We give a partial description of the (s, t)− p-path polytope of a directed graph D which is the convex hull of the incidence vectors of simple directed (s, t)-paths in D of length p. First, we point out how the (s, t) − p-path polytope is located in the family of path and cycle polyhedra. Next, we give some classes of valid inequalities which are very similar to inequalities which are valid for...

It is proved that radical of every generalized ring is a G-graded ideal when its index is an abelian group G. The relation between radicals of generalized rings and Γ-rings is given. The explicit formulas for generalized ring A and radical properties r = rb, rl, rj , rn are obtained: r(A) = g.m.r(A) = ∑ {r(Aij) | i, j ∈ I}. The relation between the radicals of path algebras and connectivity of ...

In the resource constrained shortest path problem (RCSPP) there is a directed graph along with a source node and a destination node, and each arc has a cost and a vector of weights specifying its requirements from a set of resource types with finite capacities. A minimum cost source-destination directed path is sought such that the total consumption of the arcs from each resource type does not ...

A digraph obtained by replacing each edge of a complete mpartite graph with an arc or a pair of mutually opposite arcs with the same end vertices is called a complete m-partite digraph. We describe an O(n) algorithm for finding a longest path in a complete m-partite (m ≥ 2) digraph with n vertices. The algorithm requires time O(n) in case of testing only the existence of a Hamiltonian path and ...

In this paper we suggest the use of light for performing useful computations. Namely, we propose a special device which uses light rays for solving the Hamiltonian path problem on a directed graph. The device has a graph-like representation and the light is traversing it following the routes given by the connections between nodes. In each node the rays are uniquely marked so that they can be ea...

In this paper we suggest the use of light for performing useful computations. Namely, we propose a special device which uses light rays for solving the Hamiltonian path problem on a directed graph. The device has a graph-like representation and the light is traversing it following the routes given by the connections between nodes. In each node the rays are uniquely marked so that they can be ea...

ss as: M atics J (2 Abstract This paper proposes an implementation for the directed diffusion paradigm aids in studying this paradigm’s operations and evaluates its behavior according to this implementation. The directed diffusion is evaluated with respect to the loss percentage, lifetime, end-to-end delay, and throughput. From these evaluations some suggestions and modifications are proposed t...

Edge-directed routing, a paradigm where sources and sinks of traffic, rather than the network, specify the communication path has recently gained attention as a means to deal effectively with potential conflicts that may arise between various stakeholders in the future Internet. In this paper, we use a simple economic model to show that contrary to current economic thinking, networks can deploy...