Distributed Approximation Algorithms via LP-Duality and Randomization
نویسندگان
چکیده
The spread of computer networks, from sensor networks to the Internet, creates an ever growing need for efficient distributed algorithms. In such scenarios, familiar combinatorial structures such as spanning trees and dominating sets are often useful for a variety of tasks. Others, like maximal independent sets, turn out to be a very useful primitive for computing other structures. In a distributed setting, where transmission of messages can be orders of magnitude slower than local computation, the expensive resource is communication. Therefore the running time of an algorithm is given by the number of communication rounds that are needed by the algorithm. This will be made precise below. In what follows we will survey a few problems and their solutions in a distributed setting: Dominating sets; edge and vertex colorings; matchings; vertex covers, and minimum spanning trees. These problems were chosen for a variety of reasons: They are fundamental combinatorial structures; computing them is useful in distributed settings; and they serve to illustrate some interesting techniques and methods. Randomization, whose virtues are well-known to people coping with parallel and distributed algorithms, will be a recurrent theme. In fact, only rarely it has been possible to develop deterministic distributed algorithms for non-trivial
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