Online and Offline Algorithms for the Time-Dependent TSP with Time Zones

The time dependent traveling salesman problem is a variant of TSP with time dependent edge costs. We study some restrictions of TDTSP where the number of edge cost changes are limited. We find competitive ratios for online versions of \tdtsp. From these we derive polynomial time approximation algorithms for graphs with edge costs one and two. In addition, we present an approximation algorithm for the orienteering problem with edge costs one and two