Interdicting Structured Combinatorial Optimization Problems with {0, 1}-Objectives

Chestnut, Stephen R.; Zenklusen, Rico

doi:10.1287/moor.2016.0798

Cited by 13 publications

(7 citation statements)

References 42 publications

(99 reference statements)

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“…It would be very interesting to know whether there is any

α < 2

and polynomial time algorithm that returns an interdiction set

R

with cost at most

α B

and residual flow at most

α OPT

. The technique of Burch et al can be applied to get bicriteria approximation algorithms for many other interdiction problems , and one can hope that an improvement would also generalize.…”

Section: Resultsmentioning

confidence: 99%

Hardness and approximation for network flow interdiction

Chestnut

Zenklusen

2017

Networks

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In the Network Flow Interdiction problem, an adversary attacks a network in order to minimize the maximum s‐t‐flow. Very little is known about the approximatibility of this problem, despite decades of interest in it. It is, surprisingly, nontrivial to obtain in polynomial time an approximation guarantee that is independent of the number of edges in the graph and their capacities. We present the first such approximation algorithm, which has approximation ratio at most 2(n−1) for any graph with n vertices. We complement the algorithm with a hardness theorem. Past work has shown that Network Flow Interdiction cannot be much easier to approximate than Densest k‐Subgraph. We show that any nϵ‐approximation algorithm for Network Flow Interdiction, or one of several variants, would imply a 2n4ϵ‐approximation algorithm for Densest k‐Subgraph, which is an improvement over past work in terms of the polynomial factor. We also show that Network Flow Interdiction is essentially the same as the Budgeted Minimum s‐t‐Cut problem, and transferring our results gives hardness and an approximation algorithm for that problem, as well. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 69(4), 378–387 2017

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“…It would be very interesting to know whether there is any

α < 2

and polynomial time algorithm that returns an interdiction set

R

with cost at most

α B

and residual flow at most

α OPT

. The technique of Burch et al can be applied to get bicriteria approximation algorithms for many other interdiction problems , and one can hope that an improvement would also generalize.…”

Section: Resultsmentioning

confidence: 99%

Hardness and approximation for network flow interdiction

Chestnut

Zenklusen

2017

Networks

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“…E.1 A Simple Bicriteria Algorithm for WNVIP We first provide a polynomial time algorithm that finds a (1+1/ , 1) or (1, 1+ )approximation for any > 0 for WNVIP in digraphs using a more direct proof than the earlier methods [3,6]. This proof was also given by Chuzhoy et al [8] in their study of k-route cuts, but we reproduce it since we build on it later.…”

Section: E Simple Approximations For Interdiction Problemsmentioning

confidence: 99%

“…However, we do not know which case occurs a priori. In this line of work, Chestnut and Zenklusen [6] have extended the technique of Burch et al to derive pseudo-approximation algorithms for a larger class of NFI problems that have good LP descriptions (such as duals that are box-TDI).…”

Section: Related Workmentioning

confidence: 99%

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Downgrading to Minimize Connectivity

Aissi¹,

Chen²,

Ravi³

2019

Preprint

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We study the problem of interdicting a directed graph by deleting nodes with the goal of minimizing the local edge connectivity of the remaining graph from a given source to a sink. We show hardness of obtaining strictly unicriterion approximations for this basic vertex interdiction problem. We introduce and study a general downgrading variant of the interdiction problem where the capacity of an arc is a function of the subset of its endpoints that are downgraded, and the goal is to minimize the downgraded capacity of a minimum source-sink cut subject to a node downgrading budget. This models the case when both ends of an arc must be downgraded to remove it, for example. For this generalization, we provide a bicriteria (4, 4)-approximation that downgrades nodes with total weight at most 4 times the budget and provides a solution where the downgraded connectivity from the source to the sink is at most 4 times that in an optimal solution. WE accomplish this with an LP relaxation and round using a ball-growing algorithm based on the LP values. We further generalize the downgrading problem to one where each vertex can be downgraded to one of k levels, and the arc capacities are functions of the pairs of levels to which its ends are downgraded. We generalize our LP rounding to get (4k, 4k)-approximation for this case.

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“…Bar-Noy et al 1995;Boros et al 2006;Israeli and Wood 2002;Khachiyan et al 2008), but in the meantime, the list of combinatorial problems studied in the context of interdiction has grown rapidly (cf. Chestnut and Zenklusen 2016;Dinitz and Gupta 2013;Furini et al 2019;Zenklusen 2014Zenklusen , 2010. A recent survey by Smith and Song (2020) captures the research in this area.…”

Section: Introductionmentioning

confidence: 99%

Interdicting facilities in tree networks

Fröhlich

Ruzika

2021

TOP

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This article investigates a network interdiction problem on a tree network: given a subset of nodes chosen as facilities, an interdictor may dissect the network by removing a size-constrained set of edges, striving to worsen the established facilities best possible. Here, we consider a reachability objective function, which is closely related to the covering objective function: the interdictor aims to minimize the number of customers that are still connected to any facility after interdiction. For the covering objective on general graphs, this problem is known to be NP-complete (Fröhlich and Ruzika In: On the hardness of covering-interdiction problems. Theor. Comput. Sci., 2021). In contrast to this, we propose a polynomial-time solution algorithm to solve the problem on trees. The algorithm is based on dynamic programming and reveals the relation of this location-interdiction problem to knapsack-type problems. However, the input data for the dynamic program must be elaborately generated and relies on the theoretical results presented in this article. As a result, trees are the first known graph class that admits a polynomial-time algorithm for edge interdiction problems in the context of facility location planning.

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Interdicting Structured Combinatorial Optimization Problems with {0, 1}-Objectives

Cited by 13 publications

References 42 publications

Hardness and approximation for network flow interdiction

Hardness and approximation for network flow interdiction

Downgrading to Minimize Connectivity

Interdicting facilities in tree networks

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