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The shortest path problem is a classical network problem that has been extensively studied. The problem of determining not only the shortest path, but also listing the K shortest paths (for a given integer K>1) is also a classical one but has not been studied so intensively, despite its obvious practical interest. Two different types of problems are usually considered: the unconstrained and the constrained K shortest paths problem. While in the former no restriction in considered in the definition of a path, in the constrained K shortest paths problem all the paths have to satisfy some condition – for example, to be loopless. In this paper new algorithms are proposed for the uncontrained problem, which compute a super set of the K shortest paths. It is also shown that ranking loopless paths does not hold in general the Optimality Principle and how the proposed algorithms for the unconstrained problem can be adapted for ranking loopless paths.

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Use of the theory of splines to approximate the potential energy surface in molecular dynamics is examined. It is envisaged that such an approximation should be able to accurately capture the potentials' behavior and be computationally cost effective, both for one-dimensional and n-dimensional problems with n arbitrary.