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

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Abstract

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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Acknowledgements

The authors are grateful for the comments of two anonymous referees, whose remarks led to an improved version of this paper. The authors also gratefully acknowledge the support of the “National Science Foundation under grants CMMI-1100765 and CAREER 0953284”, the Defense Threat Reduction Agency under grant HDTRA-10-01-0050, the Air Force Office of Scientific Research under grant FA9550-12-1-0353, and the Office of Naval Research under grant N000141310036.

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  1. University of Florida, Gainesville, FL, 32611, USA

    Mehdi Hemmati, J. Cole Smith & My T. Thai

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  1. Mehdi Hemmati
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  2. J. Cole Smith
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Correspondence to J. Cole Smith.

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Hemmati, M., Cole Smith, J. & Thai, M.T. A cutting-plane algorithm for solving a weighted influence interdiction problem. Comput Optim Appl 57, 71–104 (2014). https://doi.org/10.1007/s10589-013-9589-9

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