TY - GEN

T1 - Distributed 2-Approximation Algorithm for the Semi-matching Problem

AU - Czygrinow, Andrzej

AU - Hanćkowiak, Michal

AU - Szymańska, Edyta

AU - Wawrzyniak, Wojciech

PY - 2012/11/9

Y1 - 2012/11/9

N2 - In this paper we consider the problem of matching clients with servers, each of which can process a subset of clients. It is known as the semi-matching or load balancing problem in a bipartite graph G = (V,U,E), where U corresponds to the clients, V to the servers, and E is the set of available connections between them. The goal is to find a set of edges M ⊆ E such that every vertex in U is incident to exactly one edge in M. The load of a server v ε V is defined as (d M (v)+1/2) where d M (v) is the degree of v in M, and the problem is to find an optimal semi-matching, i.e. a semi-matching that minimizes the sum of the loads of the servers. An optimal solution can be found sequentially in polynomial time but the distributed complexity is not well understood. Our algorithm yields (1 + 1/α)-approximation (where α = max{1, 1/2 (|U|/|V| + 1)}) and has time complexity O(Δ 5), where Δ is the maximum degree of a vertex in V. In particular, for Δ = O(1) it gives constant approximation with constant time complexity. We also give a fast algorithm for the case when Δ is large and the degrees in V and U satisfy some additional properties. Both algorithms are deterministic.

AB - In this paper we consider the problem of matching clients with servers, each of which can process a subset of clients. It is known as the semi-matching or load balancing problem in a bipartite graph G = (V,U,E), where U corresponds to the clients, V to the servers, and E is the set of available connections between them. The goal is to find a set of edges M ⊆ E such that every vertex in U is incident to exactly one edge in M. The load of a server v ε V is defined as (d M (v)+1/2) where d M (v) is the degree of v in M, and the problem is to find an optimal semi-matching, i.e. a semi-matching that minimizes the sum of the loads of the servers. An optimal solution can be found sequentially in polynomial time but the distributed complexity is not well understood. Our algorithm yields (1 + 1/α)-approximation (where α = max{1, 1/2 (|U|/|V| + 1)}) and has time complexity O(Δ 5), where Δ is the maximum degree of a vertex in V. In particular, for Δ = O(1) it gives constant approximation with constant time complexity. We also give a fast algorithm for the case when Δ is large and the degrees in V and U satisfy some additional properties. Both algorithms are deterministic.

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U2 - 10.1007/978-3-642-33651-5_15

DO - 10.1007/978-3-642-33651-5_15

M3 - Conference contribution

AN - SCOPUS:84868359325

SN - 9783642336508

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 210

EP - 222

BT - Distributed Computing - 26th International Symposium, DISC 2012, Proceedings

T2 - 26th International Symposium on Distributed Computing, DISC 2012

Y2 - 16 October 2012 through 18 October 2012

ER -