Distributed approximation: a survey

Distributed Approximation - A Survey1 Michael Elkin Abstract Recently considerable progress was achieved in designing e cient distributed approximation algorithms, and in demonstrating hardness of distributed approximation for various problems. In this survey we overview the research in this area and propose several directions for future research. Introduction The area of distributed approximation is a new rapidly developing discipline that lies on the boundary between two well-established areas, speci cally distributed computing and approximability. 1.1 Distributed Computing Distributed computing is a very broad area that encompasses a plethora of disciplines. The particular subarea of distributed computing that is relevant to this survey focuses on the so-called messagepassing model of computation [5, 13, 23]. In this model we are given a network of processors modeled by an unweighted undirected N -vertex graph G = (V, E). The processors reside in the vertices of the graph, and the edges of E model the links of the network. The processors (henceforth, vertices) have in nite computational power, but their initial knowledge is limited to their immediate neighborhood. The network is to solve (cooperatively) some global problem, whose resolution requires communication between the vertices. The vertices are allowed to communicate via the links of the network (henceforth, edges). The communication is synchronous, that is, it occurs in discrete rounds. On each round at most B bits can be sent through each edge in each direction, where B is the bandwidth parameter of the network. A particularly interesting case emerges when B is equal to in nity [24]. The most commonly used measure of e ciency of distributed algorithms is the (worst-case) number of rounds of communication. (Note that that the local computation is completely free under this measure.) This e ciency measure naturally gives rise to the time complexity measure of problems. The message-passing...

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