TY - GEN
T1 - Distributed weighted stable marriage problem
AU - Amira, Nir
AU - Giladi, Ran
AU - Lotker, Zvi
PY - 2010/7/14
Y1 - 2010/7/14
N2 - The Stable Matching problem was introduced by Gale and Shapley in 1962. The input for the stable matching problem is a complete bipartite Kn,n graph together with a ranking for each node. Its output is a matching that does not contain a blocking pair, where a blocking pair is a pair of elements that are not matched together but rank each other higher than they rank their current mates. In this work we study the Distributed Weighted Stable Matching problem. The input to the Weighted Stable Matching problem is a complete bipartite K n,n graph and a weight function W. The ranking of each node is determined by W, i.e. node v prefers node u1 over node u2 if W((v,u1)) > W((v, u2)). Using this ranking we can solve the original Stable Matching problem. We consider two different communication models: the billboard model and the full distributed model. In the billboard model, we assume that there is a public billboard and each participant can write one message on it in each time step. In the distributed model, we assume that each node can send O(log n) bits on each edge of the Kn,n. In the billboard model we prove a somewhat surprising tight bound: any algorithm that solves the Stable Matching problem requires at least n - 1 rounds. We provide an algorithm that meets this bound. In the distributed communication model we provide an algorithm named intermediation agencies algorithm, in short (IAA), that solves the Distributed Weighted Stable Marriage problem in O(√n) rounds. This is the first sub-linear distributed algorithm that solves some subcase of the general Stable Marriage problem.
AB - The Stable Matching problem was introduced by Gale and Shapley in 1962. The input for the stable matching problem is a complete bipartite Kn,n graph together with a ranking for each node. Its output is a matching that does not contain a blocking pair, where a blocking pair is a pair of elements that are not matched together but rank each other higher than they rank their current mates. In this work we study the Distributed Weighted Stable Matching problem. The input to the Weighted Stable Matching problem is a complete bipartite K n,n graph and a weight function W. The ranking of each node is determined by W, i.e. node v prefers node u1 over node u2 if W((v,u1)) > W((v, u2)). Using this ranking we can solve the original Stable Matching problem. We consider two different communication models: the billboard model and the full distributed model. In the billboard model, we assume that there is a public billboard and each participant can write one message on it in each time step. In the distributed model, we assume that each node can send O(log n) bits on each edge of the Kn,n. In the billboard model we prove a somewhat surprising tight bound: any algorithm that solves the Stable Matching problem requires at least n - 1 rounds. We provide an algorithm that meets this bound. In the distributed communication model we provide an algorithm named intermediation agencies algorithm, in short (IAA), that solves the Distributed Weighted Stable Marriage problem in O(√n) rounds. This is the first sub-linear distributed algorithm that solves some subcase of the general Stable Marriage problem.
KW - Billboard
KW - Distributed Algorithms
KW - Matching
KW - Scheduling
KW - Stable Marriage
UR - http://www.scopus.com/inward/record.url?scp=77954389123&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-13284-1_4
DO - 10.1007/978-3-642-13284-1_4
M3 - Conference contribution
AN - SCOPUS:77954389123
SN - 3642132839
SN - 9783642132834
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 29
EP - 40
BT - Structural Information and Communication Complexity - 17th International Colloquium, SIROCCO 2010, Proceedings
T2 - 17th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2010
Y2 - 7 June 2010 through 11 June 2010
ER -