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Summary form only given. We study the problem of redistributing in parallel data between clusters interconnected by a backbone. This problem is a generalization of the well-known redistribution problem that appears in parallelism. We suppose that at most k communications can be performed at the same time (the value of k depending on the characteristics of the platform). We use the knowledge of the application in order to schedule the messages and perform a control of the congestion by ourselves. Previous results show that this problem is NP-complete. We propose and study two fast and efficient algorithms for this problem. We prove that these algorithms are 2-approximation algorithms. Simulation results show that both algorithms perform very well compared to the optimal solution. These algorithms have been implemented using MPI. Experimental results show that both algorithms outperform a brute-force TCP based solution, where no scheduling of the messages is performed.