Contention Resolution, Matrix Scaling and Fair Allocation
A contention resolution (CR) scheme is a basic algorithmic primitive, that deals with how to allocate items among a random set S of competing players, while maintaining various properties. We consider the most basic setting where a single item must be allocated to some player in S. Here, in a semina...
Saved in:
Published in | Approximation and Online Algorithms Vol. 12982; pp. 252 - 274 |
---|---|
Main Authors | , |
Format | Book Chapter |
Language | English |
Published |
Switzerland
Springer International Publishing AG
2021
Springer International Publishing |
Series | Lecture Notes in Computer Science |
Online Access | Get full text |
Cover
Loading…
Summary: | A contention resolution (CR) scheme is a basic algorithmic primitive, that deals with how to allocate items among a random set S of competing players, while maintaining various properties. We consider the most basic setting where a single item must be allocated to some player in S. Here, in a seminal work, Feige and Vondrak (2006) designed a fair CR scheme when the set S is chosen from a product distribution. We explore whether such fair schemes exist for arbitrary non-product distributions on sets of players S, and whether they admit simple algorithmic primitives. Moreover, can we go beyond fair allocation and design such schemes for all possible achievable allocations.
We show that for any arbitrary distribution on sets of players S, and for any achievable allocation, there exist several natural CR schemes that can be succinctly described, are simple to implement and can be efficiently computed to any desired accuracy. We also characterize the space of achievable allocations for any distribution, give algorithms for computing an optimum fair allocation for arbitrary distributions, and describe other natural fair CR schemes for product distributions. These results are based on matrix scaling and various convex programming relaxations. |
---|---|
Bibliography: | Part of the work has been done while the author was a postdoctoral fellow at CWI Amsterdam and TU Eindhoven, and was supported by the ERC Consolidator Grant 617951 and the NWO VICI grant 639.023.812. |
ISBN: | 9783030927011 3030927016 |
ISSN: | 0302-9743 1611-3349 |
DOI: | 10.1007/978-3-030-92702-8_16 |