Robust Subgraphs for Trees and Paths

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 an 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−α2 n edges which contains an α-approximate

• Type: Conference
• Year: 2004
• Where: SWAT
• Authors: Refael Hassin, Danny Segev
• Keywords: Algorithms, Graph Problem, Robust Subgraph, Small Subgraph, SWAT 2004