No abstract

We consider a multicast game with selfish non-cooperative players. There is a special source node and each player is interested in connecting to the source by making a routing decision that minimizes its payment. The mutual influence of the players is determined by a cost sharing mechanism, which in our case evenly splits the cost of an edge among the players using it. We consider two different models: an integral model, where each player connects to the source by choosing a single path, and a fractional model, where a player is allowed to split the flow it receives from the source between several paths. In both models we explore the overhead incurred in network cost due to the selfish behavior of the users, as well as the computational complexity of finding a Nash equilibrium. The existence of a Nash equilibrium for the integral model was previously established by the means of a potential function. We prove that finding a Nash equilibrium that minimizes the potential function is NP-hard. We focus on the price of anarchy of a Nash equilibrium resulting from the best-response dynamics of a game course, where the players join the game sequentially. For a game with n players, we establish an upper bound of O(√ n log 2 n) on the price of anarchy, and a lower bound of Ω(log n/ log log n). For the fractional model, we prove the existence of a Nash equilibrium via a potential function and give a polynomial time algorithm for computing an equilibrium that minimizes the potential function. Finally, we consider a weighted extension of the multicast game, and prove that in the fractional model, the game always has a Nash equilibrium. Index Terms Multicast game, Nash equilibrium, Price of anarchy, Price of stability.. 2 I. INTRODUCTION In many networking scenarios, including the Internet, network users are free to act according to their individual interests, without taking into account overall network performance. Users thus may make selfish decisions (strategy choices) based on the state of the network, which depends (among other factors) on the behavior of other users, resulting in a non-cooperative game. Naturally, these scenarios call for a game-theoretic approach for studying both the behavior of such non-cooperative users, as well as their impact on the network performance. More specifically, we are interested in the properties of Nash equilibrium solutions which are the stable outcomes of a non-cooperative game. We note that there is a considerable amount of research dealing with non-cooperative games in networks [16], [19], [26], [29], [30], [32]. A scenario frequently encountered is the situation where each edge has a load-dependent latency function, and each user aims to minimize the total latency from its source to its destination. In this framework, both simple and general network topologies were studied, as well as various types of latency functions and different constraints on the strategies of the users [16], [26], [29], [30], [32]. While unicast is the traditional form of routing, it results in a waste of re...

Software Defined Networks (SDNs) are becoming the leading technology behind many traffic engineering solutions, both for backbone and data-center networks, since it allows a central controller to globally plan the path of the flows according to the operator's objective. Nevertheless, networking devices' forwarding table is a limited and expensive resource (e.g., TCAM-based switches) which should thus be considered upon configuring the network. In this paper, we concentrate on satisfying global network objectives, such as maximum flow, in environments where the size of the forwarding table in network devices is limited. We formulate this problem as an (NP-hard) optimization problem and present approximation algorithms for it. We show through extensive simulations that practical use of our algorithms (both in Data Center and backbone scenarios) result in a significant reduction (factor 3) in forwarding table size, while having a small effect on the global objective (maximum flow).

Clustering, the partitioning of objects with respect to a similarity measure, has been extensively studied as a global optimization problem. We investigate clustering from a game-theoretic approach, and consider the class of hedonic clustering games. Here, a self-organized clustering is obtained via decisions made by independent players, corresponding to the elements clustered. Being a hedonic setting, the utility of each player is determined by the identity of the other members of her cluster. This class of games seems to be quite robust, as it fits with rather different, yet commonly used, clustering criteria. Specifically, we investigate hedonic clustering games in two different models: fixed clustering, which subdivides into k-median and k-center, and correlation clustering. We provide a thorough analysis of these games, characterizing Nash equilibria, and proving upper and lower bounds on the price of anarchy and price of stability. For fixed clustering we focus on the existence of a Nash equilibrium, as it is a rather nontrivial issue in this setting. We study it both for general metrics and special cases, such as line and tree metrics. In the correlation clustering model, we study both minimization and maximization variants, and provide almost tight bounds on both the price of anarchy and price of stability.

The provisioning of quality-of-service for real-time network applications may require the network to reserve resources. A natural way to do this is to allow advance reservations of network resources prior to the time they are needed. We consider several two-dimensional admission control problems in simple topologies such as a line and a tree. The input is a set of connection requests, each specifying its spatial characteristics, that is, its source and destination; its temporal characteristics, that is, its start time and duration time; and, potentially, also a bandwidth requirement. In addition, each request is associated with a profit gained by accommodating it. We address the related admission control problem, where the goal is to maximize the total profit gained by the accommodated requests. We provide approximation algorithms for several problem variations. Our results imply a 4c-approximation algorithm for finding a maximum weight independent set of axis-parallel rectangles in the plane, where c is the size of a maximum set of overlapping rectangles.