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Abstract: . The parallel time complexity of the linear programming problem 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((log m+ log 2 n) log 2 n) time parallel algorithm under the concurrent-read-exclusive-write PRAM model for deciding feasibility. It requires mn O(logn) processors in the worst case, though we do not know whether this bound is tight.... (Update)
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...per inequality (TVPI) It is probably the case that the MDP(2) problem is in NC, meaning that it can be eciently solved in parallel. In [81], the same open question is 139 raised about the TVPI problem. Linear optimization over TVPI is P complete [81] Deterministic MDP...
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BibTeX entry: (Update)
G. S. Lueker, N. Megiddo, and V. Ramachandran. Linear programming with two variables per inequality in poly log time. SIAM J. Comput., 19(6):1000--1010, 1990. http://citeseer.ist.psu.edu/lueker90linear.html More
@inproceedings{ lueker86linear,
author = "G. S. Lueker and N. Megiddo and V. Ramachandran",
title = "Linear programming with two variables per inequality in poly-log time",
pages = "196--205",
year = "1986",
url = "citeseer.ist.psu.edu/lueker90linear.html" }
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