Automatic identification of network rows in large-scale optimization models.

TLDR: The problem of identifying the maximum size embedded pure network rows within the coefficient matrix of such models is shown to be among the class of NP-hard problems, therefore, the polynomially-bounded algorithms presented here do not guarantee network sets of maximum size.

Abstract: : The solution of contemporary large-scale linear, integer, and mixed integer programming problems is often facilitated by the exploitation of intrinsic special structure in the model. This paper deals with the problem of identifying embedded pure network rows within the coefficient matrix of such models and presents two heuristic algorithms for identifying such structure. The problem of identifying the maximum size embedded pure network is shown to be among the class of NP-hard problems, therefore, the polynomially-bounded algorithms presented here do not guarantee network sets of maximum size. However, upper bounds on the size of the maximum network set are developed and used to evalaute the algorithms. Finally, the algorithms were tested with a number of large-scale, real-world models and the results of these benchmark runs are presented. (Author)