Solving the single-vehicle scheduling problems for all home locations under depth-first routing on a tree
We consider a single-vehicle scheduling problem on a tree, where each vertex has a job with a release time and a processing time and each edge has a travel time. There is a single vehicle which starts from a start vertex s and reaches a goal vertex g after finishing all jobs. In particular, s is called a home location if s = g. The objective of the problem is to find a depth-first routing on T so as to minimize the completion time. In this paper, we first show that the minimum completion times of the problem for all home locations s ' is an element of V can be simultaneously computed in O(n) time, once the problem with a specified home location s ' is an element of V has been solved, where n is the number of vertices. We also show that given a specified start vertex s, the minimum completion times for all goal vertices g can be computed in O(n) time.
tree vehicle-scheduling algorithm location problem