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International Workshop on Algorithms and Computation

WALCOM 2017: WALCOM: Algorithms and Computation pp 320–332Cite as

Space-Efficient and Output-Sensitive Implementations of Greedy Algorithms on Intervals

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10167))

Abstract

We consider the space-efficient implementation of greedy algorithms for several fundamental problems on intervals. We assume a random access machine model with read-only access to input stored in \(\varTheta (n)\) words of memory, augmented with a random access memory (workspace) of size \(\varTheta (s)\) bits, where \(\lg n \le s \le n\). Our implementations are based on the efficient realization of an abstract data structure that we call a temporal priority queue that supports extract-min and advance-time operations for a static collection of entities, each of which is active for some pre-specified interval of time. This realization is a generalization of the memory-adjustable navigation pile proposed by Asano et al. in studying time-space tradeoffs for sorting.

Using temporal priority queues we are able to implement familiar greedy algorithms for the maximum independent set problem and a variety of dominating set problems on intervals, using \({O(m(\lg {(sk/m)}+n/s))}\) time and \(\varTheta (s)\) bits of workspace, where k is the size of output and \(m=\min (sk, n)\). Choosing \(s = \varTheta (n)\) this achieves \(O(n\lg {k})\) output-sensitive time complexity for the maximum independent set problem on intervals, previously realized using \(\varOmega (n)\) words of workspace.

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Notes

  1. 1.

    The symbol \(\lg \) denotes \(\log _2\).

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Author information

Authors and Affiliations

  1. Graduate School of Engineering, Kobe University, Kobe, Japan

    Toshiki Saitoh

  2. Department of Computer Science, UBC, Vancouver, Canada

    David G. Kirkpatrick

Authors
  1. Toshiki Saitoh
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  2. David G. Kirkpatrick
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Correspondence to Toshiki Saitoh .

Editor information

Editors and Affiliations

  1. Universiti Teknologi Brunei, Bandar Seri Begawan, Brunei Darussalam

    Sheung-Hung Poon

  2. Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

    Md. Saidur Rahman

  3. National Taiwan University, Taipei, Taiwan

    Hsu-Chun Yen

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Saitoh, T., Kirkpatrick, D.G. (2017). Space-Efficient and Output-Sensitive Implementations of Greedy Algorithms on Intervals. In: Poon, SH., Rahman, M., Yen, HC. (eds) WALCOM: Algorithms and Computation. WALCOM 2017. Lecture Notes in Computer Science(), vol 10167. Springer, Cham. https://doi.org/10.1007/978-3-319-53925-6_25

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  • DOI: https://doi.org/10.1007/978-3-319-53925-6_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53924-9

  • Online ISBN: 978-3-319-53925-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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