On Bounded Leg Shortest Paths Problems

Let V be a set of points in a d-dimensional lp-metric space. Let s, t ∈ V and let L be any real number. An L-bounded leg path from s to t is an ordered set of points which connects s to t such that the leg between any two consecutive points in the set is at most L. The minimal path among all these paths is the L-bounded leg shortest path from s to t. In the s-t Bounded Leg Shortest Path (stBLSP) problem we are given two points s and t and a real number L, and are required to compute an Lbounded leg shortest path from s to t. In the All-Pairs Bounded Leg Shortest Path (apBLSP) problem we are required to build a data structure that, given any two query points from V and any real number L, outputs the length of the L-bounded leg shortest path (a distance query) or the path itself (a path query). In this paper present first an algorithm for the apBLSP problem in any lp-metric which, for any fixed ε > 0, computes in O(n3 (log3 n + log2 n · ε−d )) time a data structure which app...

• Type: Journal
• Year: 2011
• Where: ALGORITHMICA
• Authors: Liam Roditty, Michael Segal
• Keywords: ALGORITHMICA 2011, Algorithms, Artificial Intelligence, Leg Shortest Path, Real Number