Scheduling independent tasks on uniform processors
SIAM Journal on Computing
Tighter bounds for LPT scheduling on uniform processors
SIAM Journal on Computing
An On-Line Algorithm for Some Uniform Processor Scheduling
SIAM Journal on Computing
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
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
Truthful Mechanisms for One-Parameter Agents
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Fast monotone 3-approximation algorithm for scheduling related machines
ESA'05 Proceedings of the 13th annual European conference on Algorithms
A deterministic truthful PTAS for scheduling related machines
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Lower bound for envy-free and truthful makespan approximation on related machines
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
The price of anarchy on uniformly related machines revisited
Information and Computation
Hi-index | 0.00 |
Q||C"m"a"x denotes the problem of scheduling n jobs on m machines of different speeds such that the makespan is minimized. In the paper two special cases of Q||C"m"a"x are considered: case I, when m-1 machine speeds are equal, and there is only one faster machine; and case II, when machine speeds are all powers of 2 (2-divisible machines). Case I has been widely studied in the literature, while case II is significant in an approach to design so called monotone algorithms for the scheduling problem. We deal with the worst case approximation ratio of the classic list scheduling algorithm 'Largest Processing Time (LPT)'. We provide an analysis of this ratio Lpt/Opt for both special cases: For 'one fast machine', a tight bound of (3+1)/2~1.3660 is given. For 2-divisible machines, we show that in the worst case 1.3673(3+1)/2 when LPT breaks ties arbitrarily. To our knowledge, the best previous lower and upper bounds were (4/3,3/2-1/2m] in case I [T. Gonzalez, O.H. Ibarra, S. Sahni, Bounds for LPT schedules on uniform processors, SIAM Journal on Computing 6 (1) (1977) 155-166], respectively [4/3-1/3m,3/2] in case II [R.L. Graham, Bounds on multiprocessing timing anomalies, SIAM Journal on Applied Mathematics 17 (1969) 416-429; A. Kovacs, Fast monotone 3-approximation algorithm for scheduling related machines, in: Proc. 13th Europ. Symp. on Algs. (ESA), in: LNCS, vol. 3669, Springer, 2005, pp. 616-627]. Moreover, Gonzalez et al. conjectured the lower bound 4/3 to be tight in the 'one fast machine' case [T. Gonzalez, O.H. Ibarra, S. Sahni, Bounds for LPT schedules on uniform processors, SIAM Journal on Computing 6 (1) (1977) 155-166].