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Algorithmic methods based on the theory of fixed-parameter tractability are combined with powerful computational platforms to launch systematic attacks on combinatorial problems of significance. As a case study, optimal solutions to very large instances of the N P-hard vertex cover problem are computed. To accomplish this, an efficient sequential algorithm and various forms of parallel algorithms are devised, implemented and compared. The importance of maintaining a balanced decomposition ofdoi:10.1007/s00453-006-1214-1 fatcat:vzmvskuvtba6veze7o7ekbntii