We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles or paths satisfying certain requirements. In particular, many basic combinatorial optimization problems fit in this framework, including the shortest path, minimum-cost spanning tree, minimum-weight perfect matching, traveling salesman and Steiner tree problems. Our techniqueproduces approximation algorithms that run in O(n² log n) time and come within a factor of 2 of optimal for most of these problems. For instance, we obtain a 2-approximationalgorithm for the minimum-weight perfect matching problem under the triangle inequality. Our running time of O(n² log n) time compares favorably with the best strongly polynomial exact algorithms running in O(n³) time for dense graphs. A similar result is obtained for the 2-matchingproblem and its variants. We also derive the first approxi...

Task execution in multi-agent environments may require cooperation among agents. Given a set of agents and a set of tasks which they have to satisfy, we consider situations where each task should be attached to a group of agents that will perform the task. Task allocation to groups of agents is necessary when tasks cannot be performed by a single agent. However it may also be beneficial when groups perform more efficiently with respect to the single agents' performance. In this paper we present several solutions to the problem of task allocation among autonomous agents, and suggest that the agents form coalitions in order to perform tasks or improve the efficiency of their performance. We present efficient distributed algorithms with low ratio bounds and with low computational complexities. These properties are proven theoretically and supported by simulations and an implementation in an agent system. Our methods are based on both the algorithmic aspects of combinatorics and approximat...

We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyper-strips (resp. hyper-cylinders) so that the maximum width of a hyper-strip (resp., the maximum diameter of a hyper-cylinder) is minimized. Let w be the smallest value so that S can be covered by k hyper-strips (resp. hyper-cylinders), each of width (resp. diameter) at most w : In the plane, the two problems are equivalent. It is NP-Hard to compute k planar strips of width even at most Cw ; for any constant C ? 0 [50]. This paper contains four main results related to projective clustering: (i) For d = 2, we present a randomized algorithm that computes O(k log k) strips of width at most 6w that cover S. Its expected running time is O(nk 2 log 4 n) if k 2 log k n; it also works for larger values of k, but then the expected running time is O(n 2=3 k 8=3 log 4 n). We also propose another algorithm that computes a c...

Connected dominating set (CDS) has been proposed as virtual backbone or spine of wireless ad hoc networks. Three distributed approximation algorithms have been proposed in the literature for minimum CDS.

Abstract not found

In this paper we discuss the mechanism of multipoint relays (MPRs) to efficiently do the flooding of broadcast messages in the mobile wireless networks. Multipoint relaying is a technique to reduce the number of redundant re-transmissions while diffusing a broadcast message in the network. We discuss the principle and the functioning of MPRs, and propose a heuristic to select these MPRs in a mobile wireless environment. We also analyze the complexity of this heuristic and prove that the computation of a multipoint relay set with minimal size is NP-complete. Finally, we present some simulation results to show the efficiency of multipoint relays.

Contents 1 Introduction 2 1.1 Notations and Definitions . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Problem Formulations 4 2.1 Integer Programming Formulations . . . . . . . . . . . . . . . . . . . 5 2.2 Continuous Formulations . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Computational Complexity 12 4 Bounds and Estimates 15 5 Exact Algorithms 19 5.1 Enumerative Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.2 Exact Algorithms for the Unweighted Case . . . . . . . . . . . . . . 21 5.3 Exact Algorithms for the Weighted Case . . . . . . . . . . . . . . . . 25 6 Heuristics 27 6.1 Sequential Greedy Heuristics . . . . . . . . . . . . . . . . . . . . . . 28 6.2 Local Search Heuristics . . . . . . . . . . . . . . . . . . . . . . . . . 29 6.3 Advanced Search Heuristics . . . . . . . . . . . . . . . . . . . . . . . 30 6.3.1 Simulated annealing . . . . . . . . . . . . . . . . . . . . . . . 30 6.3.2 Neural networks . . . . . . . . . . . . . . . . . . . . . . . .

The primal-dual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primal-dual method can be modified to provide good approximation algorithms for a wide variety of NP-hard problems. We concentrate on results from recent research applying the primal-dual method to problems in network design.

Automated intelligent agents inhabiting a shared environmentmust coordinate their activities. Cooperation { not merely coordination { may improve the performance of the individual agents or the overall behavior of the system they form. Research in Distributed Arti cial Intelligence (DAI) addresses the problem of designing automated intelligent systems which interact e ectively. DAI is not the only eld to take on the challenge of understanding cooperation and coordination. There are a variety of other multi-entity environments in which the entities coordinate their activity and cooperate. Among them are groups of people, animals, particles, and computers. We argue that in order to address the challenge of building coordinated and collaborated intelligent agents, it is bene cial to combine AI techniques with methods and techniques from a range of multi-entity elds, such as game theory, operations research, physics and philosophy. To support this claim, we describe some of our projects, where we have successfully taken an interdisciplinary approach. We demonstrate the bene ts in applying multi-entity methodologies and show the adaptations, modi cations and extensions necessary for solving the DAI problems.

Abstract | Energy conservation is a critical issue in ad hoc wireless networks for node and network life, as the nodes are powered by batteries only. One major approach for energy conservation is to route a communication session along the routes which requires the lowest total energy consumption. This optimization problem is referred to as minimum-energy routing. While minimum-energy unicast routing can be solved in polynomial time by shortest-path algorithms, it remains open whether minimum-energy broadcast routing can be solved in polynomial time, despite of the NP-hardness of its general graph version. Recently three greedy heuristics were proposed in [8]: MST (minimum spanning tree), SPT (shortest-path tree), and BIP (broadcasting incremental power). They have been evaluated through simulations in [8], but little is known about their analytical performance. The main contribution of this paper is the quantitative characterization of their performances in terms of approximation ratios. By exploring geometric structures of Euclidean MSTs, we havebeen able to prove that the approximation ratio of MST is between 6 and 12, and the approximation ratio of BIP is between 13 and 12. On the 3 other hand, the approximation ratio of SPT is shown to be at least n,wherenis the number of receiving nodes. To 2 our best knowledge, these are the rst analytical results for minimum-energy broadcasting. I.