Dávid Szeszlér

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.

Game-theoretic Robustness of Many-to-one Networks

In this paper, we study the robustness of networks that are characterized by many-to-one communications (e.g., access networks and sensor networks) in a game-theoretic model. More specifically, we model the interactions between a network operator and an adversary as a two player zero-sum game, where the network operator chooses a spanning tree in the network, the adversary chooses an edge to be removed from the network, and the adversary’s payoff is proportional to the number of nodes that can no longer reach a designated node through the spanning tree. We show that the payoff in every Nash equilibrium of the game is equal to the reciprocal of the persistence of the network. We describe optimal adversarial and operator strategies and give efficient, polynomial-time algorithms to compute optimal strategies. We also generalize our game model to include varying node weights, as well as attacks against nodes.

Designing robust network topologies for wireless sensor networks in adversarial environments

Abstract In this paper, we address the problem of deploying sink nodes in a wireless sensor network such that the resulting network topology be robust. In order to measure network robustness, we propose a new metric, called persistence, which better captures the notion of robustness than the widely known connectivity based metrics. We study two variants of the sink deployment problem: sink selection and sink placement. We prove that both problems are NP-hard, and show how the problem of sink placement can be traced back to the problem of sink selection using an optimal search space reduction technique, which may be of independent interest. To solve the problem of sink selection, we propose efficient heuristic algorithms. Finally, we provide experimental results on the performance of our proposed algorithms.

Optimal selection of sink nodes in wireless sensor networks in adversarial environments

In this paper, we address the problem of assigning the sink role to a subset of nodes in a wireless sensor network with a given topology such that the resulting network configuration is robust against denial-of-service type attacks such as node destruction, battery exhaustion and jamming. In order to measure robustness, we introduce new metrics based on a notion defined in [1]. We argue that our metrics are more appropriate to measure the robustness of network configurations than the widely known connectivity based metrics. We formalize the problem of selecting the sink nodes as an optimization problem aiming at minimizing the deployment budget while achieving a certain level of robustness.We propose an efficient greedy heuristic algorithm that approximates the optimal solution reasonably well.

3-Dimensional Single Active Layer Routing

Suppose that the terminals to be interconnected are situated in a rectangular area of length n and width w and the routing should be realized in a box of size w?×n?×h over this rectangle (single active layer routing) where w? = cw and n ? n? ? n + 1. We prove that it is always possible with height h = O(n) and in time t = O(n) for a fixed w and both estimates are best possible (as far as the order of magnitude of n is concerned). The more theoretical case when the terminals are situated in two opposite parallel planes of the box (the 3-dimensional analogue of channel routing) is also studied.

On a generalization of Chvátal's condition giving new hamiltonian degree sequences

By imposing a structural criterion on a graph, we generalize the well-known Chvatals sufficient condition for hamiltonicity (J. Combin. Theory Ser. B 12 (1972) 163-168). Using this result, we describe a new class of hamiltonian degree sequences which contains the sequences given by Chvatals condition, as well as a class of degree sequences described by Fan and Liu (J. Systems Sci. Math. Sci. 4 (1) (1984) 27-32).

Security games on matroids

Two players, the Defender and the Attacker play the following game. A matroid

The Evolution of an Idea — Gallai’s Algorithm

M=(S,\mathcal {I})