Recently a new least-squares primal-dual (LSPD) algorithm, that is impervious to degeneracy, has effectively been applied to solving linear programming problems by Barnes et al., 2002. In this paper, we show an application of LSPD to shortest path problems with nonnegative arc length is equivalent to the Dijkstra’s algorithm. We also compare the LSPD algorithm with the conventional primal-dual ...

We discuss the generalization of the point-to-point (and single-source) shortest path problem to instances where the shortest path must satisfy a formal language constraint. We describe theoretical and experimental results on a generalization of Dijkstra’s algorithm to finding regular-language-constrained shortest paths. This algorithm forms a model for single-source shortest paths and point-to...

We give algorithmic results for combinatorial problems with cost arrays possessing certain algebraic Monge properties. We extend Monge-array results for two shortest path problems to a general algebraic setting, with values in an ordered commutative semigroup, if the semigroup operator is strictly compatible with the order relation. We show how our algorithms can be modified to solve bottleneck...

Shortest path problems are a well-studied class of problems in theoretical computer science. One particularly applicable type of shortest path problem is to find the geodesic shortest path on a terrain. This type of algorithm finds the shortest path between two points that stays on the surface of a terrain. The most popular methods for finding such a shortest path involve a variant of Dijkstra’...

In real-world optimization problems, effective path planning is important. The Shortest Path Problem (SPP) model a classical operations research that can be applied to determine an efficient from the starting point end in plan. However, real world, uncertainty often encountered and must faced. Significant factors problem of determining shortest are problems difficult predict, therefore new crit...

Given a communication network or a road network one of the most natural algorithmic question is how to determine the shortest path from one point to another. In this paper we deal with one of the most fundamental problems of Graph Theory, the All Pairs Shortest Path (APSP) problem. We study three algorithms namely The FloydWarshall algorithm, APSP via Matrix Multiplication and the Johnson’s alg...

When facing a real world, optimization problems mainly become multiobjective i.e. they have several criteria of excellence. A multi-criteria problem submitted for multi-criteria evaluation is a complex problem, as usually there is no optimal solution, and no alternative is the best one according to all criteria. However, if a metaheuristic algorithm is combined with a Multi-Criteria Decision-Ma...