Consider a graph problem which is associated with a parameter, for example, that of finding a longest tour spanning k vertices. The following question is natural: Is there a small subgraph which contains optimal or near optimal solution for every possible value of the given parameter? Such a subgraph is said to be robust. In this paper we consider the problems of finding heavy paths and heavy trees of k edges. In these two cases we prove surprising bounds on the size of a robust subgraph for a variety of approximation ratios. For both problems we show that in every complete weighted graph on n vertices there exists a subgraph with approximately α/1-α2n edges which contains an α-approximate solution for every k = 1, . . . , n - 1. In the analysis of the tree problem we also describe a new result regarding balanced decomposition of trees. In addition, we consider variations in which the subgraph itself is restricted to be a path or a tree. For these problems we describe polynomial time algorithms and corresponding proofs of negative results. © Springer-Verlag Berlin Heidelberg 2004.
CITATION STYLE
Hassin, R., & Segev, D. (2004). Robust subgraphs for trees and paths. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3111, 51–63. https://doi.org/10.1007/978-3-540-27810-8_6
Mendeley helps you to discover research relevant for your work.