Exact and approximation algorithms for routing a convoy through a graph Exact and approximation algorithms for routing a convoy through a graph

We study routing problems of a convoy in a graph, generalizing the shortest path problem (SPP), the travelling salesperson problem (TSP), and the Chinese postman problem (CPP) which are all well-studied in the classical (non-convoy) setting. We assume that each edge in the graph has a length and a s...

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Bibliographic Details
Published in:Mathematical programming Vol. 213; no. 1-2; pp. 985 - 1008
Main Authors: van Ee, Martijn, Oosterwijk, Tim, Sitters, René, Wiese, Andreas
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2025
Springer Nature B.V
Subjects:
Algorithms
Approximation
Automobiles
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Full Length Paper
Graph theory
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Pareto optimum
Polynomials
Shortest-path problems
Theoretical
Traveling salesman problem
Vehicles
Shortest path problem
68Q25
90C39
Approximation algorithms
68W25
90C27
Convoy routing
Traveling salesperson problem
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:We study routing problems of a convoy in a graph, generalizing the shortest path problem (SPP), the travelling salesperson problem (TSP), and the Chinese postman problem (CPP) which are all well-studied in the classical (non-convoy) setting. We assume that each edge in the graph has a length and a speed at which it can be traversed and that our convoy has a given length. While the convoy moves through the graph, parts of it can be located on different edges. For safety requirements, at all time the whole convoy needs to travel at the same speed which is dictated by the slowest edge on which currently a part of the convoy is located. For Convoy-SPP, we give a strongly polynomial time exact algorithm. For Convoy-TSP, we provide an O ( log n ) -approximation algorithm and an O (1)-approximation algorithm for trees. Both results carry over to Convoy-CPP which—maybe surprisingly—we prove to be NP -hard in the convoy setting. This contrasts the non-convoy setting in which the problem is polynomial time solvable.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-024-02159-z