Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
The asymptotic optimality of the LPT rule
Mathematics of Operations Research
Asymptotic analysis of an algorithm for balanced parallel processor scheduling
SIAM Journal on Computing
Tighter bounds on a heuristic for a partition problem
Information Processing Letters
The modified differencing method for the set partitioning problem with cardinality constraints
Discrete Applied Mathematics
Algorithms for Scheduling Independent Tasks
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Differencing Method of Set Partitioning
The Differencing Method of Set Partitioning
A tight upper bound for the k-partition problem on ideal sets
Operations Research Letters
Hi-index | 5.23 |
Given a set of positive numbers, the max-min partition problem asks for a k-partition such that the minimum part is maximized. The min-ratio partition problem has the similar definition but the objective is to minimize the ratio of the maximum to the minimum parts. In this paper, we analyze the performances of the longest processing time (LPT) algorithm for the two problems. We show that the tight bounds of the LPT are, respectively (4k - 2)/(3k - 1) and 7/5.