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A New Algorithm for the Shortest Path Problems in a Directed Graph with Negative Weights

Xin Wang

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Abstract

The Dijkstra algorithm is a classical way for finding the shortest path,but it is not able to solve the shortest path problems with negative weights.This paper studies the shortest path problems with negative weights and brings forward a new algorithm to change a shortest path problem with negative weights to a shortest way problem with nonnegative weights.Finally we use the Dijkstra algorithm to solve the problem and the validity of the method is demonstrated by an example.Eventually the algorithm has some practical meaning.

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What this paper is about

The Dijkstra algorithm is a classical way for finding the shortest path,but it is not able to solve the shortest path problems with negative weights.This paper studies the shortest path problems with negative weights and brings forward a new algorithm to change a shortest path problem with negative weights to a shortest way problem with nonnegative weights.Finally we use the Dijkstra algorithm to solve the problem and the validity of the method is demonstrated by an example.Eventually the algorithm has some practical meaning.

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Available abstract

The Dijkstra algorithm is a classical way for finding the shortest path,but it is not able to solve the shortest path problems with negative weights.This paper studies the shortest path problems with negative weights and brings forward a new algorithm to change a shortest path problem with negative weights to a shortest way problem with nonnegative weights.Finally we use the Dijkstra algorithm to solve the problem and the validity of the method is demonstrated by an example.Eventually the algorithm has some practical meaning.

Key concepts: Yen's algorithm, Shortest path problem, Shortest Path Faster Algorithm, K shortest path routing, Dijkstra's algorithm, Suurballe's algorithm, Euclidean shortest path, Mathematics

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