Outerstring graphs are the intersection graphs of curves that lie inside a disk such that each curve intersects the boundary of the disk. Outerstring graphs are among the most general classes of intersection graphs studied. To date, no polynomial time algorithm is known for any of the classical graph optimization problems on outerstring graphs; in fact, most are NP-hard. It is known that there ...

In this paper, a new method for developing a lower bound on exact completion time distribution function of stochastic PERT networks is provided that is based on simplifying the structure of this type of network. The designed mechanism simplifies network structure by arc duplication so that network distribution function can be calculated only with convolution and multiplication. The selection of...

in this survey, we give an overview over some aspects of the set of tilting objects in an $m-$cluster category, with focus on those properties which are valid for all $m geq 1$. we focus on the following three combinatorial aspects: modeling the set of tilting objects using arcs in certain polygons, the generalized assicahedra of fomin and reading, and colored quiver mutation.

The Minimum Cost Path Problem with Relays (MCPPR) consists of finding a minimum cost path from a source to a destination, along which relay nodes are located at a certain cost, subject to a weight constraint. This paper first models the MCPPR as a particular bicriteria path problem involving an aggregated function of the path and relay costs, as well as a weight function. A variant of this prob...

In a network, each arc is assigned a weight. The weight of a path or a cycle is defined as the minimum weight of its arcs. The maximum of weights of all paths between two nodes is defined as the strength of connectedness between the nodes. In network applications, the reduction in the strength of connectedness is more relevant than the total disconnection of the graph. A graph is totally weight...

OSPF, or Open Shortest Path First, is a commonly used interior gateway protocol. An integer weight is assigned to each arc and the entire network topology and arc weights are known to each router. Each router computes a graph of shortest weight paths from itself to every other router in the network. Traffic is routed on the shortest weight paths. All traffic leaving router s with destination ro...

The main purpose of this paper is to characterize the continuous images of arcs by their images of the weight ≤ א1. More precisely, we will show that a compact space X is the continuous image of an arc if and only if every continuous image Y = f(X) with w(Y)≤ א1 is a continuous image of an arc.