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Workshop on Algorithms and Data Structures

WADS 1991: Algorithms and Data Structures pp 165–176Cite as

Geometric knapsack problems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 519))

Abstract

We study a variety of geometric versions of the classical knapsack problem. In particular, we consider the following “fence enclosure” problem: Given a set S of n points in the plane with values v i ≥ 0, we wish to enclose a subset of the points with a fence (a simple closed curve) in order to maximize the “value” of the enclosure. The value of the enclosure is defined to be the sum of the values of the enclosed points minus the cost of the fence. We consider various versions of the problem, such as allowing S to consist of points and/or simple polygons. Other versions of the problems are obtained by restricting the total amount of fence available and also allowing the enclosure to consist of up to K connected components. When there is an upper bound on the length of fence available, we show that the problem is N P-complete. Additionally we provide polynomial-time algorithms for many versions of the fence problem when an unrestricted amount of fence is available.

Partially supported by NSF Grants DMC-8451984, ECSE-8857642, and DMS-8903304. Email: estie@orie.cornell.edu

Partially supported by NSF grant CCR-8906949. Part of this research was done while this author was at Cornell University, and supported by NSF Grant DCR 85-52938, an IBM Graduate Fellowship, and PYI matching funds from AT&T Bell Labs and Sun Microsystems. Email: samir@umiacs.umd.edu

Partially supported by NSF Grants IRI-8710858, ECSE-8857642 and a grant from Hughes Research Labs. Email: jsbm@cs.cornell.edu

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Author information

Authors and Affiliations

  1. School of Operations Research & Industrial Engineering, Cornell University, 14853, Ithaca, NY

    Esther M. Arkin & Joseph S. B. Mitchell

  2. Institute for Advanced Computer Studies, University of Maryland, 20742, College Park, MD

    Samir Khuller

Authors
  1. Esther M. Arkin
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  2. Samir Khuller
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  3. Joseph S. B. Mitchell
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Editor information

Frank Dehne Jörg-Rüdiger Sack Nicola Santoro

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© 1991 Springer-Verlag Berlin Heidelberg

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Arkin, E.M., Khuller, S., Mitchell, J.S.B. (1991). Geometric knapsack problems. In: Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1991. Lecture Notes in Computer Science, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028259

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  • DOI: https://doi.org/10.1007/BFb0028259

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54343-5

  • Online ISBN: 978-3-540-47566-8

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