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Geometric Shortest Paths in the Plane

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  • First Online:
Encyclopedia of Algorithms

  • 340 Accesses

Years and Authors of Summarized Original Work

  • 1996; Mitchell

  • 1999; Hershberger, Suri

Problem Definition

Finding the shortest path between a source and a destination is a natural optimization problem with many applications. Perhaps the oldest variant of the problem is the geometric shortest path problem, in which the domain is physical space: the problem is relevant to human travelers, migrating animals, and even physical phenomena like wave propagation. The key feature that distinguishes the geometric shortest path problem from the corresponding problem in graphs or other discrete spaces is the unbounded number of paths in a multidimensional space. To solve the problem efficiently, one must use the “shortness” criterion to limit the search.

In computational geometry, physical space is modeled abstractly as the union of some number of constant-complexity primitive elements. The traditional formulation of the shortest path problem considers paths in a domain bounded by linear elements –...

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Author information

Authors and Affiliations

  1. Mentor Graphics Corporation, 8005 SW Boeckman Road, Wilsonville, OR, USA

    John Hershberger

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  1. John Hershberger
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Correspondence to John Hershberger .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Hershberger, J. (2016). Geometric Shortest Paths in the Plane. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_509

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