In this paper, we introduce the Steiner Bi-objective Shortest Path Problem. This problem is defined on a directed graph G=(V,A), with subset T?V of terminals. Arcs are labeled travel time and cost. The goal to find complete set efficient paths between every pair nodes in T. motivation behind stems from data preprocessing for vehicle routing problems. We propose solution method based labeling ap...

We study a new robust path problem, the Online Replacement Path problem (ORP). Consider the problem of routing a physical package through a faulty network G = (V,E) from a source s ∈ V to a destination t ∈ V as quickly as possible. An adversary, whose objective is to maximize the latter routing time, can choose to remove a single edge in the network. In one setup, the identity of the edge is re...

The shortest path problem is solved and applied to the calculations of half lives with respect to spontaneous fission of heavy nuclei. The dynamical programming method of Bellman and Kalaba is used to find the fission path in the d-dimensional space of deformation parameters. Fission half lives of heavy isotopes (100<Z<110) are shown and compared to the experimental data. 1. Introductory remark...

The optimal path planning of cooperative manipulators is studied in the present research. Optimal Control Theory is employed to calculate the optimal path of each joint choosing an appropriate index of the system to be minimized and taking the kinematics equations as the constraints. The formulation has been derived using Pontryagin Minimum Principle and results in a Two Point Boundary Value Pr...

multiple traveling salesman problem (mtsp) is one of the most popular operation research problem and is known as combinatorial optimization problems. mtsp is an extension version of the famous and widely used problem named traveling salesman problem (tsp). because of its benefices in various domains, many researchers have tried to solve that, and many methods have proposed so far. mtsp is a np-...

We study a problem related to finding shortest paths in weighted graphs. We ask whether or not there is a path between two nodes that has a given total cost k. The edge weights of the graph can be both positive and negative integers or even integer vectors. We show that many variants of this problem are NP-complete. We develop a pseudo-polynomial algorithm for (both positive and negative) integ...

In this paper, we consider the Hamiltonian alternating path problem for graphs, multigraphs, and digraphs. We describe an approach to solve the problem. This approach is based on constructing logical models for the problem. We use logical models for the Hamiltonian alternating path problem to solve the Hamiltonian path problem and the planning a typical working day for indoor service robots pro...

Let τ(G) denote the number of vertices in a longest path of the graph G and let k1 and k2 be positive integers such that τ(G) = k1+k2. The question at hand is whether the vertex set V (G) can be partitioned into two subsets V1 and V2 such that τ(G[V1]) ≤ k1 and τ(G[V2]) ≤ k2. We show that several classes of graphs have this partition property.