Assignment Problems in Rental Markets

  • David Abraham
  • Ning Chen
  • Vijay Kumar
  • Vahab S. Mirrokni
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4286)

Abstract

Motivated by the dynamics of the ever-popular online movie rental business, we study a range of assignment problems in rental markets. The assignment problems associated with rental markets possess a rich mathematical structure and are closely related to many well-studied one-sided matching problems. We formalize and characterize the assignment problems in rental markets in terms of one-sided matching problems, and consider several solution concepts for these problems. In order to evaluate and compare these solution concepts (and the corresponding algorithms), we define some “value” functions to capture our objectives, which include fairness, efficiency and social welfare. Then, we bound the value of the output of these algorithms in terms of the chosen value functions.

We also consider models of rental markets corresponding to static, online, and dynamic customer valuations. We provide several constant-factor approximation algorithms for the assignment problem, as well as hardness of approximation results for the different models. Finally, we describe some experiments with a discrete event simulator compare the various algorithms in a practical setting, and present some interesting experimental results.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • David Abraham
    • 1
  • Ning Chen
    • 2
  • Vijay Kumar
    • 3
  • Vahab S. Mirrokni
    • 4
  1. 1.Department of Computer ScienceCarnegie Mellon University 
  2. 2.Department of Computer Science & EngineeringUniversity of Washington 
  3. 3.Strategic Planning and Optimization Team 
  4. 4.Microsoft ResearchRedmondUSA

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