## Abstract

A partition (C_{1},C_{2},...,C_{q}) of G = (V,E) into clusters of strong (respectively, weak) diameter d, such that the supergraph obtained by contracting each C_{i} is ℓ-colorable is called a strong (resp., weak) (d, ℓ)-network-decomposition. Network-decompositions were introduced in a seminal paper by Awerbuch, Goldberg, Luby and Plotkin in 1989. Awerbuch et al. showed that strong network-decompositions can be computed in distributed deterministic time. Even more importantly, they demonstrated that network-decompositions can be used for a great variety of applications in the message-passing model of distributed computing. Much more recently Barenboim (2012) devised a distributed randomized constant-time algorithm for computing strong network decompositions with d = O(1). However, the parameter ℓ in his result is O(n^{1/2 + ε}). In this paper we drastically improve the result of Barenboim and devise a distributed randomized constant-time algorithm for computing strong (O(1), O(n^{ε}))-network-decompositions. As a corollary we derive a constant-time randomized O(n^{ε})-approximation algorithm for the distributed minimum coloring problem. This improves the best previously-known O(n^{1/2 + ε}) approximation guarantee. We also derive other improved distributed algorithms for a variety of problems. Most notably, for the extremely well-studied distributed minimum dominating set problem currently there is no known deterministic polylogarithmic -time algorithm. We devise a deterministic polylogarithmic-time approximation algorithm for this problem, addressing an open problem of Lenzen and Wattenhofer (2010).

Original language | English |
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Title of host publication | Structural Information and Communication Complexity - 22nd International Colloquium, SIROCCO 2015, Post-Proceedings |

Editors | Christian Scheideler |

Publisher | Springer Verlag |

Pages | 209-223 |

Number of pages | 15 |

ISBN (Print) | 9783319252575 |

DOIs | |

State | Published - 2015 |

Event | 22nd International Colloquium on Structural Information and Communication Complexity, SIROCCO 2015 - Montserrat, Spain Duration: 14 Jul 2015 → 16 Jul 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9439 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 22nd International Colloquium on Structural Information and Communication Complexity, SIROCCO 2015 |
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Country/Territory | Spain |

City | Montserrat |

Period | 14/07/15 → 16/07/15 |

### Bibliographical note

Publisher Copyright:© Springer International Publishing Switzerland 2015.