Domination Problems

Shen, Siqian

doi:10.1002/9780470400531.eorms0266

Cited by 1 publication

(1 citation statement)

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“…The attacker's problem that we consider in this paper is related to the classical dominating set problem [17]. In the dominating set problem, a minimum-cardinality subset of nodes D is sought in an undirected graph G = (V , E) such that every node in V \D is adjacent to at least one of the nodes in D [9].…”

Section: Literature Reviewmentioning

confidence: 99%

A cutting-plane algorithm for solving a weighted influence interdiction problem

2013

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We consider a two-stage defender-attacker game that takes place on a network, in which the attacker seeks to take control over (or "influence") as many nodes as possible. The defender acts first in this game by protecting a subset of nodes that cannot be influenced by the attacker. With full knowledge of the defender's action, the attacker can then influence an initial subset of unprotected nodes. The influence then spreads over a finite number of time stages, where an uninfluenced node becomes influenced at time t if a threshold number of its neighbors are influenced at time t − 1. The attacker's objective is to maximize the weighted number of nodes that are influenced over the time horizon, where the weights depend both on the node and on the time at which that is influenced. This defender-attacker game is especially difficult to optimize, because the attacker's problem itself is NP-hard, which precludes a standard inner-dualization approach that is common in many interdiction studies. We provide three models for solving the attacker's problem, and develop a tailored cutting-plane algorithm for solving the defender's problem. We then demonstrate the computational efficacy of our proposed algorithms on a set of randomly generated instances.

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Section: Literature Reviewmentioning

confidence: 99%