Affiliation:
1. Department of Computer Science and Engineering, HKUST, Hong Kong, China
Abstract
Consider a directed temporal graph [Formula: see text] with time ranges on the edges. There can be more than one range on an edge, and each range carries a positive traversal time. Let [Formula: see text] and let [Formula: see text] be the total number of time ranges in [Formula: see text]. We assume that [Formula: see text]. We study the problem of computing shortest journeys that start from a fixed source vertex [Formula: see text] within a given time interval [Formula: see text], where the cost of a journey is equal to the sum of traversal times of the edges on it at the times of crossing those edges. We can construct in [Formula: see text] time a data structure of size [Formula: see text] such that for any vertex [Formula: see text] and any time [Formula: see text], we can report in [Formula: see text] time the cost of the shortest journey that starts from [Formula: see text] within [Formula: see text] and arrives at [Formula: see text] no later than [Formula: see text]. The journey achieving the reported cost can be produced in time linear in its complexity.
Funder
Research Grants Council, Hong Kong, China
Publisher
World Scientific Pub Co Pte Ltd
Subject
Computer Science (miscellaneous)