We call a line l a separator for a set S of objects in the plane if l avoids all the objects and partitions S into two nonempty subsets, one consisting of objects lying above l and the other of objects lying below l. In this paper we present an O(n log n)-time algorithm for finding a separator line for a set of n segments, provided the ratio between the diameter of the set of segments and the length of the smallest segment is bounded. The general case is an 'n2-hard' problem, in the sense defined in  (see also ). Our algorithm is based on the recent results of , concerning the union of 'fat' triangles, but we also include an analysis which improves the bounds obtained in .
ASJC Scopus subject areas
- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics