Improved results for data migration and open shop scheduling

The data migration problem is to compute an efficient plan for moving data stored on devices in a network from one configuration to another. We consider this problem with the objective of minimizing the sum of completion times of all storage devices. 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 nonnegative weight, and each edge has a release time and a 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 a 9-approximation algorithm for the problem when edges have arbitrary processing times and are released at time zero. We improve Kim's result by giving a 5.06-approximation algorithm. We also address the open shop scheduling problem, O|r_j| Σ w_jC _j, and show that it is a special case of the data migration problem. Queyranne and Sviridenko (Journal of Scheduling, 5:287-305, 2002) gave a 5.83 -approximation algorithm for the nonpreemptive 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.