### Abstract

We study a dynamic network game between an attacker and a user. The user wishes to find a shortest path between a pair of nodes in a directed network, and the attacker seeks to interdict a subset of arcs to maximize the user's shortest-path cost. In contrast to most previous studies, the attacker can interdict arcs any time the user reaches a node in the network, and the user can respond by dynamically altering its chosen path. We assume that the attacker can interdict a limited number of arcs, and that an interdicted arc can still be traversed by the user at an increased cost. The challenge is therefore to find an optimal path (possibly repeating arcs in the network), coupled with the attacker's optimal interdiction strategy (i.e., which arcs to interdict and when to interdict them). We propose an exact exponential-state dynamic-programming algorithm for this problem, which can be reduced to a polynomial-time algorithm in the case of acyclic networks. We also develop lower and upper bounds on the optimal objective function value based on classical interdiction and robust optimization models, or based on an exact solution to variations of this problem. We examine the efficiency of our algorithms and the quality of our bounds on a set of randomly generated instances.

Original language | English (US) |
---|---|

Pages (from-to) | 315-330 |

Number of pages | 16 |

Journal | Networks |

Volume | 68 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2016 |

### Fingerprint

### Keywords

- bounds
- dynamic programming
- network interdiction
- NP-hardness
- relaxations
- robust optimization
- shortest path

### ASJC Scopus subject areas

- Information Systems
- Computer Networks and Communications

### Cite this

*Networks*,

*68*(4), 315-330. https://doi.org/10.1002/net.21712

**Dynamic shortest-path interdiction.** / Sefair, Jorge; Smith, J. Cole.

Research output: Contribution to journal › Article

*Networks*, vol. 68, no. 4, pp. 315-330. https://doi.org/10.1002/net.21712

}

TY - JOUR

T1 - Dynamic shortest-path interdiction

AU - Sefair, Jorge

AU - Smith, J. Cole

PY - 2016/12/1

Y1 - 2016/12/1

N2 - We study a dynamic network game between an attacker and a user. The user wishes to find a shortest path between a pair of nodes in a directed network, and the attacker seeks to interdict a subset of arcs to maximize the user's shortest-path cost. In contrast to most previous studies, the attacker can interdict arcs any time the user reaches a node in the network, and the user can respond by dynamically altering its chosen path. We assume that the attacker can interdict a limited number of arcs, and that an interdicted arc can still be traversed by the user at an increased cost. The challenge is therefore to find an optimal path (possibly repeating arcs in the network), coupled with the attacker's optimal interdiction strategy (i.e., which arcs to interdict and when to interdict them). We propose an exact exponential-state dynamic-programming algorithm for this problem, which can be reduced to a polynomial-time algorithm in the case of acyclic networks. We also develop lower and upper bounds on the optimal objective function value based on classical interdiction and robust optimization models, or based on an exact solution to variations of this problem. We examine the efficiency of our algorithms and the quality of our bounds on a set of randomly generated instances.

AB - We study a dynamic network game between an attacker and a user. The user wishes to find a shortest path between a pair of nodes in a directed network, and the attacker seeks to interdict a subset of arcs to maximize the user's shortest-path cost. In contrast to most previous studies, the attacker can interdict arcs any time the user reaches a node in the network, and the user can respond by dynamically altering its chosen path. We assume that the attacker can interdict a limited number of arcs, and that an interdicted arc can still be traversed by the user at an increased cost. The challenge is therefore to find an optimal path (possibly repeating arcs in the network), coupled with the attacker's optimal interdiction strategy (i.e., which arcs to interdict and when to interdict them). We propose an exact exponential-state dynamic-programming algorithm for this problem, which can be reduced to a polynomial-time algorithm in the case of acyclic networks. We also develop lower and upper bounds on the optimal objective function value based on classical interdiction and robust optimization models, or based on an exact solution to variations of this problem. We examine the efficiency of our algorithms and the quality of our bounds on a set of randomly generated instances.

KW - bounds

KW - dynamic programming

KW - network interdiction

KW - NP-hardness

KW - relaxations

KW - robust optimization

KW - shortest path

UR - http://www.scopus.com/inward/record.url?scp=84991709159&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84991709159&partnerID=8YFLogxK

U2 - 10.1002/net.21712

DO - 10.1002/net.21712

M3 - Article

AN - SCOPUS:84991709159

VL - 68

SP - 315

EP - 330

JO - Networks

JF - Networks

SN - 0028-3045

IS - 4

ER -