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

Hiroshi NAGAMOCHI; Koji MOCHIZUKI; Toshihide IBARAKI

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

Hiroshi NAGAMOCHI, Koji MOCHIZUKI, Toshihide IBARAKI

Full Text Views

0

Cite this

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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E84-A No.5 pp.1135-1143

Publication Date: 2001/05/01

Publicized

Online ISSN

DOI

Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

Category

Cite this

Copy

Hiroshi NAGAMOCHI, Koji MOCHIZUKI, Toshihide IBARAKI, "Solving the Single-Vehicle Scheduling Problems for All Home Locations under Depth-First Routing on a Tree" in IEICE TRANSACTIONS on Fundamentals, vol. E84-A, no. 5, pp. 1135-1143, May 2001, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_5_1135/_p

Copy

@ARTICLE{e84-a_5_1135,
author={Hiroshi NAGAMOCHI, Koji MOCHIZUKI, Toshihide IBARAKI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Solving the Single-Vehicle Scheduling Problems for All Home Locations under Depth-First Routing on a Tree},
year={2001},
volume={E84-A},
number={5},
pages={1135-1143},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={May},}

Copy

TY - JOUR
TI - Solving the Single-Vehicle Scheduling Problems for All Home Locations under Depth-First Routing on a Tree
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1135
EP - 1143
AU - Hiroshi NAGAMOCHI
AU - Koji MOCHIZUKI
AU - Toshihide IBARAKI
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E84-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2001
AB - 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.
ER -