TY - GEN

T1 - Exact and Approximation Algorithms for Routing a Convoy Through a Graph

AU - van Ee, Martijn

AU - Oosterwijk, Tim

AU - Sitters, René

AU - Wiese, Andreas

N1 - Publisher Copyright:
© Martijn van Ee, Tim Oosterwijk, René Sitters, and Andreas Wiese;

PY - 2023/8

Y1 - 2023/8

N2 - 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.

AB - 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.

KW - approximation algorithms

KW - convoy routing

KW - shortest path problem

KW - traveling salesperson problem

UR - http://www.scopus.com/inward/record.url?scp=85171484142&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.MFCS.2023.86

DO - 10.4230/LIPIcs.MFCS.2023.86

M3 - Conference contribution

AN - SCOPUS:85171484142

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 48th International Symposium on Mathematical Foundations of Computer Science, MFCS 2023

A2 - Leroux, Jerome

A2 - Lombardy, Sylvain

A2 - Peleg, David

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 48th International Symposium on Mathematical Foundations of Computer Science, MFCS 2023

Y2 - 28 August 2023 through 1 September 2023

ER -