Scheduling parallel machines on-line
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Balanced allocations (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On-line routing of virtual circuits with applications to load balancing and machine scheduling
Journal of the ACM (JACM)
Online computation and competitive analysis
Online computation and competitive analysis
Expected Length of the Longest Probe Sequence in Hash Code Searching
Journal of the ACM (JACM)
Balanced allocations: the heavily loaded case
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
On-line Load Balancing for Related Machines
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Developments from a June 1996 seminar on Online algorithms: the state of the art
Developments from a June 1996 seminar on Online algorithms: the state of the art
How Asymmetry Helps Load Balancing
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Efficient job scheduling algorithms with multi-type contentions
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Hi-index | 0.00 |
In this paper we study the problem of assigning unit-size tasks to related machines when only limited online information is provided to each task. This is a general framework whose special cases are the classical multiple-choice games for the assignment of unit-size tasks to identical machines. The latter case was the subject of intensive research for the last decade. The problem is intriguing in the sense that the natural extensions of the greedy oblivious schedulers, which are known to achieve near-optimal performance in the case of identical machines, are proved to perform quite poorly in the case of the related machines.(MATH) In this work we present a rather surprising lower bound stating that any oblivious scheduler that assigns an arbitrary number of tasks to $n$ related machines would need $\Omega\left(\frac{\log n}{\l2 n}\right)$ polls of machine loads per task, in order to achieve a constant competitive ratio versus the optimum offline assignment of the same input sequence to these machines. On the other hand, we prove that the missing information for an oblivious scheduler to perform almost optimally, is the amount of tasks to be inserted into the system. In particular, we provide an oblivious scheduler that only uses $\O(\l2 n)$ polls, along with the additional information of the size of the input sequence, in order to achieve a constant competitive ratio vs. the optimum offline assignment. The philosophy of this scheduler is based on an interesting exploitation of the slowfit concept ([1, 5, 3]; for a survey see [6, 9, 16]) for the assignment of the tasks to the related machines despite the restrictions on the provided online information, in combination with a layered induction argument for bounding the tails of the number of tasks passing from slower to faster machines. We finally use this oblivious scheduler as the core of an adaptive scheduler that does not demand the knowledge of the input sequence and yet achieves almost the same performance.