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We propose a built-in scheme for generating all patterns of a given deterministic test set T. The scheme is based on grouping the columns of T, so that in each group of columns the number ri of unique representatives (row subvectors) as well as their product R over all such groups is kept at a minimum. The representatives of each group (segment) are then generated by a small finite state machine (FSM)...
In this paper, a subspace analysis method called the orthogonal local linear projection (OLLP) is proposed. OLLP is an unsupervised linear dimensionality reduction method with orthogonal basis functions. OLLP aims to find the projective map that optimally preserves the local structure of the data set. It shares many of the data representation properties of nonlinear techniques and resolves the out-of-sample...
We present a preprocessing algorithm to make certain polynomial algorithms strongly polynomial. The running time of some of the known combinatorial optimization algorithms depends on the size of the objective function w. Our preprocessing algorithm replaces w by an integral valued w whose size is polynomially bounded in the size of the combinatorial structure and which yields the same set of optimal...
We show that there can be no computationally tractable description by linear inequalities of the polyhedron associated with any NP-complete combinatorial optimization problem unless NP = co-NP -- a very unlikely event. We also apply the ellipsoid method for linear programming to show that a combinatorial optimization problem is solvable in polynomial time if and only if it admits a small generator...
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