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An improved approximation scheme for the Group Steiner Problem

✍ Scribed by C. S. Helvig; Gabriel Robins; Alexander Zelikovsky

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
322 KB
Volume
37
Category
Article
ISSN
0028-3045

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✦ Synopsis

the Group Steiner Problem asks for a minimumcost tree which contains at least one node from each group N i N i N i . In this paper, we give polynomial-time O O O(k k k )approximation algorithms for any fixed > > > 0. This result improves the previously known O O O(k k k)-approximation. We also apply our approximation algorithms to the Steiner problem in directed graphs, while guaranteeing the same performance ratio.

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An improved projection scheme is proposed and applied to pseudospectral collocation-Chebyshev approximation for the incompressible Navier-Stokes equations. It consists of introducing a correct predictor for the pressure, one which is consistent with a divergence-free velocity field at each time step