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New Directions in Approximate Nearest-Neighbor Searching

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Algorithms and Discrete Applied Mathematics (CALDAM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11394))

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Abstract

Approximate nearest-neighbor searching is an important retrieval problem with numerous applications in science and engineering. This problem has been the subject of many research papers spanning decades of work. Recently, a number of dramatic improvements and extensions have been discovered. In this paper, we will survey some of recent techniques that underlie these developments. In particular, we discuss local convexification, Macbeath regions, Delone sets, and how to apply these concepts to develop new data structures for approximate polytope membership queries and approximate vertical ray-shooting queries.

Research supported by NSF grant CCF–1618866.

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Notes

  1. 1.

    There is a significant literature on approximate nearest-neighbor searching in spaces of high dimension, but the techniques are very different, and it will be beyond the scope of this paper to discuss them.

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Authors and Affiliations

  1. Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD, 20742, USA

    David M. Mount

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  1. David M. Mount
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Correspondence to David M. Mount .

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Editors and Affiliations

  1. Indian Institute of Technology, Kharagpur, India

    Sudebkumar Prasant Pal

  2. Cochin University of Science and Technology, Cochin, India

    Ambat Vijayakumar

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Mount, D.M. (2019). New Directions in Approximate Nearest-Neighbor Searching. In: Pal, S., Vijayakumar, A. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2019. Lecture Notes in Computer Science(), vol 11394. Springer, Cham. https://doi.org/10.1007/978-3-030-11509-8_1

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  • DOI: https://doi.org/10.1007/978-3-030-11509-8_1

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-11509-8

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