TY - GEN

T1 - On the power of the congested clique model

AU - Drucker, Andrew

AU - Kuhn, Fabian

AU - Oshman, Rotem

PY - 2014

Y1 - 2014

N2 - We study the computation power of the congested clique, a model of distributed computation where n players communicate with each other over a complete network in order to compute some function of their inputs. The number of bits that can be sent on any edge in a round is bounded by a parameter b. We consider two versions of the model: in the first, the players communicate by unicast, allowing them to send a different message on each of their links in one round; in the second, the players communicate by broadcast, sending one message to all their neighbors. It is known that the unicast version of the model is quite powerful; to date, no lower bounds for this model are known. In this paper we provide a partial explanation by showing that the unicast congested clique can simulate powerful classes of bounded-depth circuits, implying that even slightly super-constant lower bounds for the congested clique would give new lower bounds in circuit complexity. Moreover, under a widely-believed conjecture on matrix multiplication, the triangle detection problem, studied in [8], can be solved in O(nε) time for any ε > 0. The broadcast version of the congested clique is the wellknown multi-party shared-blackboard model of communication complexity (with number-in-hand input). This version is more amenable to lower bounds, and in this paper we show that the subgraph detection problem studied in [8] requires polynomially many rounds for several classes of sub-graphs. We also give upper bounds for the subgraph detection problem, and relate the hardness of triangle detection in the broadcast congested clique to the communication complexity of set disjointness in the 3-party number-on-forehead model.

AB - We study the computation power of the congested clique, a model of distributed computation where n players communicate with each other over a complete network in order to compute some function of their inputs. The number of bits that can be sent on any edge in a round is bounded by a parameter b. We consider two versions of the model: in the first, the players communicate by unicast, allowing them to send a different message on each of their links in one round; in the second, the players communicate by broadcast, sending one message to all their neighbors. It is known that the unicast version of the model is quite powerful; to date, no lower bounds for this model are known. In this paper we provide a partial explanation by showing that the unicast congested clique can simulate powerful classes of bounded-depth circuits, implying that even slightly super-constant lower bounds for the congested clique would give new lower bounds in circuit complexity. Moreover, under a widely-believed conjecture on matrix multiplication, the triangle detection problem, studied in [8], can be solved in O(nε) time for any ε > 0. The broadcast version of the congested clique is the wellknown multi-party shared-blackboard model of communication complexity (with number-in-hand input). This version is more amenable to lower bounds, and in this paper we show that the subgraph detection problem studied in [8] requires polynomially many rounds for several classes of sub-graphs. We also give upper bounds for the subgraph detection problem, and relate the hardness of triangle detection in the broadcast congested clique to the communication complexity of set disjointness in the 3-party number-on-forehead model.

KW - Congested clique

KW - Lower bounds

KW - Subgraph detection

UR - http://www.scopus.com/inward/record.url?scp=84905485557&partnerID=8YFLogxK

U2 - 10.1145/2611462.2611493

DO - 10.1145/2611462.2611493

M3 - פרסום בספר כנס

AN - SCOPUS:84905485557

SN - 9781450329446

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

SP - 367

EP - 376

BT - PODC 2014 - Proceedings of the 2014 ACM Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

Y2 - 15 July 2014 through 18 July 2014

ER -