Abstract—We investigate the large scale of networks in the context of network survivability under attack. We use appropriate techniques to evaluate and the attacker-based- and the defender- based-network survivability. The attacker is unaware of the operated links by the defender. Each attacked link has some pre-specified probability to be disconnected. The defender choice is so that to maximize the chance of successfully sending the flow to the destination node. The attacker however will select the cut-set with the highest chance to be disabled in order to partition the network. Moreover, we extend the problem to the case of selecting the best p paths to operate by the defender and the best k cut-sets to target by the attacker, for arbitrary integers p,k>1. We investigate some variations of the problem and suggest polynomial-time solutions. Keywords—Defense/attack strategies, large scale, networks, partitioning a network. I. INTRODUCTION N this paper, we treat the case of attacks on large networks. We will provide optimal policies both for the attacker and defender of the network in a game-theoretic spirit. Networks are considered as good targets for intelligent threats including terrorism, wars, and rebellions. Many of the oil pipeline networks have been attacked in various places in the world such as Iraq, Saudi Arabia, and Libya in the last few years. Road networks as well as computer systems have been also attacked. Consequently, it is important to develop defense tools to protect our homeland infrastructure. One should not however under-estimate the skills and the destruction capacities of potential attackers. Therefore, defensive strategies should be devised in anticipation of intelligent attacks suggesting the determination of optimal attack strategies. II. LITERATURE REVIEW Some important literature in defense/attack strategies has been developed in the last decade. Interested readers may refer to [1] and [2]. Two nice papers on attacks on telecommunication and transportation networks are given respectively in [3] and [4]. Reference [5] discusses least-cost attack strategies on networks and provides a variety of operations research techniques to assess the network least-cost cut sets in a branch and bound fashion. A. Ben Yaghlane, M. N. Azaiez are with the Université de Tunis, Institut Supérieur de Gestion, Tunis Business School, Tunis, Tunisia (e-mail: asma_benyaghlane@yahoo.fr, naceur.azaiez@tbs.rnu.tn). M. Mrad is with the King Saud University, Department of Industrial Engineering, College of engineering, Riadh, Saudi Arabia (e-mail: mradmehdiisg@yahoo.fr). Reference [6] defines network survivability both for the case of perfect information, in which the attacker may observe the operated paths and hence attack those of interest, and absence of information where the attacker would select the links to target independently of the defender strategy of operating the network. In the latter case, they distinguish two types of network survivability; namely the defender-based- and the attacker-based- network survivability. They provide tools for assessing network survivability and compare the defender-based-network survivability against the attacker- based-network survivability as well as against network reliability. All the assessments are made for relatively small networks. For this paper to be self-contained, we will display in Section III the main developments by [6]. In this paper, we extend [6] to the large scale and suggest some interesting generalizations. III. BACKGROUND We will start by discussing the case of perfect information in which both types of network survivability coincide. Then, we will display the main findings for the case of absence of information. We assume that the defender of the network is interested in sending some flow (in sufficient capacity) from a source node to a destination node. The attacker’s objective is to prevent the flow from reaching the destination; in which case the attack succeeds. Else, the attack is considered as failing. We assume that the attacker may target any link of the network. Each attacked link has a pre-defined survival probability. A link can be attacked only once. Attacks are made sequentially. The attacker is interested in determining the set of links to target in order to disable the network. The attack resources are limited so that the attacker would only consider a limited number of links in a specific order. In the case of perfect information, the network survivability is defined to be the highest probability of a breakthrough path to survive an attack. The case of absence of information is assumed to be the case where the attacker need not know the breakthrough path that has been effectively used by the defender. The attacker would opt for a conservative approach by disabling an entire cut set to make sure that the flow cannot reach its destination no matter what breakthrough path is used. The corresponding network probability to survive is referred to as the attacker- based-network survivability. In contrast, the defender-based- network survivability coincides with the one given in the case of perfect information. Determining the attacker-based-network survivability suggests solving a min-cut problem (by duality) which can A. Ben Yaghlane, M. N. Azaiez, M. Mrad System Survivability in Networks in the Context of Defense/Attack Strategies: The Large Scale I World Academy of Science, Engineering and Technology International Journal of Computer and Information Engineering Vol:9, No:12, 2015 2521 International Scholarly and Scientific Research & Innovation 9(12) 2015 scholar.waset.org/1307-6892/10003274 International Science Index, Computer and Information Engineering Vol:9, No:12, 2015 waset.org/Publication/10003274