Sparsest cuts and concurrent flows in product graphs

Bonsma, Paul (2004) Sparsest cuts and concurrent flows in product graphs. Discrete Applied Mathematics, 136 (2-3). pp. 173-182. ISSN 0166-218X

PDF
Restricted to UT campus only: Request a copy
282Kb

Abstract:	A cut [S.S] is a sparsest cut of a graph G if its cut value [S][S]/[S.S] is maximum (this is the reciprocal of the well-known edge-density of the cut). In the (undirected) uniform concurrent flow problem on G, between every vertex pair of G flow paths with a total flow of 1 have to be established. The objective is to minimize the maximum amount of flow through an edge (edge congestion). The minimum congestion value of the uniform concurrent flow problem on G is an upper bound for the maximum cut value of cuts in G. If both values are equal, G is called a bottleneck graph. The bottleneck properties of cartesian product graphs G×H are studied. First, a flow in G×H is constructed using optimal flows in G and H, and proven to be optimal. Secondly, two cuts are constructed in G×H using sparsest cuts of G and H. It is shown that one of these cuts is a sparsest cut of G×H. As a consequence, we can prove that G×H is (not) a bottleneck graph if both G and H are (not) bottleneck graphs.
Item Type:	Article
Copyright:	© 2004 Elsevier
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Discrete Mathematics and Mathematical Programming (DMMP)
Link to this item:	http://purl.utwente.nl/publications/72726
Official URL:	http://dx.doi.org/10.1016/S0166-218X(03)00439-6
Export this item as:	BibTeX EndNote HTML Citation Reference Manager

Repository Staff Only: item control page

Metis ID: 219903