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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Bibliographic Details
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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Summary: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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ISSN:1997-1397
2313-6022
DOI:10.17516/1997-1397-2019-12-5-621-627