Panyukov, A. V.; Gorbik, V. V. The parallel simplex-method achievements for errorless solving of linear programming problems. (Russian. English summary) Zbl 1352.90062 Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Model. Program. 25(242), No. 9, 107-118 (2011). Summary: Techniques for obtaining exact solutions of linear programming problems are the subjects of this paper. Absolute accuracy is derived at the implementation of simplex-algorithms with exact rational-fractional computation. In this case, if \(m\) is minimal of problem dimensions, and \(l\) is the number of bits for a source data item, then the space complexity is not greater than \(4lm^4+o(m^3)\), one iteration time complexity is not greater than \(O(lm^4)\), and the paralleling efficiency (i.e., the ratio of acceleration to the number of processors) asymptotical estimate is 100%. MSC: 90C05 Linear programming 90C60 Abstract computational complexity for mathematical programming problems Keywords:linear programming; simplex method; distributed computing; parallel computing; rational computations; optimization; arbitrary precision; interval arithmetic PDFBibTeX XMLCite \textit{A. V. Panyukov} and \textit{V. V. Gorbik}, Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Model. Program. 25(242), No. 9, 107--118 (2011; Zbl 1352.90062) Full Text: MNR