In this study, a new fast algorithm for optimal design of block digital filters is proposed based on the skew circulant matrix, the Toeplitz and the skew shift cyclic matrices. The developed skew-cyclic filter, compared with the cyclic filter, not only achieves the same computational complexity of the design process and the memory requirements, but is more efficient with only approximately half of the computational cost for the real signals. † C: the skew cyclic matrix † π −1 :t h eM × M matrix of the skew cyclic right shift operator † F M : the M × M matrix corresponding to a M-point DFT; and F −1 M as its inverse † S: the L × M selection matrix, a binary matrix which selects the L values out of the M from the middle † A(:, j): an m × 1 vector composed of the elements of the jth column of an m × 1 matrix A www.ietdl.org

In the past 20 years, the connected dominating set (CDS) as a virtual backbone network has been widely used in the wireless networks. Many researchers have been devoted to designing approximate algorithms for CDS problem since constructing the minimum CDS (MCDS) is NP-hard problem. Different from the most existing algorithms with two phases, we employ greedy strategy to design a centralized algorithm GR CDS in only one phase to get MCDS, with the time complexity of ((Δ 2 + log ) ). Afterwards, another algorithm P CDS is designed for pruning redundant nodes in the obtained MCDS with the time complexity of ( 2 ).

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