## 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 t away from them in t 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 Ω(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 2τ/3 requires at least Ω(√d) colors. In an n-vortex graph of largest degree Δ, O(Δ^{2})-coloring may be found in time O(log n).

Original language | American English |
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Pages (from-to) | 193-201 |

Number of pages | 9 |

Journal | SIAM Journal on Computing |

Volume | 21 |

Issue number | 1 |

DOIs | |

State | Published - 1992 |