Thek-partitioning problem
- 1 February 1998
- journal article
- Published by Springer Science and Business Media LLC in Mathematical Methods of Operations Research
- Vol. 47 (1), 59-82
- https://doi.org/10.1007/bf01193837
Abstract
Thek-partitioning problem is defined as follows: Given a set of items {I 1,I 2,...,I n} where itemIj is of weightwj ≥ 0, find a partitionS 1,S 2,...,S m of this set with ¦S i ¦ =k such that the maximum weight of all subsetsS i is minimal,k-partitioning is strongly related to the classical multiprocessor scheduling problem of minimizing the makespan on identical machines. This paper provides suitable tools for the construction of algorithms which solve exactly the problem. Several approximation algorithms are presented for this NP-hard problem. The worst-case behavior of the algorithms is analyzed. The best of these algorithms achieves a performance bound of 4/3.Keywords
This publication has 5 references indexed in Scilit:
- A note on LPT schedulingOperations Research Letters, 1993
- A tight bound for 3-partitioningDiscrete Applied Mathematics, 1993
- An Application of Bin-Packing to Multiprocessor SchedulingSIAM Journal on Computing, 1978
- Bounds on Multiprocessing Timing AnomaliesSIAM Journal on Applied Mathematics, 1969
- Bounds for Certain Multiprocessing AnomaliesBell System Technical Journal, 1966