\u0000<mn>3</mn>\u0000</mrow>\u0000</msup>\u0000<mo stretchy=\"false\">)</mo>\u0000</mrow>\u0000$$ Oleft({n}^3right) $$</annotation>\u0000</semantics></math> time, while the <math altimg=\"urn:x-wiley:net:media:net22207:net22207-math-0003\" display=\"inline\" location=\"graphic/net22207-math-0003.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mi>p</mi>\u0000</mrow>\u0000$$ p $$</annotation>\u0000</semantics></math>-facility problem is NP-hard even with uniform costs and upper bounds (maximal upgrading per edge), as well as, integer parameter values. Furthermore, a pseudo-polynomial algorithm is developed for the single facility problem on trees with integer parameters.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139482271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Shortest path network interdiction with asymmetric uncertainty","authors":"She'ifa Z. Punla-Green, John E. Mitchell, Jared L. Gearhart, William E. Hart, Cynthia A. Phillips","doi":"10.1002/net.22208","DOIUrl":"https://doi.org/10.1002/net.22208","url":null,"abstract":"This paper considers an extension of the shortest path network interdiction problem that incorporates robustness to account for parameter uncertainty. The shortest path interdiction problem is a game of two players with conflicting agendas and capabilities: an evader, who traverses the arcs of a network from a source node to a sink node using a path of shortest length, and an interdictor, who maximizes the length of the evader's shortest path by interdicting arcs on the network. It is usually assumed that the parameters defining the network are known exactly by both players. We consider the situation where the evader assumes the nominal parameter values while the interdictor uses robust optimization techniques to account for parameter uncertainty or sensor degradation. We formulate this problem as a nonlinear mixed-integer semi-infinite bilevel program and show that it can be converted into a mixed-integer linear program with a second order cone constraint. We use random geometric networks and transportation networks to perform computational studies and demonstrate the unique decision strategies that our variant produces. Solving the shortest path interdiction problem with asymmetric uncertainty protects the interdictor from investing in a strategy that hinges on key interdictions performing as promised. It also provides an alternate strategy that mitigates the risk of these worst-case possibilities.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139482347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Special cases of the minimum spanning tree problem under explorable edge and vertex uncertainty","authors":"Corinna Mathwieser, Eranda Çela","doi":"10.1002/net.22204","DOIUrl":"https://doi.org/10.1002/net.22204","url":null,"abstract":"This article studies the Minimum Spanning Tree Problem under Explorable Uncertainty as well as a related vertex uncertainty version of the problem. We particularly consider special instance types, including cactus graphs, for which we provide randomized algorithms. We introduce the problem of finding a minimum weight spanning star under uncertainty for which we show that no algorithm can achieve constant competitive ratio.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"32 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139422158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"How vulnerable is an undirected planar graph with respect to max flow","authors":"Lorenzo Balzotti, Paolo G. Franciosa","doi":"10.1002/net.22205","DOIUrl":"https://doi.org/10.1002/net.22205","url":null,"abstract":"We study the problem of computing the vitality of edges and vertices with respect to the &lt;mjx-container aria-label=\"Menu available. Press control and space , or space\" ctxtmenu_counter=\"1\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"&gt;&lt;mjx-math aria-hidden=\"true\" location=\"graphic/net22205-math-0001.png\"&gt;&lt;mjx-semantics&gt;&lt;mjx-mrow data-semantic-annotation=\"clearspeak:simple;clearspeak:unit\" data-semantic-children=\"0,1\" data-semantic-content=\"2\" data-semantic- data-semantic-role=\"implicit\" data-semantic-speech=\"s t\" data-semantic-type=\"infixop\"&gt;&lt;mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"&gt;&lt;mjx-c&gt;&lt;/mjx-c&gt;&lt;/mjx-mi&gt;&lt;mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"3\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"&gt;&lt;mjx-c&gt;&lt;/mjx-c&gt;&lt;/mjx-mo&gt;&lt;mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"&gt;&lt;mjx-c&gt;&lt;/mjx-c&gt;&lt;/mjx-mi&gt;&lt;/mjx-mrow&gt;&lt;/mjx-semantics&gt;&lt;/mjx-math&gt;&lt;mjx-assistive-mml aria-hidden=\"true\" display=\"inline\" unselectable=\"on\"&gt;&lt;math altimg=\"urn:x-wiley:net:media:net22205:net22205-math-0001\" display=\"inline\" location=\"graphic/net22205-math-0001.