Skip to main content
SpringerLink
Log in

Large Neighborhood Local Search for the Maximum Set Packing Problem

  • Conference paper
Automata, Languages, and Programming (ICALP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7965))

Included in the following conference series:

Abstract

In this paper we consider the classical maximum set packing problem where set cardinality is upper bounded by a constant k. We show how to design a variant of a polynomial-time local search algorithm with performance guarantee (k + 2)/3. This local search algorithm is a special case of a more general procedure that allows to swap up to Θ(logn) elements per iteration. We also design problem instances with locality gap k/3 even for a wide class of exponential time local search procedures, which can swap up to cn elements for a constant c. This shows that our analysis of this class of algorithms is almost tight.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alon, N., Yuster, R., Zwick, U.: Color-coding. Journal of the ACM 42(4), 844–856 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. Berman, P., Fürer, M.: Approximating maximum independent set in bounded degree graphs. In: SODA (1994)

    Google Scholar 

  3. Cygan, M., Grandoni, F., Mastrolilli, M.: How to sell hyperedges: the hypermatching assignment problem. In: SODA (2013)

    Google Scholar 

  4. Fellows, M., Knauer, C., Nishimura, N.: Faster fixed-parameter tractable algorithms for matching and packing problems. Algorithmica, 167–176 (2004)

    Google Scholar 

  5. Halldórsson, M.: Approximating Discrete Collections via Local Improvements. In: SODA (1995)

    Google Scholar 

  6. Hazan, Safra, S., Schwartz, O.: On the complexity of approximating k-set packing. Computational Complexity 15(1), 20–39 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hurkens, C., Schrijver, A.: On the Size of Systems of Sets Every t of Which Have an SDR, with an Application to the Worst-Case Ratio of Heuristics for Packing Problems. SIAM Journal of Discrete Mathematics 2(1), 68–72 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  8. Paschos, V.: A survey of approximately optimal solutions to some covering and packing problems. ACM Computing Surveys 29(2), 171–209 (1997)

    Article  Google Scholar 

  9. Schmidt, J.P., Siegel, A.: The spatial complexity of oblivious k-probe hash functions. SIAM Journal on Computing 19(5), 775–786 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  10. Fredman, M., Komlós, J., Szemerédi, E.: Storing a sparse table with O(1) worst case access time. Journal of the ACM 31(3), 538–544 (1984)

    Article  MATH  Google Scholar 

  11. Alon, N., Naor, M.: Derandomization, witnesses for boolean matrix multiplication and construction of perfect hash functions. Algorithmica 16(4/5), 434–449 (1996)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Warwick, UK

    Maxim Sviridenko & Justin Ward

Authors
  1. Maxim Sviridenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Justin Ward
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Postboks 7803, 5020, Bergen, Norway

    Fedor V. Fomin

  2. Faculty of Computing, University of Latvia, Raina bulv. 19, 1586, Riga, Latvia

    Rūsiņš Freivalds

  3. Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Marta Kwiatkowska

  4. Faculty of Mathematics and Computer Science, Weizmann Institute of Science, POB 26, 76100, Rehovot, Israel

    David Peleg

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sviridenko, M., Ward, J. (2013). Large Neighborhood Local Search for the Maximum Set Packing Problem. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39206-1_67

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39206-1_67

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39205-4

  • Online ISBN: 978-3-642-39206-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation