We obtain the first polynomial relationship between treewidth and grid-minor size by showing that f(k) = Ω(kδ) for some fixed constant δ > 0, and describe an algorithm that finds a model of such a grid minor in G.Expand

The authors consider the job interval selection problem (JISP), a simple scheduling model with a rich history and numerous applications, and show an approximation guarantee of less than 1.582 for arbitrary instances of JISP.Expand

In the Survivable Network Design problem (SNDP), we are given an undirected graph $G(V, E)$ with costs on edges, along with a connectivity requirement $r(u, v)$ for each pair of vertices.Expand

We show that the ASYMMETRIC <i>k</i>-CENTER problem is hard to approximate up to a factor of log<sup>*</sup><i>n</ i>−<i>O</i>(1) unless an asymptotic approximability algorithm is known for this problem.Expand

This is one of many network design problems widely studied where the bandwidth allocation being governed by side constraints: edges may only allow a subset of cables to be purchased on them, or certain quality-of-service requirements may have to be met.Expand

We study the Maximum Independent Set of Rectangles (MISR) problem: given a collection R of n axis-parallel rectangles, find a maximum-cardinality subset of disjoint rectangles.Expand