Amortized efficiency of list update and paging rules
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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
Journal of Algorithms
The Power of Reordering for Online Minimum Makespan Scheduling
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Online Scheduling with Bounded Migration
Mathematics of Operations Research
Online scheduling with reassignment on two uniform machines
Theoretical Computer Science
Optimal semi-online algorithms for scheduling problems with reassignment on two identical machines
Information Processing Letters
Optimal algorithms for online scheduling with bounded rearrangement at the end
Theoretical Computer Science
Online scheduling with reassignment
Operations Research Letters
An optimal algorithm for preemptive on-line scheduling
Operations Research Letters
SIGACT news online algorithms column 21: APPROX and ALGO
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Recent advances for a classical scheduling problem
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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Makespan minimization on identical parallel machines is a classical scheduling problem. We consider the online scenario where a sequence of n jobs has to be scheduled non-preemptively on m machines so as to minimize the maximum completion time of any job. The best competitive ratio that can be achieved by deterministic online algorithms is in the range [1.88,1.9201]. Currently no randomized online algorithm with a smaller competitiveness is known, for general m. In this paper we explore the power of job migration, i.e. an online scheduler is allowed to perform a limited number of job reassignments. Migration is a common technique used in theory and practice to balance load in parallel processing environments. As our main result we settle the performance that can be achieved by deterministic online algorithms. We develop an algorithm that is αm-competitive, for any m≥2, where αm is the solution of a certain equation. For m=2, α2=4/3 and limm→∞αm=W−1(−1/e2)/(1+W−1(−1/e2))≈1.4659. Here W−1 is the lower branch of the Lambert W function. For m≥11, the algorithm uses at most 7m migration operations. For smaller m, 8m to 10m operations may be performed. We complement this result by a matching lower bound: No online algorithm that uses o(n) job migrations can achieve a competitive ratio smaller than αm. We finally trade performance for migrations. We give a family of algorithms that is c-competitive, for any 5/3≤c≤2. For c=5/3, the strategy uses at most 4m job migrations. For c=1.75, at most 2.5m migrations are used.