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On-line algorithms for weighted bipartite matching and stable marriages

  • Algorithms (Session 18)
  • Conference paper
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Automata, Languages and Programming (ICALP 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 510))

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Abstract

We give an on-line deterministic algorithm for the weighted bipartite matching problem that achieves a competitive ratio of (2n − 1) in any metric space. This algorithm is optimal — there is no on-line deterministic algorithm that achieves a competitive ratio better than (2n − 1) in all metric spaces.

We also study the stable marriage problem, where we are interested in the number of unstable pairs produced. We show that the simple “first come, first served” deterministic algorithm yields on the average O(n log n) unstable pairs, but in the worst case no deterministic or randomized on-line algorithm can do better than ω(n 2) unstable pairs. This appears to be the first on-line problem for which provably one cannot do better with randomization; for most on-line problems studied in the past, randomization has helped in improving the performance.

Supported by NSF grant DCR 85-52938 and PYI matching funds from AT&T Bell Labs and Sun Microsystems, Inc.

Partially supported by NSF grant CCR-8906949. Part of this research was done while this author was supported by an IBM Graduate Fellowship at Cornell University.

Work done while at Cornell University.

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Author information

Authors and Affiliations

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

    Samir Khuller

  2. Computer Science Department, Cornell University, 14853, Ithaca, NY

    Stephen G. Mitchell

  3. Dept. of Computer Science & Engg., Indian Institute of Technology, 110016, New Delhi, India

    Vijay V. Vazirani

Authors
  1. Samir Khuller
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  2. Stephen G. Mitchell
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  3. Vijay V. Vazirani
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Editor information

Javier Leach Albert Burkhard Monien Mario Rodríguez Artalejo

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© 1991 Springer-Verlag Berlin Heidelberg

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Khuller, S., Mitchell, S.G., Vazirani, V.V. (1991). On-line algorithms for weighted bipartite matching and stable marriages. In: Albert, J.L., Monien, B., Artalejo, M.R. (eds) Automata, Languages and Programming. ICALP 1991. Lecture Notes in Computer Science, vol 510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54233-7_178

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  • DOI: https://doi.org/10.1007/3-540-54233-7_178

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54233-9

  • Online ISBN: 978-3-540-47516-3

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