TY - GEN

T1 - The communication complexity of distributed task allocation

AU - Drucker, Andrew

AU - Kuhn, Fabian

AU - Oshman, Rotem

PY - 2012

Y1 - 2012

N2 - We consider a distributed task allocation problem in which m players must divide a set of n tasks between them. Each player i receives as input a set X i of tasks such that the union of all input sets covers the task set. The goal is for each player to output a subset Y i ⊆ X i, such that the outputs (Y 1,...,Y m) form a partition of the set of tasks. The problem can be viewed as a distributed one-shot variant of the well-known k-server problem, and we also show that it is closely related to the problem of finding a rooted spanning tree in directed broadcast networks. We study the communication complexity and round complexity of the task allocation problem. We begin with the classical two-player communication model, and show that the randomized communication complexity of task allocation is Ω(n), even when the set of tasks is known to the players in advance. For the multi-player setting with m = O(n) we give two upper bounds in the shared-blackboard model of communication. We show that the problem can be solved in O(log n) rounds and O(n log n) total bits for arbitrary inputs; moreover, if for any set X of tasks, there are at least α|X| players that have at least one task from X in their inputs, then O((1/α + log m)log n) rounds suffice even if each player can only write O(log n) bits on the blackboard in each round. Finally, we extend our results to the case where the players communicate over an arbitrary directed communication graph instead of a shared blackboard. As an application of these results, we also consider the related problem of constructing a directed spanning tree in strongly-connected directed networks and we show lower and upper bounds for that problem.

AB - We consider a distributed task allocation problem in which m players must divide a set of n tasks between them. Each player i receives as input a set X i of tasks such that the union of all input sets covers the task set. The goal is for each player to output a subset Y i ⊆ X i, such that the outputs (Y 1,...,Y m) form a partition of the set of tasks. The problem can be viewed as a distributed one-shot variant of the well-known k-server problem, and we also show that it is closely related to the problem of finding a rooted spanning tree in directed broadcast networks. We study the communication complexity and round complexity of the task allocation problem. We begin with the classical two-player communication model, and show that the randomized communication complexity of task allocation is Ω(n), even when the set of tasks is known to the players in advance. For the multi-player setting with m = O(n) we give two upper bounds in the shared-blackboard model of communication. We show that the problem can be solved in O(log n) rounds and O(n log n) total bits for arbitrary inputs; moreover, if for any set X of tasks, there are at least α|X| players that have at least one task from X in their inputs, then O((1/α + log m)log n) rounds suffice even if each player can only write O(log n) bits on the blackboard in each round. Finally, we extend our results to the case where the players communicate over an arbitrary directed communication graph instead of a shared blackboard. As an application of these results, we also consider the related problem of constructing a directed spanning tree in strongly-connected directed networks and we show lower and upper bounds for that problem.

KW - directed spanning trees

KW - multiparty communication complexity

KW - task allocation

KW - unidirectional links

UR - http://www.scopus.com/inward/record.url?scp=84864972863&partnerID=8YFLogxK

U2 - 10.1145/2332432.2332443

DO - 10.1145/2332432.2332443

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84864972863

SN - 9781450314503

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 67

EP - 76

BT - PODC'12 - Proceedings of the 2012 ACM Symposium on Principles of Distributed Computing

T2 - 2012 ACM Symposium on Principles of Distributed Computing, PODC'12

Y2 - 16 July 2012 through 18 July 2012

ER -