An Optimal Rebuilding Strategy for an Incremental Tree Problem

This paper is devoted to the following incremental problem. Initially, a graph and a distinguished subset of vertices, called initial group, are given. This group is connected by an initial tree. The incremental part of the input is given by an on-line sequence of vertices of the graph, not yet in the current group, revealed on-line one after one. The goal is to connect each new member to the current tree, while satisfying a quality constraint: the average distance between members in each constructed tree must be kept in a given range compared to the best possible one. Under this quality constraint, our objectives are to minimize the number of critical stages and the number of elementary changes of the sequence of constructed trees. We call ”critical” a stage where the inclusion of a new member implies heavy changes in the current tree. Otherwise, the new member is just added by connecting it with a (well chosen) path to the current tree. In both cases, updating a tree implies a c...

• Type: Journal
• Year: 2007
• Where: JOIN
• Authors: Nicolas Thibault, Christian Laforest
• Keywords: Critical Stages, Elementary Changes, JOIN 2007, Tree