We study variants of the capacitated vehicle routing problem. In the multiple depot capacitated k-travelling repairmen problem (MD-CkTRP), we have a collection of clients to be served by one vehicle in a fleet of k identical vehicles based at given depots. Each client has a given demand that must be satisfied, and each vehicle can carry a total of at most Q demand before it must resupply at its...

The monoclonal anti-phosphotyrosine antibody (PTA) recognized proteins related to relative molecular mass regions of 94,000 +/- 3000 and 46,000 +/- 3000 Mr on Western blots of detergent-solubilized non-capacitated human sperm extract (HSE). The pattern of phosphorylation at tyrosine residues depended upon the physiological state of the sperm cells. At least six protein bands corresponding to fo...

Many classical results in graph theory are equivalent to the maximum-flow minimum-cut theorem of network-flow theory [l]. These results include Tutte’s characterization of maximum matchings in general graphs, Hall’s theorem on bipartite matching, and Menger’s theorem on connectivity. Equivalence among these problems is established by constructing appropriate (O,l)communication networks which pe...

In mammals, after coitus a small number of spermatozoa enter the uterine tube and following attachment to uterine tube epithelium are arrested in a non-capacitated state until peri-ovulatory signalling induces their detachment. Whilst awaiting release low numbers of spermatozoa continually detach from the epithelium and the uterine tube reservoir risks depletion. There is evidence of attachment...

In this paper we study the capacitated vertex cover problem, a generalization of the well-known vertex cover problem. Given a graph G = (V ,E) with weights on the vertices, the goal is to cover all the edges by picking a cover of minimum weight from the vertices. When we pick a copy of a vertex, we pay the weight of the vertex and cover up to a pre-specified number of edges incident on this ver...