@inbook{caf5458d515c41fba466dc9aa6d0eb16,

title = "Robust subgraphs for trees and paths",

abstract = "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.",

author = "Refael Hassin and Danny Segev",

year = "2004",

doi = "10.1007/978-3-540-27810-8_6",

language = "English",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "51--63",

editor = "Torben Hagerup and Jyrki Katajainen",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

address = "Germany",

}