An O(n log n) algorithm for the zoo-keeper's problem

Authors:
Sergei Bespamyatnikh
Affiliations:
Department of Computer Science, Duke University, Box 90129, Durham, NC
Venue:
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Year:
2003

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Abstract

We consider the zoo-keeper's problem which asks for the shortest closed zoo-keeper's path starting at a given point of the zoo and touching all the cages in the zoo. We present an O(n log n) time algorithm for the zoo-keeper's problem where n is the input size. The algorithm is based on a new data structure called the floodlight tree. We extend the approach to answer zoo-keeper's queries where one wants to find a zoo-keeper's path with a fixed start point, but an arbitrary final point. We show that zoo-keeper's queries can be answered in optimal time O(logn+K) where K is the output size.