A Strip-Packing Algorithm with Absolute Performance Bound 2
SIAM Journal on 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
On-line load balancing for related machines
Journal of Algorithms
Reverse-Fit: A 2-Optimal Algorithm for Packing Rectangles
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
On strip packing With rotations
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Competitiveness via primal-dual
ACM SIGACT News
Online algorithm for parallel job scheduling and strip packing
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
A fast 5/2-approximation algorithm for hierarchical scheduling
EuroPar'10 Proceedings of the 16th international Euro-Par conference on Parallel processing: Part I
Theoretical Computer Science
A (5/3 + ε)-approximation for strip packing
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Approximation algorithms for multiple strip packing
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
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We consider the on-line scheduling of parallel jobs in heterogeneous multiple clusters, in which a set of clusters is given and the parallel jobs arrive one by one, and the goal is to schedule all the jobs while minimizing the makespan. A cluster consists of many identical processors. A parallel job may require several processors in one cluster to execute it simultaneously. In this paper, we investigate two variants of the heterogeneous clusters. First, for the clusters of different widths (number of processors) but identical processor speeds, we provide an on-line algorithm with a competitive ratio at most of 14.2915. Second, for the clusters of different speeds but identical widths, we provide an on-line algorithm with a competitive ratio at most of 18.2788.