TY - JOUR

T1 - On the complexity of distributed stable matching with small messages

AU - Kipnis, Alex

AU - Patt-Shamir, Boaz

N1 - Funding Information:
Boaz Patt-Shamir: Supported in part by the Israel Science Foundation (Grant 664/05).

PY - 2010/11

Y1 - 2010/11

N2 - We consider the distributed complexity of the stable matching problem (a.k.a. "stable marriage"). 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 unmatched 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 matching problem requires Ω√n/B\log n}) communication rounds in the worst case, even for graphs of diameter O(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, and if a pair is considered blocking only if they like each other much more then their assigned match.

AB - We consider the distributed complexity of the stable matching problem (a.k.a. "stable marriage"). 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 unmatched 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 matching problem requires Ω√n/B\log n}) communication rounds in the worst case, even for graphs of diameter O(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, and if a pair is considered blocking only if they like each other much more then their assigned match.

UR - http://www.scopus.com/inward/record.url?scp=78149407881&partnerID=8YFLogxK

U2 - 10.1007/s00446-010-0105-5

DO - 10.1007/s00446-010-0105-5

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AN - SCOPUS:78149407881

SN - 0178-2770

VL - 23

SP - 151

EP - 161

JO - Distributed Computing

JF - Distributed Computing

IS - 3

ER -