The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Faster scaling algorithms for network problems
SIAM Journal on Computing
Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
Improved Approximation Algorithms for Shop Scheduling Problems
SIAM Journal on Computing
On Local Search for Weighted K-Set Packing
Mathematics of Operations Research
Better approximation guarantees for job-shop scheduling
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Linear time 1/2 -approximation algorithm for maximum weighted matching in general graphs
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Pareto optimality in house allocation problems
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
SIAM Journal on Discrete Mathematics
ACM Transactions on Algorithms (TALG)
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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.