## Abstract

Consider an n-node undirected graph G(V,E) with a pre-assigned port numbering for the outgoing edges of each node. The port numbers assigned to a node u of degree are . In certain contexts it is necessary to maintain a directed spanning tree of G, in which case each node needs to remember the port number leading to its parent. Hence the cost of a spanning tree T is the total number of bits the nodes need to store in order to remember T. This paper addresses the question of asymptotically bounding the cost of the optimal tree, as a function of the graph size. A tight upper bound of O(n) is established on this cost, thus improving on the best previously known bound of O(nloglogn) [6] and proving the conjecture raised therein. This is achieved by presenting a polynomial time algorithm for constructing a spanning tree T of cost O(n) for a given general graph G with an arbitrary port labeling.

Original language | English |
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Title of host publication | Graph-Theoretic Concepts in Computer Science - 35th International Workshop, WG 2009, Revised Papers |

Pages | 66-76 |

Number of pages | 11 |

DOIs | |

State | Published - 2010 |

Externally published | Yes |

Event | 35th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2009 - Montpellier, France Duration: 24 Jun 2009 → 26 Jun 2009 |

### 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 | 5911 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 35th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2009 |
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Country/Territory | France |

City | Montpellier |

Period | 24/06/09 → 26/06/09 |

### Bibliographical note

Funding Information:Supported by a grant from the Israel Science Foundation.