Linear Loss Function for the Network Blocking Game: An Efficient Model for Measuring Network Robustness and Link Criticality

In order to design robust networks, first, one has to be able to measure robustness of network topologies. In [1], a game-theoretic model, the network blocking game, was proposed for this purpose, where a network operator and an attacker interact in a zero-sum game played on a network topology, and the value of the equilibrium payoff in this game is interpreted as a measure of robustness of that topology. The payoff for a given pair of pure strategies is based on a loss-in-value function. Besides measuring the robustness of network topologies, the model can be also used to identify critical edges that are likely to be attacked. Unfortunately, previously proposed loss-in-value functions are either too simplistic or lead to a game whose equilibrium is not known to be computable in polynomial time. In this paper, we propose a new, linear loss-in-value function, which is meaningful and leads to a game whose equilibrium is efficiently computable. Furthermore, we show that the resulting game-theoretic robustness metric is related to the Cheeger constant of the topology graph, which is a well-known metric in graph theory.

[1]  Edward F. Schmeichel,et al.  Toughness in Graphs – A Survey , 2006, Graphs Comb..

[2]  F. Chung Laplacians and the Cheeger Inequality for Directed Graphs , 2005 .

[3]  A. L. O N On the edge-expansion of graphs , 2002 .

[4]  Matthias Hein,et al.  Spectral clustering based on the graph p-Laplacian , 2009, ICML '09.

[5]  Levente Buttyán,et al.  Game-theoretic Robustness of Many-to-one Networks , 2012, GAMENETS.

[6]  Bojan Mohar,et al.  Isoperimetric numbers of graphs , 1989, J. Comb. Theory, Ser. B.

[7]  Jean C. Walrand,et al.  How to Choose Communication Links in an Adversarial Environment? , 2011, GAMENETS.

[8]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[9]  William H. Cunningham,et al.  Optimal attack and reinforcement of a network , 1985, JACM.

[10]  B. Mohar Isoperimetric inequalities, growth, and the spectrum of graphs , 1988 .

[11]  Jean C. Walrand,et al.  Network design game with both reliability and security failures , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[12]  Jean C. Walrand,et al.  Design of Network Topology in an Adversarial Environment , 2010, GameSec.

[13]  Éva Tardos,et al.  A Strongly Polynomial Algorithm to Solve Combinatorial Linear Programs , 1986, Oper. Res..

[14]  Noga Alon,et al.  Spectral Techniques in Graph Algorithms , 1998, LATIN.

[15]  Levente Buttyán,et al.  Optimal selection of sink nodes in wireless sensor networks in adversarial environments , 2011, 2011 IEEE International Symposium on a World of Wireless, Mobile and Multimedia Networks.

[16]  John S. Baras,et al.  Decision and Game Theory for Security , 2010, Lecture Notes in Computer Science.

[17]  Jean C. Walrand,et al.  Towards a Metric for Communication Network Vulnerability to Attacks: A Game Theoretic Approach , 2012, GAMENETS.