@MISC{Linialt_localityin, author = {Nathan Linialt}, title = {LOCALITY IN DISTRIBUTED GRAPH ALGORITHMS*}, year = {} }

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Abstract

Abstract. This paper concerns a number of algorithmic problems on graphs and how they may be solved in a distributed fashion. The computational model is such that each node of the graph is occupied by a processor which has its own ID. Processors are restricted to collecting data from others which are at a distance at most away from them in time units, but are otherwise computationally unbounded. This model focuses on the issue of locality in distributed processing, namely, to what extent a global solution to a computational problem can be obtained from locally available data. Three results are proved within this model: A 3-coloring of an n-cycle requires time f(log * n). This bound is tight, by previous work of Cole and Vishkin. Any algorithm for coloring the d-regular tree of radius r which runs for time at most 2r/3 requires at least f(x/-) colors. In an n-vertex graph of largest degree A, an O(A2)-coloring may be found in time O(log * n). Key words, distributed algorithms, graph theory, locality, lower bounds AMS(MOS) subject classifications. 05C35, 68R10, 68Q99 1. Introduction. In