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
A better lower bound for on-line scheduling
Information Processing Letters
Tighter bounds on a heuristic for a partition problem
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
Algorithms for Scheduling Independent Tasks
Journal of the ACM (JACM)
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
Off-line temporary tasks assignment
Theoretical Computer Science
On-Line Load Balancing of Temporary Tasks on Identical Machines
SIAM Journal on Discrete Mathematics
An Optimal On-Line Algorithm for Preemptive Scheduling on Two Uniform Machines in the lpNorm
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
A Lower Bound for the On-Line Preemptive Machine Scheduling with lpNorm
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Distributed flow detection over multi-path sessions
Computer Communications
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We consider the on-line load balancing problem where there are m identical machines (servers). Jobs arrive at arbitrary times, where each job has a weight and a duration. A job has to be assigned upon its arrival to exactly one of the machines. The duration of each job becomes known only upon its termination (this is called temporary tasks of unknown durations). Once a job has been assigned to a machine it cannot be reassigned to another machine. The goal is to minimize the maximum over time of the sum (over all machines) of the squares of the loads, instead of the traditional maximum load.Minimizing the sum of the squares is equivalent to minimizing the load vector with respect to the l2 norm. We show that for the l2 norm the greedy algorithm performs within at most 1.493 of the optimum. We show (an asymptotic) lower bound of 1.33 on the competitive ratio of the greedy algorithm. We also show a lower bound of 1.20 on the competitive ratio of any algorithm.We extend our techniques and analyze the competitive ratio of the greedy algorithm with respect to the lp norm. We show that the greedy algorithm performs within at most 2 - Ω(1/p) of the optimum. We also show a lower bound of 2 - O(In p/p) on the competitive ratio of any on-line algorithm.