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
Better bounds for online scheduling
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A lower bound for randomized on-line multiprocessor scheduling
Information Processing Letters
Randomized Algorithms for that Ancient Scheduling Problem
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
New lower and upper bounds for on-line scheduling
Operations Research Letters
Semi on-line algorithms for the partition problem
Operations Research Letters
Ordinal algorithms for parallel machine scheduling
Operations Research Letters
An optimal algorithm for preemptive on-line scheduling
Operations Research Letters
(Incremental) priority algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal Non-preemptive Semi-online Scheduling on Two Related Machines
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Semi-online scheduling with machine cost
Journal of Computer Science and Technology
Journal of Global Optimization
Preemptive semi-online scheduling with tightly-grouped processing times
Journal of Computer Science and Technology
Optimal preemptive semi-online scheduling on two uniform processors
Information Processing Letters
Optimal non-preemptive semi-online scheduling on two related machines
Journal of Algorithms
Optimal semi-online preemptive algorithms for machine covering on two uniform machines
Theoretical Computer Science
Semi-online scheduling jobs with tightly-grouped processing times on three identical machines
Discrete Applied Mathematics - Special issue: Max-algebra
Optimal semi-online algorithms for machine covering
Theoretical Computer Science
Semi-online scheduling problems on two identical machines with inexact partial information
Theoretical Computer Science
List scheduling for jobs with arbitrary release times and similar lengths
Journal of Scheduling
Semi-online machine covering for two uniform machines
Theoretical Computer Science
Semi-online scheduling jobs with tightly-grouped processing times on three identical machines
Discrete Applied Mathematics
Optimal preemptive semi-online scheduling on two uniform processors
Information Processing Letters
Optimal non-preemptive semi-online scheduling on two related machines
Journal of Algorithms
Randomized priority algorithms
Theoretical Computer Science
Best semi-online algorithms for unbounded parallel batch scheduling
Discrete Applied Mathematics
Semi-online scheduling with known partial information about job sizes on two identical machines
Theoretical Computer Science
Preemptive Online Scheduling with Reordering
SIAM Journal on Discrete Mathematics
Semi-online problems on identical machines with inexact partial information
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Preemptive semi-online scheduling on parallel machines with inexact partial information
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Online scheduling with reassignment
Operations Research Letters
Online and semi-online scheduling of two machines under a grade of service provision
Operations Research Letters
Semi-on-line problems on two identical machines with combined partial information
Operations Research Letters
Optimal preemptive semi-online scheduling to minimize makespan on two related machines
Operations Research Letters
Several semi-online scheduling problems on two identical machines with combined information
Theoretical Computer Science
Semi-online scheduling for jobs with release times
Journal of Combinatorial Optimization
Hi-index | 0.01 |
We investigate the problem of semi-online scheduling jobs on m identical parallel machines where the jobs arrive in order of decreasing sizes. We present a complete solution for the preemptive variant of semi-online scheduling with decreasing job sizes. We give matching lower and upper bounds on the competitive ratio for any fixed number m of machines; these bounds tend to (1+3)/2~1.36603, as the number of machines goes to infinity. Our results are also the best possible for randomized algorithms. For the non-preemptive variant of semi-online scheduling with decreasing job sizes, a result of Graham (SIAM J. Appl. Math. 17 (1969) 263-269) yields a (4/3-1/(3m))-competitive deterministic non-preemptive algorithm. For m=2 machines, we prove that this algorithm is the best possible (it is 7/6-competitive). For m=3 machines we give a lower bound of (1+37)/6~1.18046. Finally, we present a randomized non-preemptive 8/7-competitive algorithm for m=2 machines and prove that this is optimal.