TY - GEN

T1 - Brief announcement

T2 - 25th International Symposium on Distributed Computing, DISC 2011

AU - Czygrinow, Andrzej

AU - Hanćkowiak, Michal

AU - Krzywdziński, Krzysztof

AU - Szymańska, Edyta

AU - Wawrzyniak, Wojciech

PY - 2011/11/2

Y1 - 2011/11/2

N2 - We consider the semi-matching problem in bipartite graphs. The network is represented by a bipartite graph G = (U ∪ V, E), where U corresponds to clients, V to 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 the square of its degree 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. Formally, given a bipartite graph G = ∪ V,E), a semi-matching in G is a subgraph M such that deg M (u) = 1 for every u ε U. A semi-matching M is called optimal if cost(M): = Σ v ε V (deg M (v))2 is minimal. It is not difficult to see that for any semi-matching M, where Δ is such that max v ε V d(v) ≤ Δ. Consequently, if M* is optimal and M is arbitrary, then cost (M) ≤ Δ|V|cost(M*)/|U|. Our main result shows that in some networks the Δ|V|/|U| factor can be reduced to a constant (Theorem 1).

AB - We consider the semi-matching problem in bipartite graphs. The network is represented by a bipartite graph G = (U ∪ V, E), where U corresponds to clients, V to 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 the square of its degree 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. Formally, given a bipartite graph G = ∪ V,E), a semi-matching in G is a subgraph M such that deg M (u) = 1 for every u ε U. A semi-matching M is called optimal if cost(M): = Σ v ε V (deg M (v))2 is minimal. It is not difficult to see that for any semi-matching M, where Δ is such that max v ε V d(v) ≤ Δ. Consequently, if M* is optimal and M is arbitrary, then cost (M) ≤ Δ|V|cost(M*)/|U|. Our main result shows that in some networks the Δ|V|/|U| factor can be reduced to a constant (Theorem 1).

UR - http://www.scopus.com/inward/record.url?scp=80055057821&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80055057821&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-24100-0_18

DO - 10.1007/978-3-642-24100-0_18

M3 - Conference contribution

AN - SCOPUS:80055057821

SN - 9783642240997

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

SP - 200

EP - 201

BT - Distributed Computing - 25th International Symposium, DISC 2011, Proceedings

Y2 - 20 September 2011 through 22 September 2011

ER -