Panagiotis Kanellopoulos

Tight bounds for selfish and greedy load balancing

We study the load balancing problem in the context of a set of clients each wishing to run a job on a server selected among a subset of permissible servers for the particular client. We consider two different scenarios. In selfish load balancing, each client is selfish in the sense that it selects to run its job to the server among its permissible servers having the smallest latency given the assignments of the jobs of other clients to servers. In online load balancing, clients appear online and, when a client appears, it has to make an irrevocable decision and assign its job to one of its permissible servers. Here, we assume that the clients aim to optimize some global criterion but in an online fashion. A natural local optimization criterion that can be used by each client when making its decision is to assign its job to that server that gives the minimum increase of the global objective. This gives rise to greedy online solutions. The aim of this paper is to determine how much the quality of load balancing is affected by selfishness and greediness. We characterize almost completely the impact of selfishness and greediness in load balancing by presenting new and improved, tight or almost tight bounds on the price of anarchy and price of stability of selfish load balancing as well as on the competitiveness of the greedy algorithm for online load balancing when the objective is to minimize the total latency of all clients on servers with linear latency functions.

On the efficiency of equilibria in generalized second price auctions

In sponsored search auctions, advertisers compete for a number of available advertisement slots of different quality. The auctioneer decides the allocation of advertisers to slots using bids provided by them. Since the advertisers may act strategically and submit their bids in order to maximize their individual objectives, such an auction naturally defines a strategic game among the advertisers. In order to quantify the efficiency of outcomes in generalized second price auctions, we study the corresponding games and present new bounds on their price of anarchy, improving the recent results of Paes Leme and Tardos [16] and Lucier and Paes Leme [13]. For the full information setting, we prove a surprisingly low upper bound of 1.282 on the price of anarchy over pure Nash equilibria. Given the existing lower bounds, this bound denotes that the number of advertisers has almost no impact on the price of anarchy. The proof exploits the equilibrium conditions developed in [16] and follows by a detailed reasoning about the structure of equilibria and a novel relation of the price of anarchy to the objective value of a compact mathematical program. For more general equilibrium classes (i.e., mixed Nash, correlated, and coarse correlated equilibria), we present an upper bound of 2.310 on the price of anarchy. We also consider the setting where advertisers have incomplete information about their competitors and prove a price of anarchy upper bound of 3.037 over Bayes-Nash equilibria. In order to obtain the last two bounds, we adapt techniques of Lucier and Paes Leme [13] and significantly extend them with new arguments.

Geometric clustering to minimize the sum of cluster sizes

We study geometric versions of the min-size k-clustering problem, a clustering problem which generalizes clustering to minimize the sum of cluster radii and has important applications. We prove that the problem can be solved in polynomial time when the points to be clustered are located on a line. For Euclidean spaces of higher dimensions, we show that the problem is NP-hard and present polynomial time approximation schemes. The latter result yields an improved approximation algorithm for the related problem of k-clustering to minimize the sum of cluster diameters.

Energy-Efficient Wireless Network Design

AbstractA crucial issue in wireless networks is to support efficiently communication patterns that are typical in traditional (wired) networks. These include broadcasting, multicasting, and gossiping (all-to-all communication). In this work we study such problems in static ad hoc networks. Since, in ad hoc networks, energy is a scarce resource, the important engineering question to be solved is to guarantee a desired communication pattern minimizing the total energy consumption. Motivated by this question, we study a series of wireless network design problems and present new approximation algorithms and inapproximability results.

New Results for Energy-Efficient Broadcasting in Wireless Networks

Motivated by the problem of supporting energy-efficient broadcasting in ad hoc wireless networks, we study the Minimum Energy Consumption Broadcast Subgraph (MECBS) problem. We present the first logarithmic approximation algorithm for the problem which uses an interesting reduction to Node-Weighted Connected Dominating Set. We also show that an important special instance of the problem can be solved in polynomial time, solving an open problem of Clementi et al. [2].

Tight Bounds for Selfish and Greedy Load Balancing

We study the load balancing problem in the context of a set of clients each wishing to run a job on a server selected among a subset of permissible servers for the particular client. We consider two different scenarios. In selfish load balancing, each client is selfish in the sense that it chooses, among its permissible servers, to run its job on the server having the smallest latency given the assignments of the jobs of other clients to servers. In online load balancing, clients appear online and, when a client appears, it has to make an irrevocable decision and assign its job to one of its permissible servers. Here, we assume that the clients aim to optimize some global criterion but in an online fashion. A natural local optimization criterion that can be used by each client when making its decision is to assign its job to that server that gives the minimum increase of the global objective. This gives rise to greedy online solutions. The aim of this paper is to determine how much the quality of load balancing is affected by selfishness and greediness.We characterize almost completely the impact of selfishness and greediness in load balancing by presenting new and improved, tight or almost tight bounds on the price of anarchy of selfish load balancing as well as on the competitiveness of the greedy algorithm for online load balancing when the objective is to minimize the total latency of all clients on servers with linear latency functions. In addition, we prove a tight upper bound on the price of stability of linear congestion games.

New bounds on the size of the minimum feedback vertex set in meshes and butterflies

Given a graph G = (V;E), the minimum feedback vertex set S is a subset of vertices of minimum size, whose removal induces an acyclic subgraph G0 = (VnS;E 0). The problem of finding S is NP–complete in general graphs, although polynomial time solutions exist for particular classes of graphs. this paper we present upper and lower bounds on the size of the minimum feedback vertex set in meshes and butterflies improving results of Luccio [10].

On verifying game designs and playing strategies using reinforcement learning

In this paper we elaborate on the application of reinforcement learning to the design of a new strategy game. We deal with playability and learning issues, attempting to use intelligently generated self-playing sequences to determine playability of various initial board configurations. The machines a priori knowledge about the game is restricted to the rules only, so, the initially encouraging and intuitive results suggest that this design verification strategy may be useful to a board range of design problems.

Taxes for linear atomic congestion games

We study congestion games where players aim to access a set of resources. Each player has a set of possible strategies and each resource has a function associating the latency it incurs to the players using it. Players are non--cooperative and each wishes to follow a strategy that minimizes her own latency with no regard to the global optimum. Previous work has studied the impact of this selfish behavior on system performance. In this article, we study the question of how much the performance can be improved if players are forced to pay taxes for using resources. Our objective is to extend the original game so that selfish behavior does not deteriorate performance. We consider atomic congestion games with linear latency functions and present both negative and positive results. Our negative results show that optimal system performance cannot be achieved even in very simple games. On the positive side, we show that there are ways to assign taxes that can improve the performance of linear congestion games by forcing players to follow strategies where the total latency suffered is within a factor of 2 of the minimum possible; this result is shown to be tight. Furthermore, even in cases where in the absence of taxes the system behavior may be very poor, we show that the total disutility of players (latency plus taxes) is not much larger than the optimal total latency. Besides existential results, we show how to compute taxes in time polynomial in the size of the game by solving convex quadratic programs. Similar questions have been extensively studied in the model of non-atomic congestion games. To the best of our knowledge, this is the first study of the efficiency of taxes in atomic congestion games.

Bounding the inefficiency of outcomes in generalized second price auctions

The Generalized Second Price (GSP) auction is the primary auction used for monetizing the use of the Internet. It is well-known that truthtelling is not a dominant strategy in this auction and that inefficient equilibria can arise. Edelman et al. (2007) [11] and Varian (2007) [36] show that an efficient equilibrium always exists in the full information setting. Their results, however, do not extend to the case with uncertainty, where efficient equilibria might not exist.