Fast approximation algorithms for routing problems with hop-wise constraints

• Published in: Annals of operations research Vol. 222; no. 1; pp. 279 - 291
• Main Author: Elalouf, Amir
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.11.2014; Springer; Springer Nature B.V
• Subjects: Algorithms; Analysis; Approximation; Approximation theory; Business and Management; Combinatorial optimization; Combinatorics; Delay; Job shops; Mathematical analysis; Mathematical research; Maximization; Operations research; Operations Research/Decision Theory; Optimization; Polynomials; Routing; Studies; Theory of Computation; Shortest path; Approximation algorithms; Combinatorial problems; Routing
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-013-1308-5

Given a graph G ( N , A ) with a cost (or benefit) and a delay on each arc, the constrained routing problem (CRP) aims to find a minimum-cost or a maximum-benefit path from a given source to a given destination node, subject to an end-to-end delay constraint. The problem (with a single constraint) is NP-hard, and has been studied by many researchers who found fully polynomial approximation schemes (FPAS) for this problem. The current paper focuses on a generalized CRP version, CRP with hop-wise constraints (CRPH). In the generalized version, instead of one constraint there are up to n −1 special-type constraints, where n is the number of nodes. An FPAS based on interval partitioning is proposed for both the minimization and the maximization versions of CRPH. For G ( N , A ) with n nodes and m arcs, the complexity of the algorithm is O( mn 2 / ε ).