TY - GEN

T1 - Coordination complexity

T2 - 7th ACM Conference on Innovations in Theoretical Computer Science, ITCS 2016

AU - Cummings, Rachel

AU - Ligett, Katrina

AU - Radhakrishnan, Jaikumar

AU - Roth, Aaron

AU - Wu, Zhiwei Steven

PY - 2016/1/14

Y1 - 2016/1/14

N2 - We study 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 cen-Tralized 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 complex-ity of a problem imply the existence of good jointly differ-entially 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 coordi-nation complexity for the problem of computing a many-To-one matching in a bipartite graph by giving almost matching lower and upper bounds. Our upper bound in fact extends much more generally, to the problem of solving a linearly separable convex program. We also give a different uppe 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.

AB - We study 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 cen-Tralized 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 complex-ity of a problem imply the existence of good jointly differ-entially 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 coordi-nation complexity for the problem of computing a many-To-one matching in a bipartite graph by giving almost matching lower and upper bounds. Our upper bound in fact extends much more generally, to the problem of solving a linearly separable convex program. We also give a different uppe 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.

KW - Coordination complexity

KW - Privacy

UR - http://www.scopus.com/inward/record.url?scp=84966668221&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966668221&partnerID=8YFLogxK

U2 - 10.1145/2840728.2840767

DO - 10.1145/2840728.2840767

M3 - Conference contribution

AN - SCOPUS:84966668221

T3 - ITCS 2016 - Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science

SP - 281

EP - 290

BT - ITCS 2016 - Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science

PB - Association for Computing Machinery, Inc

Y2 - 14 January 2016 through 16 January 2016

ER -