In wireless communication QoS is an important parameter needed to be discussed for research analysis. The previous works faces problem in QoS in ad hoc networks increasingly in throughput analysis. Here we adopted a new approach for energy saving control provisions in ad hoc networks. Here a set of nodes is given in a plane which have end-to-end traffic demands and has delay bound between all n...

A multigraph is degree-splittable if it decomposes into two submultigraphs whose degree lists are the same, plus one leftover edge when the total number of edges is odd. We prove that a connected multigraph is degree-splittable if it has an even number of vertices of each odd degree. For caterpillars, we characterize the splittable caterpillars with diameter at most 4, provide a general suffici...

Variable-length splittable codes are derived from encoding sequences of ordered integer pairs, where one of the pair’s components is upper bounded by some constant, and the other one is any positive integer. Each pair is encoded by the concatenation of two fixed independent prefix encoding functions applied to the corresponding components of a pair. The codeword of such a sequence of pairs cons...

In the k-splittable flow problem, each commodity can only use at most k paths and the key point is to find the suitable transmitting paths for each commodity. To guarantee the efficiency of the network, minimizing congestion is important, but it is not enough, the cost consumed by the network is also needed to minimize. Most researches restrict to congestion or cost, but not the both. In this p...

We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of component coloring of graphs. Given a graph, the problem is to color the vertices using the minimum number of colors so that the size of each connected component of the subgraph induced by the vertices of the same color does not exceed C. We give a linear time algorithm for the problem ...

We study the quality of equilibrium in atomic splittable routing games. We show that in single-source single-sink games on seriesparallel graphs, the price of collusion — the ratio of the total delay of atomic Nash equilibrium to the Wardrop equilibrium — is at most 1. This proves that the existing bounds on the price of anarchy for Wardrop equilibria carry over to atomic splittable routing gam...

A graph G = (V, E) is called weakly four-connected if G is 4-edge-connected and G − x is 2-edge-connected for all x ∈ V . We give sufficient conditions for the existence of ‘splittable’ vertices of degree four in weakly four-connected graphs. By using these results we prove that every minimally weakly fourconnected graph on at least four vertices contains at least three ‘splittable’ vertices of...