in this article we present an algorithm for converting a network problem with several sources and several sinks including several transfer nodes and condition of supplying the demand of any sink from a particular source to the transportation problem.  towards this end, and considering the very special structure of transportation algorithm, after implementing the shortest path algorithm or solvi...

In this paper, we survey algorithms for shortest paths in dynamic networks. Although research on this problem spans over more than three decades, in the last couple of years many novel algorithmic techniques have been proposed. In this survey, we will make a special effort to abstract some combinatorial and algebraic properties, and some common data-structural tools that are at the base of thos...

This contribution investigates situations in pedestrian dynamics, where trying to walk the shortest path leads to largely different results than trying to walk the quickest path. A heuristic one-shot method to model the influence of the will to walk the quickest path is

So it suffices to consider the following two candidates for the shortest path from v and w. The first candidate follows a crossing edge to the opposite v′ of v, and then navigates around the cycle C2n to the target vertex w. The second candidate uses no crossing edges, and simply navigates around C2n. The first of these has length 1 + cv′w, and the second of these has length cvw; so to find a s...

Given a graph G on n vertices, the total distance of G is defined as σ(G) = 1 2 ∑ u,v∈V (G) d(u, v), where d(u, v) is the number of edges in a shortest path between u and v. We define the d-dimensional hypercube tree Td and show that it has a minimum total distance σ(Td) = 2σ(Hd) − ( n 2 ) = dn 2 2 − ( n 2 ) over all spanning trees of Hd, where Hd is the d-dimensional binary hypercube. It follo...

The all-pairs-shortest-length (APSL) problem of a graph is to nd the lengths of the shortest paths between all pairs of vertices. In this paper, we study the APSL problem on chordal bipartite graphs. By a simple reduction, we show that solving the APSL problem on chordal bipartite graphs can be transformed to solving the same problem on certain strongly chordal graphs. Consequently, there is an...