Linear Programming with Two Variables per Inequality in Poly Log Time

The parallel time complexity of the linear programming prob lem with at most two variables per inequality is discussed Let n and m denote the number of variables and the number of inequalities respectively in a linear programming problem We describe an O logm log n log n time parallel al gorithm under the concurrent read exclusive write PRAM model for deciding fea sibility It requires mn logn processors in the worst case though we do not know whether this bound is tight When the problem is feasible a solution can be com puted within the same complexity Moreover linear programming problems with two nonzero coe cients in the objective function can be solved in poly log time on a similar number of processors Consequently all these problems can be solved sequentially with only O logm log n log n space It is also shown that if the underlying graph has bounded tree width and an underlying tree is given then the problem is in the class NC