Efficient approximate shortest-path queries among isothetic rectangular obstacles

Mitra, Pinaki; Bhattacharya, Binay

doi:10.1007/3-540-57155-8_276

Cited by 5 publications

(3 citation statements)

References 11 publications

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“…There are also several interesting algorithms for approximate shortest path queries and approximate minimum-link path queries. 1,3,8,9,10,14,37 In this paper we present efficient techniques for solving several special cases of the above geometric path query problems, by exploiting the geometric structures of these special cases:…”

Section: Introductionmentioning

confidence: 99%

On Geometric Path Query Problems

Chen

Daescu

Klenk

2001

Int. J. Comput. Geom. Appl.

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In this paper, we study several geometric path query problems. Given a scene of disjoint polygonal obstacles with totally n vertices in the plane, we construct efficient data structures that enable fast reporting of an "optimal" obstacle-avoiding path (or its length, cost, directions, etc) between two arbitrary query points s and t that are given in an online fashion. We consider geometric paths under several optimality criteria: L m length, number of edges (called links), monotonicity with respect to a certain direction, and some combinations of length and links. Our methods are centered around the notion of gateways, a small number of easily identified points in the plane that control the paths we seek. We give efficient solutions for several special cases based upon new geometric observations. We also present solutions for the general cases based upon the computation of the minimum size visibility polygon for query points.

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Section: Introductionmentioning

confidence: 99%

On Geometric Path Query Problems

Chen

Daescu

Klenk

2001

Int. J. Comput. Geom. Appl.

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“…In this paper we consider the problem of computing a staircase separator for a set S of n axis-parallel, disjoint rectangles in the plane. The concept of staircase separator has been shown to be very helpful in solving exactly or approximately the rectilinear shortest path problem (for examples, see [2,3,5,8]). The first staircase separator theorem was proved by Atallah and Chen.…”

Section: Introductionmentioning

confidence: 99%

“…The authors proposed a divide and conquer approach for solving the rectilinear shortest path problem by using staircase separators to recursively partition the set of rectangles. Other divide and conquer algorithms using the result on staircase separators can be found in, for example, [5,8].…”

Section: Introductionmentioning

confidence: 99%

A new staircase separator theorem

Nguyen

1997

Euro-Par'97 Parallel Processing

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V iet H ai.N guyen~di.ep f i.ch A b s t r a c t . The notion of staircase separator, introduced in [2], greatly facilitates the design of divide-and-conquer algorithms for problems on rectangles. We generalize the concept of staircase separator to k-perfect staircase separator, namely a set of staircase separators which partitions a set S of n axis-parallel, disjoint rectangles into k subsets of (almost) equal size. We derive an optimal O(logn) time parallel algorithm for computing a k-perfect staircase separator, using O(n) processors on the CREW PRAM model of computation. For a special case, where k ---2, this result provides a new bound of [-~], in compared to [ ~] in [2], on the quality of staircase separators for sets of rectangles.

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Applications of a numbering scheme for polygonal obstacles in the plane

Atallah

Chen

1996

Algorithms and Computation

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Efficient approximate shortest-path queries among isothetic rectangular obstacles

Cited by 5 publications

References 11 publications

On Geometric Path Query Problems

On Geometric Path Query Problems

A new staircase separator theorem

Applications of a numbering scheme for polygonal obstacles in the plane

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