Sciweavers

Share
APPROX
2004
Springer

On the Crossing Spanning Tree Problem

10 years 5 months ago
On the Crossing Spanning Tree Problem
Given an undirected n-node graph and a set C of m cuts, the minimum crossing tree is a spanning tree which minimizes the maximum crossing of any cut in C, where the crossing of a cut is the number of edges in the intersection of this cut and the tree. This problem finds applications in fields as diverse as Computational Biology and IP Routing Table Minimization. We show that a greedy algorithm gives an O(r log n) approximation for the problem where any edge occurs in at most r cuts. We then demonstrate that the problem remains NP-hard even when G is complete. For the latter case, we design a randomized algorithm that gives a tree T with crossing O((log m + log n) · (OPT + log n)) w.h.p., where OPT is the minimum crossing of any tree. Our greedy analysis extends the traditional one used for set cover. The randomized algorithm rounds a LP relaxation of a corresponding subproblem in stages.
Vittorio Bilò, Vineet Goyal, R. Ravi, Mohit
Added 30 Jun 2010
Updated 30 Jun 2010
Type Conference
Year 2004
Where APPROX
Authors Vittorio Bilò, Vineet Goyal, R. Ravi, Mohit Singh
Comments (0)
books