We improve the running times of $ O (1) $-approximation algorithms for the set cover
problem in geometric settings, specifically, covering points by disks in the plane, or covering …

The geometric hitting set problem is one of the basic geometric combinatorial optimization
problems: given a set P of points and a set D of geometric objects in the plane, the goal is to …

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 …

A $ t $-spanner of a graph $ G=(V, E) $ is a subgraph $ H=(V, E') $ that contains a $ uv $-
path of length at most $ t $ for every $ uv\in E $. It is known that every $ n $-vertex graph …

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 …

We show that an extremely simple local search gives a PTAS for the Feedback Vertex Set
(FVS) problem in minor-free graphs. It keeps exchanging a constant number of vertices to …

Fast constant factor approximation algorithms are devised for a problem of intersecting a set
of n straight line segments with the smallest cardinality set of disks of fixed radii r> 0 where …

We study several variations of line segment covering problem with axis-parallel unit squares
in the plane. Given a set S of n line segments, the objective is to find the minimum number of …

Geometric set cover is a classical problem in computational geometry, with a long history
and many applications. Given a set $ X $ of points in $\mathbb {R}^ d $ and a set $ S $ of …

The last decade has seen the resolution of several basic NP-complete problems in
geometric combinatorial optimisation—interestingly, all with the same algorithm: local …