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acyclic information flow acyclic system adjacency matrix Algorithm amount of labor analysis best tear bipartite graph Chapter chemical engineering column s_ complex systems corresponding cycle matrix delete design equations design problems developed difficulty score discussed diversity condition equa example f-node find the optimum finding the minimum function calculations hence iables Jacobian determinant labor required least number linear programming minimum number nonzero element number of design number of function number of recycle number of tears number of variables optimization techniques optimum order order of iterations order of stage output variable procedures of finding process calculations process design process systems recycle parameters recycle streams reduced matrix required to solve rows Rudd sample system selecting design variables selection of design self-loop set of columns set of design solve the system solved simultaneously stage calculations strong component strongly connected system subgraph Subroutine subsystems tion total amount total number upper bound