Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Information Sciences: an International Journal
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Shortest zookeeper's routes in simple polygons
Information Processing Letters
An O(n log n) algorithm for the zoo-keeper's problem
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Approximation algorithms for the watchman route and zookeeper's problems
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
A 2-approximation algorithm for the zookeeper's problem
Information Processing Letters
Hi-index | 0.89 |
Consider a simple polygon P containing disjoint convex polygons each of which shares an edge with P. The Zookeeper's Problem then asks for the shortest route in P that visits all convex polygons without entering their interiors. Existing algorithms that solve this problem run in time super-linear in the size of P and the convex polygons. They also suffer from numerical problems.In this paper, we shed more light on the problem and present a simple linear time algorithm for computing an approximate solution. The algorithm mainly computes shortest paths and intersections between lines using basic data structures. It does not suffer from numerical problems. We prove that the computed approximation route is at most 6 times longer than the shortest route in the exact solution.