Cutting cycles of rods in space: Hardness and approximation

Boris Aronov, Mark De Berg, Chris Gray, Elena Mumford

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    We study the problem of cutting a set of rods (line segments in ℝ3) into fragments, using a minimum number of cuts, so that the resulting set of fragments admits a depth order. We prove that this problem is NP-complete, even when the rods have only three distinct orientations. We also give a polynomial-time approximation algorithm with no restriction on rod orientation that computes a solution of size O(τ logτ log logτ), where τ is the size of an optimal solution.

    Original languageEnglish (US)
    Title of host publicationProceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms
    Pages1241-1248
    Number of pages8
    StatePublished - 2008
    Event19th Annual ACM-SIAM Symposium on Discrete Algorithms - San Francisco, CA, United States
    Duration: Jan 20 2008Jan 22 2008

    Other

    Other19th Annual ACM-SIAM Symposium on Discrete Algorithms
    CountryUnited States
    CitySan Francisco, CA
    Period1/20/081/22/08

    Fingerprint

    Approximation algorithms
    Hardness
    Computational complexity
    Fragment
    Polynomials
    Cycle
    Approximation
    Line segment
    Polynomial-time Algorithm
    Approximation Algorithms
    NP-complete problem
    Optimal Solution
    Restriction
    Distinct

    ASJC Scopus subject areas

    • Software
    • Mathematics(all)

    Cite this

    Aronov, B., De Berg, M., Gray, C., & Mumford, E. (2008). Cutting cycles of rods in space: Hardness and approximation. In Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 1241-1248)

    Cutting cycles of rods in space : Hardness and approximation. / Aronov, Boris; De Berg, Mark; Gray, Chris; Mumford, Elena.

    Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms. 2008. p. 1241-1248.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Aronov, B, De Berg, M, Gray, C & Mumford, E 2008, Cutting cycles of rods in space: Hardness and approximation. in Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms. pp. 1241-1248, 19th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, United States, 1/20/08.
    Aronov B, De Berg M, Gray C, Mumford E. Cutting cycles of rods in space: Hardness and approximation. In Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms. 2008. p. 1241-1248
    Aronov, Boris ; De Berg, Mark ; Gray, Chris ; Mumford, Elena. / Cutting cycles of rods in space : Hardness and approximation. Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms. 2008. pp. 1241-1248
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