article

Exact algorithms for solving a Euclidean maximum flow network interdiction problem

Authors:

Kelly M. Sullivan,

J. Cole SmithAuthors Info & Claims

Networks, Volume 64, Issue 2

Pages 109 - 124

https://doi.org/10.1002/net.21561

Published: 01 September 2014 Publication History

Abstract

We consider an interdiction problem that involves an operator or defender whose goal is to maximize flow from a source node to a sink node in some network that resides in Euclidean space. The problem we examine takes the perspective of an interdictor, who seeks to minimize the defender's maximum flow by locating a set of attacks that diminish arc capacities in accordance with the distance from the arc to the attack. Attacks are not restricted to node or arc locations, and can occur anywhere on the region in which the network is located. We refer to this problem as the Euclidean maximum flow network interdiction problem E-MFNIP. We show that E-MFNIP is NP-hard, as it generalizes the maximum flow interdiction problem studied by Wood . This article contributes two approaches to solving E-MFNIP based on solving a sequence of lower-bounding integer programs from which upper bounds can be readily obtained, and shows that these bounds are convergent. Computations on a set of test instances indicate that an approach based on space-discretization tends to converge much faster than one based on linearizing the nonlinear capacity functions. We demonstrate the application of our space-discretization approach on a real geographical network. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 642, 109-124 2014

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Cited By

Dahan MAmin SJaillet P(2022)Probability Distributions on Partially Ordered Sets and Network Interdiction GamesMathematics of Operations Research10.1287/moor.2021.114047:1(458-484)Online publication date: 1-Feb-2022
https://dl.acm.org/doi/10.1287/moor.2021.1140
Contardo CSefair J(2021)A Progressive Approximation Approach for the Exact Solution of Sparse Large-Scale Binary Interdiction GamesINFORMS Journal on Computing10.1287/ijoc.2021.108534:2(890-908)Online publication date: 18-Oct-2021
https://dl.acm.org/doi/10.1287/ijoc.2021.1085
Zhang PFan N(2017)Analysis of budget for interdiction on multicommodity network flowsJournal of Global Optimization10.1007/s10898-016-0422-867:3(495-525)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1007/s10898-016-0422-8
Show More Cited By

Index Terms

Exact algorithms for solving a Euclidean maximum flow network interdiction problem
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Network flows
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
      1. Network flows

Index terms have been assigned to the content through auto-classification.

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cover image Networks

Networks Volume 64, Issue 2

September 2014

75 pages

ISSN:0028-3045

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Wiley-Interscience

United States

Publication History

Published: 01 September 2014

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Cited By

Dahan MAmin SJaillet P(2022)Probability Distributions on Partially Ordered Sets and Network Interdiction GamesMathematics of Operations Research10.1287/moor.2021.114047:1(458-484)Online publication date: 1-Feb-2022
https://dl.acm.org/doi/10.1287/moor.2021.1140
Contardo CSefair J(2021)A Progressive Approximation Approach for the Exact Solution of Sparse Large-Scale Binary Interdiction GamesINFORMS Journal on Computing10.1287/ijoc.2021.108534:2(890-908)Online publication date: 18-Oct-2021
https://dl.acm.org/doi/10.1287/ijoc.2021.1085
Zhang PFan N(2017)Analysis of budget for interdiction on multicommodity network flowsJournal of Global Optimization10.1007/s10898-016-0422-867:3(495-525)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1007/s10898-016-0422-8
Afshari Rad MKakhki H(2017)Two extended formulations for cardinality maximum flow network interdiction problemNetworks10.1002/net.2173269:4(367-377)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.1002/net.21732

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