The authors show that a system of m linear inequalities with n variables, where each inequality involves at most two variables, can be solved in ($) over tilde O (mn(2)) time (we denote ($) over tilde O(f) = O(f polyl...
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The authors show that a system of m linear inequalities with n variables, where each inequality involves at most two variables, can be solved in ($) over tilde O (mn(2)) time (we denote ($) over tilde O(f) = O(f polylog n polylog m)) deterministically, and in ($) over tilde O(n(3) + mn) expected time using randomization. parallel implementations of these algorithms run in ($) over tilde O(n) time, where the deterministic algorithm uses ($) over tilde O)(mn) processors and the randomized algorithm uses ($) over tilde On(2) + m) processors. The bounds significantly improve over previous algorithms. The randomized algorithm is based on novel insights into the structure of the problem.
We present strongly polynomial algorithms to find rational and integer flow vectors that minimize a convex separable quadratic cost function on two-terminal series-parallel graphs.
We present strongly polynomial algorithms to find rational and integer flow vectors that minimize a convex separable quadratic cost function on two-terminal series-parallel graphs.
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