We consider labeled Traveling Salesman Problems, defined upon a complete graph of n vertices with colored edges. The objective is to find a tour of maximum or minimum number of co...
Garg [10] gives two approximation algorithms for the minimum-cost tree spanning k vertices in an undirected graph. Recently Jain and Vazirani [16] discovered primal-dual approxima...
The crossing number of a graph is the least number of pairwise edge crossings in a drawing of the graph in the plane. We provide an O(n log n) time constant factor approximation al...
We consider the following planar maximum weight triangulation (MAT) problem: given a set of n points in the plane, find a triangulation such that the total length of edges in tria...
We introduce a facility location problem with submodular facility cost functions, and give an O(log n) approximation algorithm for it. Then we focus on a special case of submodula...