Labeling Schemes for Tree Representation

This paper deals with compact label-based representations for trees. Consider an n-node undirected connected graph G with a predefined numbering on the ports of each node. The all-ports tree labeling Lall gives each node v of G a label containing the port numbers of all the tree edges incident to v. The upward tree labeling Lup labels each node v by the number of the port leading from v to its parent in the tree. Our measure of interest is the worst case and total length of the labels used by the scheme, denoted Mup(T) and Sup(T) for Lup and Mall(T) and Sall(T) for Lall. The problem studied in this paper is the following: Given a graph G and a predefined port labeling for it, with the ports of each node v numbered by 0, . . . , deg(v) − 1, select a rooted spanning tree for G minimizing (one of) these measures. We show that the problem is polynomial for Mup(T), Sup(T) and Sall(T) but NP-hard for Mall(T) (even for 3-regular planar graphs). We show that for every graph G and port lab...

• Type: Conference
• Year: 2005
• Where: IWDC
• Authors: Reuven Cohen, Pierre Fraigniaud, David Ilcinkas, Amos Korman, David Peleg
• Keywords: Communications, IWDC 2005, Port, Tree, Tree Labeling Lall