The Unsplittable Stable Marriage Problem

  • Brian C. Dean
  • Michel X. Goemans
  • Nicole Immorlica
Conference paper
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 209)


The Gale-Shapley “propose/reject” algorithm is a well-known procedure for solving the classical stable marriage problem. In this paper we study this algorithm in the context of the many-to-many stable marriage problem, also known as the stable allocation or ordinal transportation problem. We present an integral variant of the Gale-Shapley algorithm that provides a direct analog, in the context of “ordinal” assignment problems, of a well-known bicriteria approximation algorithm of Shmoys and Tardos for scheduling on unrelated parallel machines with costs. If we are assigning, say, jobs to machines, our algorithm finds an unsplit (non-preemptive) stable assignment where every job is assigned at least as well as it could be in any fractional stable assignment, and where each machine is congested by at most the processing time of the largest job.


Integral Variant Stable Match Fractional Variant Preference List Unrelated Parallel Machine 
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Copyright information

© International Federation for Information Processing 2006

Authors and Affiliations

  • Brian C. Dean
    • 1
  • Michel X. Goemans
    • 2
  • Nicole Immorlica
    • 3
  1. 1.Department of Computer ScienceClemson UniversityClemsonUSA
  2. 2.Department of MahematicsM.I.TUSA
  3. 3.Microsoft ResearchUSA

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