Querying two boundary points for shortest paths in a polygonal domain

Authors:
Sang Won Bae;Yoshio Okamoto
Affiliations:
Department of Computer Science, Kyonggi University, Suwon, Republic of Korea;Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Tokyo, Japan
Venue:
Computational Geometry: Theory and Applications
Year:
2012

Citing 14
Cited 0

Approximation algorithms for shortest path motion planning

STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Optimal shortest path queries in a simple polygon

Journal of Computer and System Sciences
Finding the upper envelope of n line segments in O(n log n) time

Information Processing Letters
Davenport-Schinzel sequences and their geometric applications

Davenport-Schinzel sequences and their geometric applications
Star Unfolding of a Polytope with Applications

SIAM Journal on Computing
Computing Envelopes in Four Dimensions with Applications

SIAM Journal on Computing
Shortest paths and networks

Handbook of discrete and computational geometry
On the all-pairs Euclidean short path problem

Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Two-point Euclidean shortest path queries in the plane

Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
An Optimal Algorithm for Euclidean Shortest Paths in the Plane

SIAM Journal on Computing
Planar Spanners and Approximate Shortest Path Queries among Obstacles in the Plane

ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Shortest Path Queries in Polygonal Domains

AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Shortest Path Problems on a Polyhedral Surface

WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Improved bounds and new techniques for Davenport--Schinzel sequences and their generalizations

Journal of the ACM (JACM)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider a variant of two-point Euclidean shortest path query problem: given a polygonal domain, build a data structure for two-point shortest path query, provided that query points always lie on the boundary of the domain. As a main result, we show that a logarithmic-time query for shortest paths between boundary points can be performed using O@?(n^5) preprocessing time and O@?(n^5) space where n is the number of corners of the polygonal domain and the O@?-notation suppresses the polylogarithmic factor. This is realized by observing a connection between Davenport-Schinzel sequences and our problem in the parameterized space. We also provide a tradeoff between space and query time; a sublinear time query is possible using O(n^3^+^@e) space. Our approach also extends to the case where query points should lie on a given set of line segments.