Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons

Leonidas Guibas; John Hershberger; Daniel Leven; Micha Sharir; Robert E. Tarjan

doi:10.1007/BF01840360

Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons

Leonidas Guibas, John Hershberger, Daniel Leven, Micha Sharir, Robert E. Tarjan

Research output: Contribution to journal › Article › peer-review

285 Scopus citations

Abstract

Given a triangulation of a simple polygon P, we present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility within P. These problems include calculation of the collection of all shortest paths inside P from a given source vertex S to all the other vertices of P, calculation of the subpolygon of P consisting of points that are visible from a given segment within P, preprocessing P for fast "ray shooting" queries, and several related problems.

Original language	English (US)
Pages (from-to)	209-233
Number of pages	25
Journal	Algorithmica
Volume	2
Issue number	1
DOIs	https://doi.org/10.1007/BF01840360
State	Published - Mar 1 1987
Externally published	Yes

All Science Journal Classification (ASJC) codes

Computer Science(all)
Computer Science Applications
Applied Mathematics

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10.1007/BF01840360

Cite this

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abstract = "Given a triangulation of a simple polygon P, we present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility within P. These problems include calculation of the collection of all shortest paths inside P from a given source vertex S to all the other vertices of P, calculation of the subpolygon of P consisting of points that are visible from a given segment within P, preprocessing P for fast {"}ray shooting{"} queries, and several related problems.",

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AU - Guibas, Leonidas

AU - Hershberger, John

AU - Leven, Daniel

AU - Sharir, Micha

AU - Tarjan, Robert E.

PY - 1987/3/1

Y1 - 1987/3/1

N2 - Given a triangulation of a simple polygon P, we present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility within P. These problems include calculation of the collection of all shortest paths inside P from a given source vertex S to all the other vertices of P, calculation of the subpolygon of P consisting of points that are visible from a given segment within P, preprocessing P for fast "ray shooting" queries, and several related problems.

AB - Given a triangulation of a simple polygon P, we present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility within P. These problems include calculation of the collection of all shortest paths inside P from a given source vertex S to all the other vertices of P, calculation of the subpolygon of P consisting of points that are visible from a given segment within P, preprocessing P for fast "ray shooting" queries, and several related problems.

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ER -

Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons

Abstract

All Science Journal Classification (ASJC) codes

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