Solving the Single-Vehicle Scheduling Problems for All Home Locations under Depth-First Routing on a Tree

Hiroshi NAGAMOCHI  Koji MOCHIZUKI  Toshihide IBARAKI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.5   pp.1135-1143
Publication Date: 2001/05/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: 
Keyword: 
vehicle-scheduling,  tree,  algorithm,  location problem,  

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Summary: 
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 V can be simultaneously computed in O(n) time, once the problem with a specified home location s 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.