Abstract
We investigate online route planning problems, which find real applications in dynamic navigation systems used to avoid traffic congestion. This study focuses on several generalizations of the well-known CANADIAN TRAVELLER PROBLEM (CTP). Given a road network G=(V,E) in which there is a source s and a destination t in V, every edge e in E is associated with two possible distances: original d(e) and jam d^+ (e). A traveller only finds out which one of the two distances of an edge upon reaching an end vertex incident to the edge. The objective is to derive an adaptive strategy for travelling from s to t so that the competitive ratio, which compares the distance traversed with that of the static s, t-shortest path in hindsight, is minimized. This problem was initiated by Papadimitriou and Yannakakis. They proved that it is PSPACE-complete to obtain an algorithm with a bounded competitive ratio. In this study, we propose tight lower bounds of the problem when the number of traffic jams is a given constant k, and introduce a deterministic algorithm with a min{r,2k+1}-ratio, which meets the proposed lower bound, where r is the worst-case performance ratio. We also study an extension to the metric Travelling Salesman Problem (TSP) and propose a touring strategy within an O(√k)-competitive ratio. Finally, we discuss randomized strategies, in the hope of surpassing the barrier of obtaining better approximation algorithms.