The vertex cover game: Application to transport networks

Gusev, Vasily V.

doi:10.1016/j.omega.2019.08.009

Cited by 19 publications

(14 citation statements)

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“…The number of swings and the Banzhaf-Coleman index are given in Table 1. Table 1 also provides the values of the Shapley-Shubik index for the game (N, v) from [19]. Arranging the players in the order of decreasing Banzhaf-Coleman and Shapley-Shubik indexes we get the vectors α 1 and α 2 , respectively, α 1 = (6,2,4,7,15,8,10,11,9,13,16,12,5,14,1,3), 6,4,2,7,15,8,10,11,9,13,16,12,5,14,1,3).…”

Section: Application To Transport Networkmentioning

confidence: 99%

Set-weighted games and their application to the cover problem

Gusev

2021

SSRN Journal

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The cover of a transport, social, or communication network is a computationally complex problem. To deal with it, this paper introduces a special class of simple games in which the set of minimal winning coalitions coincides with the set of least covers. A distinctive feature of such a game is that it has a weighted form, in which weights and quota are sets rather than real numbers. This game class is termed set-weighted games. A real-life network has a large number of least covers, therefore this paper develops methods for analyzing set-weighted games in which the weighted form is taken into account. The necessary and sufficient conditions for a simple game to be a set-weighted game were found. The vertex cover game (Gusev, 2020) was shown to belong to the set-weighted game class, and its weighted form was found. The set-weighted game class has proven to be closed under operations of union and intersection, which is not the case for weighted games. The sample object is the transport network of a district in Petrozavodsk, Russia. A method is suggested for efficiently deploying surveillance cameras at crossroads so that all transport network covers are taken into account.

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Section: Application To Transport Networkmentioning

confidence: 99%

Set-weighted games and their application to the cover problem

Gusev

2021

SSRN Journal

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“…Covering in Operations Research refers to the optimization problem of deciding the location of facilities to "cover" the points of the so-called demand set, which should fall within the radius coverage of at least one of the installed facilities. This classic problem finds applications in many different domains, including health care [1], surveillance of transport networks [2], computer networks security [3], crane location for construction [4], military evacuation systems [5], homeland defense [6], and urban air mobility [7].…”

Section: Introductionmentioning

confidence: 99%

“…The set P in Definition 1.1 can represent the locations of ambulance bases [1], surveillance cameras [2],…”

Section: Introductionmentioning

confidence: 99%

Continuous Covering on Networks: Improved Mixed Integer Programming Formulations

Xu¹

2022

Preprint

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Covering problems are well-studied in the domain of Operations Research, and, more specifically, in Location Science. When the location space is a network, the most frequent assumption is to consider the candidate facility locations, the points to be covered, or both, to be discrete sets. In this work, we study the set-covering location problem when both candidate locations and demand points are continuous sets on a network. This variant has received little attention, and the scarce existing approaches have focused on particular cases, such as tree networks and integer covering radius. Here we study the general problem and present a Mixed Integer Linear Programming formulation (MILP) for networks with edges' lengths no greater than the covering radius. The model does not lose generality, as any edge not satisfying this condition can be partitioned into subedges of appropriate lengths without changing the problem. We propose a preprocessing algorithm to reduce the size of the MILP, and devise tight big-M constants and valid inequalities to strengthen our formulations.Moreover, a second MILP is proposed, which admits edges' lengths greater than the covering radius. As opposed to existing formulations of the problem (including the first MILP proposed herein), the number of variables and constraints of this second model does not depend on the lengths of the network's edges. This second model represents a scalable approach that particularly suits real-world networks, whose edges are usually greater than the covering radius. Our computational experiments show the strengths and limitations of our exact approach on both real-world and random networks. Our formulations are also tested against an existing exact method.

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“…In the paper [12], the nucleolus was proposed, including an algorithm for its construction. The paper [13] was dedicated to the Shapley value: its properties were investigated and an algorithm for calculating this value was proposed.…”

Section: Introductionmentioning

confidence: 99%