TY - GEN

T1 - Low-port tree representations

AU - Chechik, Shiri

AU - Peleg, David

N1 - Funding Information:
Supported by a grant from the Israel Science Foundation.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=72249099310&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-11409-0_6

DO - 10.1007/978-3-642-11409-0_6

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AN - SCOPUS:72249099310

SN - 3642114083

SN - 9783642114083

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 66

EP - 76

BT - Graph-Theoretic Concepts in Computer Science - 35th International Workshop, WG 2009, Revised Papers

Y2 - 24 June 2009 through 26 June 2009

ER -