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;semantics&gt;&lt;mrow data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple;clearspeak:unit\" data-semantic-children=\"0,1\" data-semantic-content=\"2\" data-semantic-role=\"implicit\" data-semantic-speech=\"s t\" data-semantic-type=\"infixop\"&gt;&lt;mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"&gt;s&lt;/mi&gt;&lt;mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"3\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"&gt;⁢&lt;/mo&gt;&lt;mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"&gt;t&lt;/mi&gt;&lt;/mrow&gt;$$ st $$&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/mjx-assistive-mml&gt;&lt;/mjx-container&gt;-max flow in undirected planar graphs, where the vitality of an edge/vertex is the &lt;mjx-container aria-label=\"Menu available. Press control and space , or space\" ctxtmenu_counter=\"2\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"&gt;&lt;mjx-math aria-hidden=\"true\" location=\"graphic/net22205-math-0002.png\"&gt;&lt;mjx-semantics&gt;&lt;mjx-mrow data-semantic-annotation=\"clearspeak:simple;clearspeak:unit\" data-semantic-children=\"0,1\" data-semantic-content","PeriodicalId":54734,"journal":{"name":"Networks","volume":"14 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Math-based reinforcement learning for the adaptive budgeted influence maximization problem","authors":"Edoardo Fadda, Evelina Di Corso, Davide Brusco, Vlad Stefan Aelenei, Alexandru Balan Rares","doi":"10.1002/net.22206","DOIUrl":"https://doi.org/10.1002/net.22206","url":null,"abstract":"In social networks, the influence maximization problem requires selecting an initial set of nodes to influence so that the spread of influence can reach its maximum under certain diffusion models. Usually, the problem is formulated in a two-stage un-budgeted fashion: The decision maker selects a given number of nodes to influence and observes the results. In the adaptive version of the problem, it is possible to select the nodes at each time step of a given time interval. This allows the decision-maker to exploit the observation of the propagation and to make better decisions. This paper considers the adaptive budgeted influence maximization problem, that is, the adaptive problem in which the decision maker has a finite budget to influence the nodes, and each node requires a cost to be influenced. We present two solution techniques: The first is an approximated value iteration leveraging mixed integer linear problems while the second exploits new concepts from graph neural networks. Extensive numerical experiments demonstrate the effectiveness of the proposed approaches.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"45 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139057131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generalizing Horn's conditions for preemptive scheduling on identical parallel machines via network flow techniques","authors":"Akiyoshi Shioura, Vitaly A. Strusevich, Natalia V. Shakhlevich","doi":"10.1002/net.22202","DOIUrl":"https://doi.org/10.1002/net.22202","url":null,"abstract":"We study the use of flow-based algorithmic and proof techniques applied to preemptive scheduling of jobs on parallel identical machines. For the classical problem in which the jobs have individual release dates and must be finished by a common deadline, we present and prove unified necessary and sufficient conditions for the existence of a feasible schedule by examining the structure of minimum cuts in a special network. We then study an enhanced model that allows the presence of additional resources, provided that some jobs at any time of their processing require one unit of a particular resource. We extend our argument developed for the classical case to this enhanced model. The generalized necessary and sufficient conditions for the existence of a feasible schedule are presented and proved using the max-flow/min-cut reasoning.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138824664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Learning to repeatedly solve routing problems","authors":"Mouad Morabit, Guy Desaulniers, Andrea Lodi","doi":"10.1002/net.22200","DOIUrl":"https://doi.org/10.1002/net.22200","url":null,"abstract":"In the last years, there has been a great interest in machine-learning-based heuristics for solving NP-hard combinatorial optimization problems. The developed methods have shown potential on many optimization problems. In this paper, we present a learned heuristic for the reoptimization of a problem after a minor change in its data. We focus on the case of the capacited vehicle routing problem with static clients (i.e., same client locations) and changed demands. Given the edges of an original solution, the goal is to predict and fix the ones that have a high chance of remaining in an optimal solution after a change of client demands. This partial prediction of the solution reduces the complexity of the problem and speeds up its resolution, while yielding a good quality solution. The proposed approach resulted in solutions with an optimality gap ranging from 0% to 1.7% on different benchmark instances within a reasonable computing time.