## Abstract

We deterministically compute a Δ+1 coloring and a maximal independent set(MIS) in time O(Δ^{1/2+Θ(1/√h)}+log*n) for Δ_{1+i}≤Δ^{1+i/h}, where Δ_{j} is defined as the maximal number of nodes within distance j for a node and Δ:=Δ_{1}. Our greedy coloring and MIS algorithms improve the state-of-the-art algorithms running in O(Δ+log*n) for a large class of graphs, i.e., graphs of (moderate) neighborhood growth with h≥36. We also state and analyze a randomized coloring algorithm in terms of the chromatic number, the run time and the used colors. Our algorithm runs in time O(logχ+log*n) for Δ∈Ω(log^{1+1/log*n}n) and χ∈O(Δ/log^{1+1/log*n}n). For graphs of polylogarithmic chromatic number the analysis reveals an exponential gap compared to the fastest Δ+1 coloring algorithm running in time O(logΔ+√log n). The algorithm works without knowledge of χ and uses less than Δ colors, i.e., (1-1/O(χ))Δ with high probability. To the best of our knowledge this is the first distributed algorithm for (such) general graphs taking the chromatic number χ into account. We also improve on the state of the art deterministic computation of (2,c)-ruling sets.

Original language | English |
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Pages (from-to) | 40-50 |

Number of pages | 11 |

Journal | Theoretical Computer Science |

Volume | 509 |

DOIs | |

State | Published - 21 Oct 2013 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science (all)