We investigate the family of intersection graphs of low density objects in low dimensional
Euclidean space. This family is quite general, includes planar graphs, and in particular is a …

We study a general family of facility location problems defined on planar graphs and on the
2-dimensional plane. In these problems, a subset of k objects has to be selected, satisfying …

We give a polynomial-time constant-factor approximation algorithm for the maximum
independent set of (axis-aligned) rectangles problem in the plane. Using a polynomial-time …

We present a (1+ ε)-approximation algorithm with quasi-polynomial running time for
computing a maximum weight independent set of polygons from a given set of polygons in …

We study the Maximum Independent Set of Rectangles (MISR) problem: given a set of n axis-
parallel rectangles, find a largest-cardinality subset of the rectangles, such that no two of …

Weighted geometric set-cover problems arise naturally in several geometric and
nongeometric settings (eg, the breakthrough of Bansal and Pruhs Proceedings of FOCS …

Weighted geometric set-cover problems arise naturally in several geometric and non-
geometric settings (eg the breakthrough of Bansal and Pruhs (FOCS 2010) reduces a wide …

Abstract In the Maximum Independent Set of Objects problem, we are given an n-vertex
planar graph G and a family D of N objects, where each object is a connected subgraph of …

In this paper, we design the first polynomial time approximation schemes for the Set Cover
and Dominating Set problems when the underlying sets are non-piercing regions (which …

Planar graphs are known to allow subexponential algorithms running in time 2^ O (n) 2 O (n)
or 2^ O (n\log n) 2 O (n log n) for most of the paradigmatic problems, while the brute-force …