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Abstract: 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 indicate the data transfers
required between pairs of devices. Each vertex has a non-negative
weight, and each edge has a release time and a processing time. A
vertex completes when all the edges incident on it complete, under the
constraint 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 (in SODA 2003) gave a
9-approximation algorithm when edges have arbitrary processing times
and are released at time 0. We improve Kim's result by giving a
5.06-approximation algorithm.
We also address the open shop scheduling problem and show that it is a
special case of the data migration problem. Queyranne and Sviridenko
(J. of Scheduling, 2002) gave a 5.83-approximation algorithm for the
non-preemptive version of the open shop problem. They state as an
obvious open question whether there exists an algorithm for open shop
scheduling that gives a performance guarantee better than 5.83. Our
5.06 algorithm for data migration proves the existence of such an
algorithm. Crucial to our improved result is a property of the linear
programming relaxation for the problem. Similar linear programs have
been used for various other scheduling problems. Our technique may be
useful in obtaining improved results for these problems as well.
(Joint work with Rajiv Gandhi, Magn\'{u}s Halld\'{o}rsson and Guy
Kortsarz)
2004:
http://www-db.research.bell-labs.com/user/pfps