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...
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...
Let p > 1 be any fixed real. We show that assuming NP RP, there is no polynomial time algorithm that approximates the Shortest Vector Problem (SVP) in p norm within a constant ...
We study the problem of aggregating partial rankings. This problem is motivated by applications such as meta-searching and information retrieval, search engine spam fighting, e-c...
We prove that various geometric covering problems, related to the Travelling Salesman Problem cannot be efficiently approximated to within any constant factor unless P = NP. This ...