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"68 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138629190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotic bounds for clustering problems in random graphs","authors":"Eugene Lykhovyd, Sergiy Butenko, Pavlo Krokhmal","doi":"10.1002/net.22203","DOIUrl":"https://doi.org/10.1002/net.22203","url":null,"abstract":"Graph clustering is an important problem in network analysis. This problem can be approached by first finding a large cluster subgraph (i.e., a subgraph in which every connected component is a complete graph), perhaps in a relaxed form (connected components may have missing edges), and then assigning each of the remaining vertices to one of the connected components of the cluster subgraph according to some optimization criteria. The more vertices can be included in the initial cluster subgraph (also referred to as independent union of clusters), the more “clusterable” the graph is. This paper proposes a framework for establishing asymptotic bounds on the cardinality of independent unions of clusters in Erdős-Rényi random graphs <math altimg=\"urn:x-wiley:net:media:net22203:net22203-math-0001\" display=\"inline\" location=\"graphic/net22203-math-0001.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mi>G</mi>\u0000<mo stretchy=\"false\">(</mo>\u0000<mi>n</mi>\u0000<mo>,</mo>\u0000<mi>p</mi>\u0000<mo stretchy=\"false\">)</mo>\u0000</mrow>\u0000$$ Gleft(n,pright) $$</annotation>\u0000</semantics></math> with constant <math altimg=\"urn:x-wiley:net:media:net22203:net22203-math-0002\" display=\"inline\" location=\"graphic/net22203-math-0002.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mi>p</mi>\u0000</mrow>\u0000$$ p $$</annotation>\u0000</semantics></math>, referred to as uniform random graphs. In particular, sufficient conditions ensuring <math altimg=\"urn:x-wiley:net:media:net22203:net22203-math-0003\" display=\"inline\" location=\"graphic/net22203-math-0003.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mi>O</mi>\u0000<mo stretchy=\"false\">(</mo>\u0000<mi>log</mi>\u0000<mi>n</mi>\u0000<mo stretchy=\"false\">)</mo>\u0000</mrow>\u0000$$ Oleft(log nright) $$</annotation>\u0000</semantics></math> (where <math altimg=\"urn:x-wiley:net:media:net22203:net22203-math-0004\" display=\"inline\" location=\"graphic/net22203-math-0004.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mi>n</mi>\u0000</mrow>\u0000$$ n $$</annotation>\u0000</semantics></math> is the number of nodes) upper bounds with probability 1 are developed and shown to be applicable for the maximum independent union of cliques as well as some clique relaxations. In addition, it is shown that every graph must have an independent union of cliques of cardinality at least <math altimg=\"urn:x-wiley:net:media:net22203:net22203-math-0005\" display=\"inline\" location=\"graphic/net22203-math-0005.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mi mathvariant=\"normal\">Ω</mi>\u0000<mo stretchy=\"false\">(</mo>\u0000<mi>log</mi>\u0000<mi>n</mi>\u0000<mo stretchy=\"false\">)</mo>\u0000</mrow>\u0000$$ Omega left(log nright) $$</annotation>\u0000</semantics></math>. Since this bound is asymptotically tight on uniform random graphs, this suggests that these graphs can be viewed as a “least clusterable” class of graphs.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"286 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138629376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The complexity landscape of disaster-aware network extension problems","authors":"Balázs Vass, Beáta Éva Nagy, Balázs Brányi, János Tapolcai","doi":"10.1002/net.22199","DOIUrl":"https://doi.org/10.1002/net.22199","url":null,"abstract":"This article deals with the complexity of problems related to finding cost-efficient, disaster-aware cable routes. We overview various mathematical problems studied to augment a backbone network topology to make it more robust against regional failures. These problems either consider adding a single cable, multiple cables, or even nodes too. They adapt simplistic or more sophisticated regional failure models. Their objective is to identify the network's weak points or minimize the investment cost concerning the risk of a network outage. We investigate the tradeoffs in mathematical modeling for the same real-world scenario, where more sophisticated models face more computationally challenging problems. We have seen how efficiently computational geometry algorithms can be used to solve simplified problems even for sufficiently large networks. In this article, we aim to understand why different mathematical models formulated for the same real-world scenario can or cannot be solved efficiently. In particular, we show simplistic mathematical models that formulate NP-hard problems.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"82 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138629368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}