Luccio, Fabrizio and Pagli, Linda (2002) *Distributed Construction of Almost-Edge-Disjoint Spanning Trees via.* Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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## Abstract

A $k$-dense tree, $k$ integer $\geq 1$, is a natural extension of a tree. A leaf is a vertex connected to the rest of the structure through $\leq k$ edges. After the removal of a leaf, the structure still has other leaves. Among other applications, dense trees can be used as interconnection structures in a network. Representing the network in connected graph form $G=(V,E)$, we construct a $k$-dense tree $T$ as a subgraph of $G$ spanning all its vertices. $T$ is then decomposed in $k$ {\em super-root spanning trees} sharing a $k$-clique $C$ of vertices. These trees are edge-disjoint except for the common edges in $C$. Each vertex is labeled with a set of $k$ integers in $\{0,1,\ldots,n-1\}$, $n=|V|$, to set up an interval routing scheme for $G$ along the edges of $T$. The constructions are implemented as distributed algorithms all requiring polynomial time.

Item Type: | Book |
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Uncontrolled Keywords: | $k$-dense tree, spanning tree, $SRS$-tree, decomposition, uted |

Subjects: | Area01 - Scienze matematiche e informatiche > INF/01 - Informatica |

Divisions: | Dipartimenti (until 2012) > DIPARTIMENTO DI INFORMATICA |

Depositing User: | dott.ssa Sandra Faita |

Date Deposited: | 17 Dec 2014 16:31 |

Last Modified: | 17 Dec 2014 16:31 |

URI: | http://eprints.adm.unipi.it/id/eprint/2079 |

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