We consider generalized shortest path problems with cost and weight functions for the arcs of a graph. According to their weight arcs may generate or consume ow. Weights may be additive or multiplicative on a path. More precisely, if x units enter an arc a = (u; v) then x + w(a) resp. x w(a) leave it. The cost is charged per unit and summed over the edges of a path. If the weights multiply, the...

In this paper, we formulate a novel problem called Which-Edge question on shortest path queries. Specifically, this problem aims to find k edges that minimize the total distance for a given set of shortest path queries on a graph. This problem has important applications in logistics, urban planning, and network planning. We show the NP-hardness of the problem, as well as present efficient algor...

Here we present a novel visible analog computing approach for solving a wide class of shortest path problems. Using a microfluidic chip for computation, based on the lighting up of a glow discharge, the solution to maze search problems, the solution of a network shortest path and k-shortest paths problems and the practical application of finding the shortest paths between several landmarks from...

EEcient management of networks requires that the shortest route from one point (node) to another is known; this is termed the shortest path. It is often necessary to be able to determine alternative routes through the network, in case any part of the shortest path is damaged or busy. The k-shortest paths represent an ordered list of the alternative routes available. Four algorithms were selecte...

We study the problem of embedding shortest-path metrics weighted graphs into $\ell_p$ spaces. introduce a new technique based on low-depth decompositions graph via shortest paths. The notion Shortest Path Decomposition depth is inductively defined: A (weighed) path has decomposition (SPD) $1$. General an SPD $k$ if it contains whose deletion leads to graph, each components at most $k-1$. In thi...

  The traveling salesman problem is a well-known and important combinatorial optimization problem. The goal of this problem is to find the shortest Hamiltonian path that visits each city in a given list exactly once and then returns to the starting city. In this paper, for the first time, the shortest Hamiltonian path is achieved for 1071 Iranian cities. For solving this large-scale problem, tw...

In this paper we show that a very simple and efficient approach can be used to solve the all pairs almost shortest path problem on the class of weakly chordal graphs and its different subclasses. Moreover, this approach works well also on graphs with small size of largest induced cycle and gives a unified way to solve the all pairs almost shortest path and all pairs shortest path problems on di...

1 This paper studies algorithmic and combinatorial properties of shortest paths of different homo2 topy types in a polygonal domain with holes. We define the “second shortest path” to be the shortest 3 path that is homotopically different from the (first) shortest path; the kth shortest path for an arbitrary 4 integer k is defined analogously. We introduce the “kth shortest path map”—a structur...

Let G be a graph with the usual shortest-path metric. A graph is δ-hyperbolic if for every geodesic triangle T , any side of T is contained in a δ-neighborhood of the union of the other two sides. A graph is chordal if every induced cycle has at most three edges. In this paper we study the relation between the hyperbolicity of the graph and some chordality properties which are natural generaliz...

In many network routing problems several conflicting objectives must be considered. Even for the bi-objective shortest path problem, generating and presenting the whole set of nondominated solutions (paths) to a decision maker, in general, is not effective because the number of these paths can be very large. Interactive procedures are adequate to overcome these drawbacks. Current et al. [1] pro...