An integer programming framework for critical elements detection in graphs

Veremyev, Alexander; Prokopyev, Oleg A.; Pasiliao, Eduardo L.

doi:10.1007/s10878-014-9730-4

Cited by 86 publications

(66 citation statements)

References 31 publications

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“…See, for instance, Shen et al (2012), Granata et al (2013), Veremyev, Boginski and Pasiliao (2014), Veremyev, Prokopyev and Pasiliao (2014), a survey in Walteros and Pardalos (2012) and the references given therein.…”

Section: Introductionmentioning

confidence: 99%

Sequential Shortest Path Interdiction with Incomplete Information

2016

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We study sequential interdiction when the interdictor has incomplete initial information about the network, and the evader has complete knowledge of the network, including its structure and arc costs. In each time period, the interdictor blocks at most k arcs from the network observed up to that period, after which the evader travels along a shortest path between two (fixed) nodes in the interdicted network. By observing the evader's actions, the interdictor learns about the network structure and arc costs, and adjusts its actions so as to maximize the cumulative cost incurred by the evader. A salient feature of our work is that the feedback in each period is deterministic and adversarial. In addition to studying the regret minimization problem, we also discuss time-stability of a policy, which is the number of time periods until the interdictor's actions match those of an oracle interdictor with prior knowledge of the network. We propose a class of simple interdiction policies that have a finite regret and detect when the instantaneous regret reaches zero in real time. More importantly, we establish that this class of policies belongs to the set of efficient policies.

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Section: Introductionmentioning

confidence: 99%

Sequential Shortest Path Interdiction with Incomplete Information

2016

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“…Two such classes of metrics are connectivity/cohesiveness-based [2,37,41] and distance-based [42]. The class of connectivity/cohesiveness-based metrics comprises objectives like maximizing the number of disconnected components (fragmentation) in the interdicted graph, minimizing the number of pairwise-connected nodes, or minimizing the size of the largest remaining component.…”

Section: Metrics and Exact Solutionsmentioning

confidence: 99%

“…Critical node detection problems (CNP) in networks are used to ascertain the strongest (weakest) nodes of a network according to various connectivity-based metrics [41] detailed later in this paper. A subset of nodes of cardinality k in a network is dubbed critical if its removal from the network brings about the maximum decrease in a given metric among all such subsets.…”

Section: Introductionmentioning

confidence: 99%

“…However, heuristics-centrality-based or otherwise-offer no guarantee of optimality. To ensure optimality, we turn to exact algorithms [3,41,42] and exploit integer programming methods to achieve a truly optimal solution given a suitable metric as an objective function. Other algorithms for CNP are explored in [2,18,36] for specific classes of networks (e.g.…”

Section: Introductionmentioning

confidence: 99%

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Robustness of solutions to critical node detection problems with imperfect data: a computational study

Gillen

Veremyev

Prokopyev

et al. 2016

Optimization Methods and Software

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A class of critical node detection problems based upon the metric of communication efficiency is considered. While both exact integer programming and heuristic centrality-based methods exist for the solution of these problems, previous work has been mostly focused on the case where perfect information about the network is available. In this paper we suppose that some level of misinformation about nodes or edges has been inflicted on the observer's perception of the network, that is, there are hidden elements or fake additional elements. An extensive computational study is conducted to ascertain whether the exact integer-programming-based solutions perform better under imperfect information than heuristic methods. For large networks, exact methods cannot produce a solution in a reasonable amount of time, hence an approximation of the exact method is also considered for such instances. The obtained approximate solutions are again compared to centrality-based heuristics under the presence of imperfect data.

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“…The minimum vertex/edge blocker and the most vital vertices/ edges problems have been studied in literature with respect to different graph properties, such as connectivity (Addis, Di Summa, & Grosso, 2013;Arulselvan, Commander, Elefteriadou, & Pardalos, 2009;Di Summa, Grosso, & Locatelli, 2011;Shen, Smith, & Goli, 2012;Veremyev, Prokopyev, & Pasiliao, 2014), shortest path (Bar-Noy et al, 1995;Israeli & Wood, 2002;Khachiyan et al 2008), maximum flow (Altner, Ergun, & Uhan, 2010;Ghare, Montgomery, & Turner, 1971;Wollmer, 1964;Wood, 1993), spanning tree (Bazgan, Toubaline, & Vanderpooten, 2012;2013;Frederickson & Solis-Oba, 1996), assignment (Bazgan, Toubaline, & Vanderpooten, 2010b), 1-median (Bazgan et al, 2010a), 1-center (Bazgan et al, 2010a), matching (Ries et al, 2010;Zenklusen, 2010;Zenklusen et al, 2009), independent sets (Bazgan et al, 2011), vertex covers (Bazgan et al, 2011), andcliques (Mahdavi Pajouh, Boginski, &.…”

Section: Previous Work and Our Contributionsmentioning

confidence: 99%