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Coordination Complexity: Small Information Coordinating Large Populations

Cummings, Rachel and Ligett, Katrina and Radhakrishnan, Jaikumar and Roth, Aaron and Wu, Zhiwei Steven (2016) Coordination Complexity: Small Information Coordinating Large Populations. In: Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science. Association for Computing Machinery , New York, NY, pp. 281-290. ISBN 978-1-4503-4057-1. https://resolver.caltech.edu/CaltechAUTHORS:20160120-105900294

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Abstract

We initiate the study of a quantity that we call coordination complexity. In a distributed optimization problem, the information defining a problem instance is distributed among n parties, who need to each choose an action, which jointly will form a solution to the optimization problem. The coordination complexity represents the minimal amount of information that a centralized coordinator, who has full knowledge of the problem instance, needs to broadcast in order to coordinate the n parties to play a nearly optimal solution. We show that upper bounds on the coordination complexity of a problem imply the existence of good jointly differentially private algorithms for solving that problem, which in turn are known to upper bound the price of anarchy in certain games with dynamically changing populations. We show several results. We fully characterize the coordination complexity for the problem of computing a many-to-one matching in a bipartite graph. Our upper bound in fact extends much more generally to the problem of solving a linearly separable convex program. We also give a different upper bound technique, which we use to bound the coordination complexity of coordinating a Nash equilibrium in a routing game, and of computing a stable matching.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1145/2840728.2840767DOIArticle
http://dl.acm.org/citation.cfm?doid=2840728.2840767PublisherArticle
http://arxiv.org/abs/1508.03735arXivDiscussion Paper
ORCID:
AuthorORCID
Ligett, Katrina0000-0003-2780-6656
Additional Information:© 2016 ACM. Supported by Simons Award for Graduate Students in Theoretical Computer Science and NSF CNS-1254169. Supported in part by NSF grant CNS-1254169, NSF grant CNS-1518941 US-Israel Binational Science Foundation grant 2012348, the Charles Lee Powell Foundation, a Google Faculty Research Award, an Okawa Foundation Research Grant, a Microsoft Faculty Fellowship. Supported in part by NSF Grant CCF-1101389, an NSF CAREER award, and an Alfred P. Sloan Foundation Fellowship. Supported in part by NSF Grant CCF-1101389.
Funders:
Funding AgencyGrant Number
Simons Award for Graduate StudentsUNSPECIFIED
NSFCNS-1254169
NSFCNS-1518941
Binational Science Foundation (USA-Israel)2012348
Charles Lee Powell FoundationUNSPECIFIED
Google Faculty Research AwardUNSPECIFIED
Okawa FoundationUNSPECIFIED
Microsoft Faculty FellowshipUNSPECIFIED
NSFCCF-1101389
Alfred P. Sloan FoundationUNSPECIFIED
NSFCCF-1101389
Record Number:CaltechAUTHORS:20160120-105900294
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160120-105900294
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:63801
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 Jan 2016 20:20
Last Modified:03 Oct 2019 09:31

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