We show that over a field of characteristic p the solution to a non-singular system of n linear equations in n unknows, with 2 ≤ p < n, whose coefficient matrix is of displacement rank α and which is given as a sum of α LU-products of Toeplitz matrices, can be computed in parallel with randomization simultaneously in O((log n)) time and a total work of O(max{αn, p}n× log n loglog n). A time uni...

This paper presents the colored farthest-neighbor graph (CFNG), a new method for finding clusters of similar objects. The method is useful because it works for both objects with coordinates and for objects without coordinates. The only requirement is that the distance between any two objects be computable. In other words, the objects must belong to a metric space. The CFNG uses graph coloring t...

Partial transmit sequences (PTS) is one of the most attractive schemes to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. However, the Optimal PTS (OPTS) scheme requires an exhaustive searching over all combinations of allowed phase factors. Consequently, the computational complexity increases exponentially with the number of the subbl...

Discrete autocorrelation wavelets have recently been applied in the statistical analysis of locally stationary time series. This form of time series analysis also requires the construction of the inner product matrix of such wavelets. To date, both discrete autocorrelation wavelets and the inner product matrix have been constructed via a brute force technique which proves to be computationally ...

Recursive Descent (RD) parsers are popular because their control flow follows the structure of the grammar and hence they are easy to write and to debug. However, the class of grammars which admit RD parsers is very limited. Backtracking techniques may be used to extend this class, but can have explosive runtimes and cannot deal with grammars with left recursion. Tomita-style RNGLR parsers are ...

Packrat parsing is a newly popular technique for efficiently implementing recursive descent parsers. Packrat parsing avoids the potential exponential costs of recursive descent parsing with backtracking by ensuring that each production rule in the grammar is tested at most once against each position in the input stream. This paper argues that (a) packrat parsers can be trivially implemented usi...