On the 1.1 edge-coloring of multigraphs
SIAM Journal on Discrete Mathematics
Structure of a simple scheduling polyhedron
Mathematical Programming: Series A and B
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
On chromatic sums and distributed resource allocation
Information and Computation
On algorithms for efficient data migration
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Non-approximability Results for Scheduling Problems with Minsum Criteria
Proceedings of the 6th International IPCO Conference on Integer Programming and Combinatorial Optimization
Improved Scheduling Algorithms for Minsum Criteria
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
An Experimental Study of Data Migration Algorithms
WAE '01 Proceedings of the 5th International Workshop on Algorithm Engineering
Algorithms for data migration with cloning
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Data migration to minimize the total completion time
Journal of Algorithms
Improved results for data migration and open shop scheduling
ACM Transactions on Algorithms (TALG)
Improved bounds for sum multicoloring and scheduling dependent jobs with minsum criteria
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Improved algorithms for data migration
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Min sum edge coloring in multigraphs via configuration LP
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Improved algorithms for data migration
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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The data migration problem is to compute an efficient plan for moving data stored on devices in a network from one configuration to another. It is modeled by a transfer graph, where vertices represent the storage devices, and the edges represent the data transfers required between pairs of devices. Each vertex has a non-negative weight, and each edge has unit processing time. A vertex completes when all the edges incident on it complete; the constraint is that two edges incident on the same vertex cannot be processed simultaneously. The objective is to minimize the sum of weighted completion times of all vertices. Kim (Journal of Algorithms, 55:42-57, 2005) gave an LP-rounding 3-approximation algorithm. We give a more efficient primal-dual algorithm that achieves the same approximation guarantee, which can be extended to yield a 5.83-approximation for arbitrary processing times. We also study a variant of the open shop scheduling problem. This is a special case of the data migration problem in which the transfer graph is bipartite and the objective is to minimize the completion times of edges. We present a simple algorithm that achieves an approximation ratio of ${\sqrt{2}}$ ≈ 1.414, thus improving the 1.796-approximation given by Gandhi et al. (ACM Transaction on Algorithms, 2(1):116-129, 2006). We show that the analysis of our algorithm is almost tight.