eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-08-23
69:1
69:15
10.4230/LIPIcs.MFCS.2024.69
article
Scheduling with Locality by Routing
Liu, Alison Hsiang-Hsuan
1
https://orcid.org/0000-0002-0194-9360
Liu, Fu-Hong
2
https://orcid.org/0000-0001-6073-8179
Department of Information and Computing Sciences, Utrecht University, The Netherlands
Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu, Taiwan
This work examines a strongly NP-hard routing problem on trees, in which multiple servers need to serve a given set of requests (on vertices), where the routes of the servers start from a common source and end at their respective terminals. Each server can travel free of cost on its source-to-terminal path but has to pay for travel on other edges. The objective is to minimize the maximum cost over all servers. As the servers may pay different costs for traveling through a common edge, balancing the loads of the servers can be difficult. We propose a polynomial-time 4-approximation algorithm that applies the parametric pruning framework but consists of two phases. The first phase of the algorithm partitions the requests into packets, and the second phase of the algorithm assigns the packets to the servers. Unlike the standard parametric pruning techniques, the challenge of our algorithm design and analysis is to harmoniously relate the quality of the partition in the first phase, the balances of the servers' loads in the second phase, and the hypothetical optimal values of the framework. For the problem in general graphs, we show that there is no algorithm better than 2-approximate unless P = NP. The problem is a generalization of unrelated machine scheduling and other classic scheduling problems. It also models scheduling problems where the job processing times depend on the machine serving the job and the other jobs served by that machine. This modeling provides a framework that physicalizes scheduling problems through the graph’s point of view.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol306-mfcs2024/LIPIcs.MFCS.2024.69/LIPIcs.MFCS.2024.69.pdf
Makespan minimization
Approximation algorithms
Routing problems
Parametric pruning framework