A 2 + ε approximation algorithm for the k-MST problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
SIAM Journal on Discrete Mathematics
Generating and Searching Sets Induced by Networks
Proceedings of the 7th Colloquium on Automata, Languages and Programming
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximation algorithms for maximum dispersion
Operations Research Letters
A sublogarithmic approximation for highway and tollbooth pricing
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Robust matchings and matroid intersections
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Improved orientations of physical networks
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Computing knapsack solutions with cardinality robustness
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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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 that 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 article 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 that 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 variants 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.