Amortized efficiency of list update and paging rules
Communications of the ACM
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
Barely random algorithms for multiprocessor scheduling
Journal of Scheduling - Special issue: On-line scheduling
Semi-online scheduling jobs with tightly-grouped processing times on three identical machines
Discrete Applied Mathematics - Special issue: Max-algebra
Preemptive online scheduling: optimal algorithms for all speeds
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Path-independent load balancing with unreliable machines
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Better bounds for online load balancing on unrelated machines
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Randomized Online Scheduling of Unit Length Intervals and Jobs
Approximation and Online Algorithms
Online parallel machines scheduling with two hierarchies
Theoretical Computer Science
Semi-online scheduling jobs with tightly-grouped processing times on three identical machines
Discrete Applied Mathematics
Distributed flow detection over multi-path sessions
Computer Communications
Randomized priority algorithms
Theoretical Computer Science
On robust online scheduling algorithms
Journal of Scheduling
An overview on automatic capacity planning
From Integrated Publication and Information Systems to Virtual Information and Knowledge Environments
Semi-online scheduling revisited
Theoretical Computer Science
Online scheduling with reassignment
Operations Research Letters
New upper and lower bounds for online scheduling with machine cost
Discrete Optimization
On the robustness of graham's algorithm for online scheduling
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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(MATH) We study one of the most basic problems in online scheduling. A sequence of jobs has to be scheduled on $m$ identical parallel machines so as to minimize the makespan. Whenever a new job arrives, its processing time is known in advance. The job has to be scheduled immediately on one of the machines without knowledge of any future jobs. In the sixties Graham presented the famous List scheduling algorithm which is $(2-{1\over m})$-competitive. In the last ten years deterministic online algorithms with an improved competitiveness have been developed. The first algorithm with a performance guarantee asymptotically smaller than 2 was 1.986- competitive. The competitive ratio was first improved to 1.945 and then to 1.923 and 1.9201. Randomized competitive algorithms that are better than (known) deterministic algorithms were proposed for specific values of $m$, i.e. for $m\in\{2,\ldots,7\}$.(MATH) In this paper we present the first randomized online algorithm that performs better than known deterministic algorithms for general $m$. The algorithm is a combination of two deterministic scheduling strategies $A_1$ and $A_2$. Initially, when starting the scheduling process, a scheduler chooses $A_i$, $i\in\{1,2\}$, with probability ${1\over 2}$ and then serves the entire job sequence using the chosen algorithm. The new randomized algorithm is 1.916-competitive. We prove that this performance cannot be achieved by a deterministic algorithm based on analysis techniques that have been used in the literature so far: Using know techniques (or generalizations) it is impossible to prove a competitiveness smaller than 1.919 for any deterministic online algorithm. Our results strictly limit the performance that can be achieved with existing techniques.