On Accuracy of Approximation for the Resource Constrained Shortest Path Problem

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...

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Published in:Journal of Siberian Federal University. Mathematics & Physics Vol. 12; no. 5; pp. 621 - 627
Main Author: Soldatenko, Aleksandr A.
Format: Journal Article
Language:English
Published: Krasnoyarsk Siberian Federal University 01.01.2019
Subjects:
Algorithms
Approximation
Critical path
Graph theory
Graphs
Mathematical analysis
Polynomials
Shortest-path problems
Weighting functions
ISSN:1997-1397, 2313-6022
Online Access:Get full text
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Abstract 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
AbstractList 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
The paper we considers the Resource Constrained Shortest Path problem (RCSP). This problem is NPhard 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 = k, which specifying its requirements from a finite set of resource. A polynomial time e-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 e approximation of the RCSP problem in O(\V|2) time. The present paper provides a proof of complexity and aproximation of RevTree algorithm.
Author Soldatenko, Aleksandr A.
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Cites_doi 10.1287/opre.42.5.977
10.1016/0022-247X(66)90020-5
10.1002/net.10090
10.1016/j.disopt.2014.08.001
10.1007/3-540-45253-2_30
10.1109/tnet.2007.900712
10.1016/j.cor.2016.04.013
10.1287/moor.17.1.36
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SubjectTerms Algorithms
Approximation
Critical path
Graph theory
Graphs
Mathematical analysis
Polynomials
Shortest-path problems
Weighting functions
Title On Accuracy of Approximation for the Resource Constrained Shortest Path Problem
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