A 3/2-Approximation Algorithm for the Student-Project Allocation Problem

Authors Frances Cooper , David Manlove

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Frances Cooper
  • School of Computing Science, University of Glasgow, Glasgow, Scotland, UK
David Manlove
  • School of Computing Science, University of Glasgow, Glasgow, Scotland, UK

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Frances Cooper and David Manlove. A 3/2-Approximation Algorithm for the Student-Project Allocation Problem. In 17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


The Student-Project Allocation problem with lecturer preferences over Students (SPA-S) comprises three sets of agents, namely students, projects and lecturers, where students have preferences over projects and lecturers have preferences over students. In this scenario we seek a stable matching, that is, an assignment of students to projects such that there is no student and lecturer who have an incentive to deviate from their assignee/s. We study SPA-ST, the extension of SPA-S in which the preference lists of students and lecturers need not be strictly ordered, and may contain ties. In this scenario, stable matchings may be of different sizes, and it is known that MAX SPA-ST, the problem of finding a maximum stable matching in SPA-ST, is NP-hard. We present a linear-time 3/2-approximation algorithm for MAX SPA-ST and an Integer Programming (IP) model to solve MAX SPA-ST optimally. We compare the approximation algorithm with the IP model experimentally using randomly-generated data. We find that the performance of the approximation algorithm easily surpassed the 3/2 bound, constructing a stable matching within 92% of optimal in all cases, with the percentage being far higher for many instances.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Matching problems
  • Approximation
  • Algorithms
  • Stability


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