Low-port tree representations

Shiri Chechik, David Peleg

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 35th International Workshop, WG 2009, Revised Papers
Number of pages11
StatePublished - 2010
Externally publishedYes
Event35th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2009 - Montpellier, France
Duration: 24 Jun 200926 Jun 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5911 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference35th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2009

Bibliographical note

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


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