k-Link shortest paths in weighted subdivisions

Ovidiu Daescu, Joseph S B Mitchell, Simeon Ntafos, James D Palmer, Chee K. Yap

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

We study the shortest path problem in weighted polygonal subdivisions of the plane, with the additional constraint of an upper bound, k, on the number of links (segments) in the path. We prove structural properties of optimal paths and utilize these results to obtain approximation algorithms that yield a path having O(k) links and weighted length at most (1 + ε) times the weighted length of an optimal k-link path, for any fixed ε > 0. Some of our results make use of a new solution for the 1-link case, based on computing optimal solutions for a special sum-of-fractionals (SOF) problem. We have implemented a system, based on the CORE library, for computing optimal 1-link paths; we experimentally compare our new solution with a previous method for 1-link optimal paths based on a prune-and-search scheme.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science
EditorsF. Dehne, A. Lopez-Ortiz, J.-R. Sack
Pages325-337
Number of pages13
Volume3608
StatePublished - 2005
Externally publishedYes
Event9th International Workshop on Algorithms and Data Structures, WADS 2005 - Waterloo, Canada
Duration: Aug 15 2005Aug 17 2005

Other

Other9th International Workshop on Algorithms and Data Structures, WADS 2005
CountryCanada
CityWaterloo
Period8/15/058/17/05

Fingerprint

Approximation algorithms
Structural properties

ASJC Scopus subject areas

  • Computer Science (miscellaneous)

Cite this

Daescu, O., Mitchell, J. S. B., Ntafos, S., Palmer, J. D., & Yap, C. K. (2005). k-Link shortest paths in weighted subdivisions. In F. Dehne, A. Lopez-Ortiz, & J-R. Sack (Eds.), Lecture Notes in Computer Science (Vol. 3608, pp. 325-337)

k-Link shortest paths in weighted subdivisions. / Daescu, Ovidiu; Mitchell, Joseph S B; Ntafos, Simeon; Palmer, James D; Yap, Chee K.

Lecture Notes in Computer Science. ed. / F. Dehne; A. Lopez-Ortiz; J.-R. Sack. Vol. 3608 2005. p. 325-337.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Daescu, O, Mitchell, JSB, Ntafos, S, Palmer, JD & Yap, CK 2005, k-Link shortest paths in weighted subdivisions. in F Dehne, A Lopez-Ortiz & J-R Sack (eds), Lecture Notes in Computer Science. vol. 3608, pp. 325-337, 9th International Workshop on Algorithms and Data Structures, WADS 2005, Waterloo, Canada, 8/15/05.
Daescu O, Mitchell JSB, Ntafos S, Palmer JD, Yap CK. k-Link shortest paths in weighted subdivisions. In Dehne F, Lopez-Ortiz A, Sack J-R, editors, Lecture Notes in Computer Science. Vol. 3608. 2005. p. 325-337
Daescu, Ovidiu ; Mitchell, Joseph S B ; Ntafos, Simeon ; Palmer, James D ; Yap, Chee K. / k-Link shortest paths in weighted subdivisions. Lecture Notes in Computer Science. editor / F. Dehne ; A. Lopez-Ortiz ; J.-R. Sack. Vol. 3608 2005. pp. 325-337
@inproceedings{cd1d3e8779bb42af9d670d153a4098f0,
title = "k-Link shortest paths in weighted subdivisions",
abstract = "We study the shortest path problem in weighted polygonal subdivisions of the plane, with the additional constraint of an upper bound, k, on the number of links (segments) in the path. We prove structural properties of optimal paths and utilize these results to obtain approximation algorithms that yield a path having O(k) links and weighted length at most (1 + ε) times the weighted length of an optimal k-link path, for any fixed ε > 0. Some of our results make use of a new solution for the 1-link case, based on computing optimal solutions for a special sum-of-fractionals (SOF) problem. We have implemented a system, based on the CORE library, for computing optimal 1-link paths; we experimentally compare our new solution with a previous method for 1-link optimal paths based on a prune-and-search scheme.",
author = "Ovidiu Daescu and Mitchell, {Joseph S B} and Simeon Ntafos and Palmer, {James D} and Yap, {Chee K.}",
year = "2005",
language = "English (US)",
volume = "3608",
pages = "325--337",
editor = "F. Dehne and A. Lopez-Ortiz and J.-R. Sack",
booktitle = "Lecture Notes in Computer Science",

}

TY - GEN

T1 - k-Link shortest paths in weighted subdivisions

AU - Daescu, Ovidiu

AU - Mitchell, Joseph S B

AU - Ntafos, Simeon

AU - Palmer, James D

AU - Yap, Chee K.

PY - 2005

Y1 - 2005

N2 - We study the shortest path problem in weighted polygonal subdivisions of the plane, with the additional constraint of an upper bound, k, on the number of links (segments) in the path. We prove structural properties of optimal paths and utilize these results to obtain approximation algorithms that yield a path having O(k) links and weighted length at most (1 + ε) times the weighted length of an optimal k-link path, for any fixed ε > 0. Some of our results make use of a new solution for the 1-link case, based on computing optimal solutions for a special sum-of-fractionals (SOF) problem. We have implemented a system, based on the CORE library, for computing optimal 1-link paths; we experimentally compare our new solution with a previous method for 1-link optimal paths based on a prune-and-search scheme.

AB - We study the shortest path problem in weighted polygonal subdivisions of the plane, with the additional constraint of an upper bound, k, on the number of links (segments) in the path. We prove structural properties of optimal paths and utilize these results to obtain approximation algorithms that yield a path having O(k) links and weighted length at most (1 + ε) times the weighted length of an optimal k-link path, for any fixed ε > 0. Some of our results make use of a new solution for the 1-link case, based on computing optimal solutions for a special sum-of-fractionals (SOF) problem. We have implemented a system, based on the CORE library, for computing optimal 1-link paths; we experimentally compare our new solution with a previous method for 1-link optimal paths based on a prune-and-search scheme.

UR - http://www.scopus.com/inward/record.url?scp=26844496069&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26844496069&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:26844496069

VL - 3608

SP - 325

EP - 337

BT - Lecture Notes in Computer Science

A2 - Dehne, F.

A2 - Lopez-Ortiz, A.

A2 - Sack, J.-R.

ER -