# Covering points: Minimizing the maximum depth

## Document Type

Conference Article

## Publication Title

CCCG 2017 - 29th Canadian Conference on Computational Geometry, Proceedings

## Abstract

We study a variation of the geometric set cover problem. Let P be a set of n points and T be a set of m objects in the plane. We find a cover T0 ⊆ T such that each point is covered by T0 and the depth of T0 is minimum. By depth of a cover T0, we mean the maximum number of objects in T0 which contain a point in P. We prove this problem to be NP-complete in IR2 where the objects are unit squares or unit disks. More precisely, we show that it is NP-complete to decide whether this problem has a cover of depth 1. We present an O((n+m) log n+m log m) time algorithm for the problem where the points are on a real line and objects are unweighted intervals. For weighted intervals, this problem can be solved in O(nm log n) time.

## First Page

37

## Last Page

42

## Publication Date

1-1-2017

## Recommended Citation

Nandy, Subhas C.; Pandit, Supantha; and Roy, Sasanka, "Covering points: Minimizing the maximum depth" (2017). *Conference Articles*. 277.

https://digitalcommons.isical.ac.in/conf-articles/277