eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-08-20
6:1
6:12
10.4230/LIPIcs.MFCS.2019.6
article
An Improved Online Algorithm for the Traveling Repairperson Problem on a Line
Bienkowski, Marcin
1
https://orcid.org/0000-0002-2453-7772
Liu, Hsiang-Hsuan
1
https://orcid.org/0000-0002-0194-9360
Institute of Computer Science, University of Wrocław, Poland
In the online variant of the traveling repairperson problem (TRP), requests arrive in time at points of a metric space X and must be eventually visited by a server. The server starts at a designated point of X and travels at most at unit speed. Each request has a given weight and once the server visits its position, the request is considered serviced; we call such time completion time of the request. The goal is to minimize the weighted sum of completion times of all requests.
In this paper, we give a 5.429-competitive deterministic algorithm for line metrics improving over 5.829-competitive solution by Krumke et al. (TCS 2003). Our result is obtained by modifying the schedule by serving requests that are close to the origin first. To compute the competitive ratio of our approach, we use a charging scheme, and later evaluate its properties using a factor-revealing linear program which upper-bounds the competitive ratio.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol138-mfcs2019/LIPIcs.MFCS.2019.6/LIPIcs.MFCS.2019.6.pdf
traveling repairperson problem
competitive analysis
minimizing completion time
factor-revealing LP