On minimum multigraphs with prescribed lower bounds on local line connectivities

Multiple path requirements for networks with integer line capacities (multigraphs) can be stated in a very general form by a reliabilIty matrixR, wherer(i,j)is the specified lower bound on the number of line-disjoint paths between points\upsilon_{i}and\upsilon_{j}in the multigraph. In light of the classical "max-flow, min-cut" theorem, this is equivalent to specifying local line connectivities. This paper presents a new and conceptually simple algorithm for constructing minimum size (total number of lines) multigraphs which satisfy the requirements specified in a reliability matrix.