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 …

Abstract We consider the Minimum Dominating Set (MDS) problem on the intersection
graphs of geometric objects. Even for simple and widely-used geometric objects such as …

Let F be a family of pseudo-disks in the plane, and P be a finite subset of F. Consider the
hyper-graph H (P, F) whose vertices are the pseudo-disks in P and the edges are all subsets …

We study a generalization of the Set Cover problem called the\emph {Partial Set Cover} in
the context of geometric set systems. The input to this problem is a set system $(X,\mathcal …

Local search for combinatorial optimization problems is becoming a dominant algorithmic
paradigm, with several papers using it to resolve long-standing open problems. In this …

Over the past several decades there has been steady progress towards the goal of
polynomial-time approximation schemes (PTAS) for fundamental geometric combinatorial …

We provide constant factor approximation algorithms for the Minimum Dominating Set (MDS)
problem on several subclasses of string graphs ie intersection graphs of simple curves on …

In their seminal work, Mustafa and Ray [Nabil H. Mustafa and Saurabh Ray, 2010] showed
that a wide class of geometric set cover (SC) problems admit a PTAS via local search-this is …

Abstract Geometric Covering and Packing problems have been extensively studied in the
last few decades and have applications in diverse areas. Several variants and …

Up until a decade ago, the algorithmic status of several basic NP-complete problems in
geometric combinatorial optimisation was unresolved. This included the existence of …