International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2009: Graph-Theoretic Concepts in Computer Science pp 66-76

Low-Port Tree Representations

  • Shiri Chechik
  • David Peleg
Conference paper

DOI: 10.1007/978-3-642-11409-0_6

Volume 5911 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Chechik S., Peleg D. (2010) Low-Port Tree Representations. In: Paul C., Habib M. (eds) Graph-Theoretic Concepts in Computer Science. WG 2009. Lecture Notes in Computer Science, vol 5911. Springer, Berlin, Heidelberg

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 \(\deg(u)\) are \(\{0,1,\ldots,\deg(u)-1\}\). 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Shiri Chechik
    • 1
  • David Peleg
    • 1
  1. 1.Department of Computer Science and Applied MathematicsThe Weizmann Institute of ScienceRehovotIsrael