Christos Kaklamanis

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.

Tight bounds for oblivious routing in the hypercube

We prove that in anyN-node communication network with maximum degreed, any deterministic oblivious algorithm for routing an arbitrary permutation requires Ω(√N/d) parallel communication steps in the worst case. This is an improvement upon the Ω(√N/d3/2) bound obtained by Borodin and Hopcroft. For theN-node hypercube, in particular, we show a matching upper bound by exhibiting a deterministic oblivious algorithm that routes any permutation in Θ(√N/logN) steps. The best previously known upper bound was Θ(√N). Our algorithm may be practical for smallN (up to about 214 nodes).

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.

Hot-potato routing on processor arrays

In this paper, we consider the problems of batch and permutation routing on d-dimensional (constant d ~ 2) torus-connected and two-dimensional mesh-connected processor arrays. We present new “hot-potato” routing algorithms which achieve the best known averagr+ case and worst-case time bounds for both problems on all such networks. In particular, our results include the following:

Communication in wireless networks with directional antennas

We study the problem of maintaining connectivity in a wireless network where the network nodes are equipped with directional antennas. Nodes correspond to points on the plane and each uses a directional antenna modeled by a sector with a given angle and radius. The connectivity problem is to decide whether or not it is possible to orient the antennas so that the directed graph induced by the node transmissions is strongly connected. We present algorithms for simple polynomial-time-solvable cases of the problem, show that the problem is NP-complete in the

Geometric clustering to minimize the sum of cluster sizes

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Branch-and-bound and backtrack search on mesh-connected arrays of processors

-dimensional case when the sector angle is small, and present algorithms that approximate the minimum radius to achieve connectivity for sectors with a given angle. We also discuss several extensions to related problems. To the best of our knowledge, the problem has not been studied before in the literature.

Energy-Efficient Wireless Network Design

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.

Constrained Bipartite Edge Coloring with Applications to Wavelength Routing

In this paper we investigate the parallel complexity of backtrack and branch-and-bound search on the mesh-connected array. We present an Ω(√dN/√logdN) lower bound for the time needed by arandomized algorithm to perform backtrack and branch-and-bound search of a tree of depthd on the √N × √N mesh, even when the depth of the tree is known in advance. The lower bound also holds for algorithms that are allowed to move tree-nodes and create multiple copies of the same tree-node.

New Results for Energy-Efficient Broadcasting in Wireless Networks

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.