Finding the shortest distance between any two locations one interesting problem often encountered, wide studied and investigated. In a given area while travelling from one place to other, there are places where movement is allowed and places where movement is not allowed. In this paper, we propose a method to find the shortest distance between two places that are a part of a wide spread area, taking into account parts from where the path may not be constructed.

The report considers solution to the problem of routing, the essence of which is to determine the shortest path length between any pair of computer network subscribers represented as an undirected graph, as one of the possible methods to increase the speed and performance of computer systems (CS). To carry out calculations and comparative analysis of the speed and productivity of CS in a positional binary number system (PNS) and in a non-positional number system in residual classes (residual number system-RNS), we consider one practical problem. Task is the routing problem, the essence of which is to determine the shortest path length, that is, to find the optimal data transmission route in the computer network.

Finding shortest path between two locations using matrix representation

Solving the Shortest Path Problem Using Integer Residual Arithmetic

http://www.civil.uwaterloo.ca/iTSS/papers/2006-3%20(Review%20of%20heuristic%20SPA).pdf

Heuristic shortest path algorithms for transportation applications: state of the art

Classical algorithms have been used to search over some space for finding the shortest paths problem between two points in a network and a minimal weight spanning tree for routing. Any classical algorithm deterministic or probabilistic will clearly used O(N) steps since on the average it will measure a large fraction of N records. Quantum algorithm is the fastest possible algorithm that can do several operations simultaneously due to their wave like properties. This wave gives an O( N ) steps quantum algorithm for identifying that record, where was used classical Dijkstra’s algorithm for finding shortest path problem in the graph of network and implement quantum search. Also we proposed the structure for non-classical
algorithms and design the various phases of the probabilistic quantum-classical algorithm for classical and
quantum parts. Finally, we represent the result of implementing and simulating Dijkstra's algorithm as the
probabilistic quantum-classical algorithm.

http://www.jatit.org/volumes/research-papers/Vol5No3/14Vol5No3.pdf

Finding shortest path between two locations using matrix representation

Citations

Solving the Shortest Path Problem Using Integer Residual Arithmetic

References

Heuristic shortest path algorithms for transportation applications: state of the art

A hybrid algorithm for finding shortest path in network routing.

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