Amortized efficiency of list update and paging rules
Communications of the ACM
Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
On the performance of on-line algorithms for partition problems
Acta Cybernetica
An on-line scheduling heuristic with better worst case ratio than Graham's list scheduling
SIAM Journal on Computing
A better lower bound for on-line scheduling
Information Processing Letters
A lower bound for randomized on-line scheduling algorithms
Information Processing Letters
New algorithms for an ancient scheduling problem
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
A better algorithm for an ancient scheduling problem
Journal of Algorithms
A lower bound for randomized on-line multiprocessor scheduling
Information Processing Letters
Better Bounds for Online Scheduling
SIAM Journal on Computing
Generating adversaries for request-answer games
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Theoretical Computer Science
On randomized online scheduling
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Improved Bounds for the Online Scheduling Problem
SIAM Journal on Computing
The On-Line Multiprocessor Scheduling Problem with Known Sum of the Tasks
Journal of Scheduling
Semi-on-line multiprocessor scheduling with given total processing time
Theoretical Computer Science
Semi-online scheduling on two uniform processors
Theoretical Computer Science
The Power of Reordering for Online Minimum Makespan Scheduling
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Semi on-line algorithms for the partition problem
Operations Research Letters
Recent advances for a classical scheduling problem
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Semi-online scheduling problems on a small number of machines
Journal of Scheduling
| Hi-index | 5.23 |
Makespan minimization on m identical machines is a fundamental scheduling problem. The goal is to assign a sequence of jobs, each specified by a processing time, to parallel machines so as to minimize the maximum completion time of any job. Deterministic online algorithms achieve a competitive ratio of about 1.92. Due to this relatively high competitiveness and the lack of progress in the area of randomized online strategies, recent research has investigated scenarios where the online constraint is relaxed. We study semi-online scheduling where at any time an online scheduler knows the sum of the jobs' processing times. This problem relaxation is well motivated by practical applications. The best known semi-online algorithm achieves a competitive ratio of 1.6 (Cheng, Kellerer, Kotov, 2005 [11]). The best known lower bound is equal to 1.565 (Angelelli, Nagy, Speranza, Tuza, 2004 [3]). In this paper, we present two contributions for semi-online scheduling. We develop an improved lower bound showing that no deterministic semi-online algorithm can attain a competitive ratio smaller than 1.585. This significantly reduces the gap between the previous lower bound and the upper bound of 1.6. Second, we present a new semi-online algorithm that is based on an approach different from that of previous strategies. The algorithm is 1.75-competitive and hence does not achieve the best possible competitiveness. However, our algorithm is extremely simple and, unlike previous strategies, does not resort to job classes. The algorithm is more in the spirit of online algorithms not using any extra information. Hence our upper bound highlights the additional power of a small piece of advice when provided to an online algorithm.