scholarly journals The Resource Constrained Shortest Path Problem with uncertain data: A robust formulation and optimal solution approach

2019 ◽  
Vol 107 ◽  
pp. 140-155 ◽  
Author(s):  
Luigi Di Puglia Pugliese ◽  
Francesca Guerriero ◽  
Michael Poss
Keyword(s):  
Shortest Path ◽  
Uncertain Data ◽  
Optimal Solution ◽  
Shortest Path Problem ◽  
Resource Constrained ◽  
Solution Approach ◽  
Constrained Shortest Path ◽  
Robust Formulation ◽  
Resource Constrained Shortest Path

scholarly journals The resource constrained shortest path problem implemented in a lazy functional language

1996 ◽  
Vol 6 (1) ◽  
pp. 29-46
Author(s):  
Pieter H. Hartel ◽  
Hugh Glaser
Keyword(s):  
Shortest Path ◽  
Imperial College ◽  
Shortest Path Problem ◽  
Functional Language ◽  
Resource Constrained ◽  
Constrained Shortest Path ◽  
Np Hard Problem ◽  
Fortran Implementation ◽  
Data Files ◽  
Resource Constrained Shortest Path

AbstractThe resource constrained shortest path problem is an NP-hard problem for which many ingenious algorithms have been developed. These algorithms are usually implemented in Fortran or another imperative programming language. We have implemented some of the simpler algorithms in a lazy functional language. Benefits accrue in the software engineering of the implementations. Our implementations have been applied to a standard benchmark of data files, which is available from the Operational Research Library of Imperial College, London. The performance of the lazy functional implementations, even with the comparatively simple algorithms that we have used, is competitive with a reference Fortran implementation.

scholarly journals On Accuracy of Approximation for the Resource Constrained Shortest Path Problem

2019 ◽  
pp. 621-627
Author(s):  
Aleksandr A. Soldatenko
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Weight Functions ◽  
Resource Constrained ◽  
Additional Weight ◽  
Constrained Shortest Path ◽  
Finite Set ◽  
Labeling Method ◽  
Resource Constrained Shortest Path ◽  
Accuracy Of Approximation

The paper we considers the Resource Constrained Shortest Path problem (RCSP). This problem is NP- hard extension of a well-known shortest path problem in the directed graph G = (V;E). In the RCSP problem each arc e from E has a cost w(e) and additional weight functions ri(e); i = 1; : : : ; k, which specifying its requirements from a finite set of resource. A polynomial time ϵ-approximation algorithm RevTree based on node labeling method is presented in the paper. The main advantage of the RevTree algorithm over existing ones is its ability to produce ϵ approximation of the RCSP problem in O(jV j2) time. The present paper provides a proof of complexity and aproximation of RevTree algorithm

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