TY - GEN

T1 - A note on distributed stable matching

AU - Kipnis, Alex

AU - Patt-Shamir, Boaz

PY - 2009

Y1 - 2009

N2 - We consider the distributed complexity of the stable marriage problem. In this problem, the communication graph is undirected and bipartite, and each node ranks its neighbors. Given a matching of the nodes, a pair of nodes is called blocking if they prefer each other to their assigned match. A matching is called stable if it does not induce any blocking pair. In the distributed model, nodes exchange messages in each round over the communication links, until they find a stable matching. We show that if messages may contain at most B bits each, then any distributed algorithm that solves the stable marriage problem requires Ω(√n/B log n) communication rounds in the worst case, even for graphs of diameter Θ(log n), where n is the number of nodes in the graph. Furthermore, the lower bound holds even if we allow the output to contain O(√n) blocking pairs. We also consider ε-stability, where a pair is called ε-blocking if they can improve the quality of their match by more than an ε fraction, for some 0 ≤ ε ≤ 1. Our lower bound extends to ε-stability where " is arbitrarily close to 1/2. We also present a simple distributed algorithm for ε-stability whose time complexity is O(n/ε)

AB - We consider the distributed complexity of the stable marriage problem. In this problem, the communication graph is undirected and bipartite, and each node ranks its neighbors. Given a matching of the nodes, a pair of nodes is called blocking if they prefer each other to their assigned match. A matching is called stable if it does not induce any blocking pair. In the distributed model, nodes exchange messages in each round over the communication links, until they find a stable matching. We show that if messages may contain at most B bits each, then any distributed algorithm that solves the stable marriage problem requires Ω(√n/B log n) communication rounds in the worst case, even for graphs of diameter Θ(log n), where n is the number of nodes in the graph. Furthermore, the lower bound holds even if we allow the output to contain O(√n) blocking pairs. We also consider ε-stability, where a pair is called ε-blocking if they can improve the quality of their match by more than an ε fraction, for some 0 ≤ ε ≤ 1. Our lower bound extends to ε-stability where " is arbitrarily close to 1/2. We also present a simple distributed algorithm for ε-stability whose time complexity is O(n/ε)

UR - http://www.scopus.com/inward/record.url?scp=70350222220&partnerID=8YFLogxK

U2 - 10.1109/ICDCS.2009.69

DO - 10.1109/ICDCS.2009.69

M3 - פרסום בספר כנס

AN - SCOPUS:70350222220

SN - 9780769536606

T3 - Proceedings - International Conference on Distributed Computing Systems

SP - 466

EP - 473

BT - 2009 29th IEEE International Conference on Distributed Computing Systems Workshops, ICDCS, 09

Y2 - 22 June 2009 through 26 June 2009

ER -