WADS 2017: Algorithms and Data Structures pp 557-568

# Covering Uncertain Points in a Tree

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10389)

## Abstract

We consider a coverage problem for uncertain points in a tree. Let T be a tree containing a set $$\mathcal {P}$$ of n (weighted) demand points, and the location of each demand point $$P_i\in \mathcal {P}$$ is uncertain but is known to be in one of $$m_i$$ points on T each associated with a probability. Given a covering range $$\lambda$$, the problem is to find a minimum number of points (called centers) on T to build facilities for serving (or covering) these demand points in the sense that for each uncertain point $$P_i\in \mathcal {P}$$, the expected distance from $$P_i$$ to at least one center is no more than $$\lambda$$. The problem has not been studied before. We present an $$O(|T|+M\log ^2 M)$$ time algorithm, where |T| is the number of vertices of T and M is the total number of locations of all uncertain points of $$\mathcal {P}$$, i.e., $$M=\sum _{P_i\in \mathcal {P}}m_i$$.

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