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In this paper we analyze the performance of two parallel sparse matrix partitioning software packages, ParMETIS and PT-SCOTCH. We focus our analysis on the parallel performance of the nested dissection partitioning stage as well as its impact on the performance of the numerical stages of the solution of sparse linear systems via multilevel ILU preconditioned iterative methods. Experimental results on a shared-memory platform with 16 processors show that ParMETIS seems to be the best choice for our approach.