The data augmentation (DA) algorithm is a widely used Markov chain Monte Carlo (MCMC) algorithm that is based on a Markov transition density of the form p(x|x′) = ∫ Y fX|Y (x|y)fY |X(y|x) dy, where fX|Y and fY |X are conditional densities. The PX-DA and marginal augmentation algorithms (Liu and Wu, 1999; Meng and van Dyk, 1999) are alternatives to DA that often converge much faster and are only...

The directed acyclic word graph (DAWG) of a string y is the smallest (partial) DFA which recognizes all suffixes of y and has only O(n) nodes and edges. We present the first O(n)-time algorithm for computing the DAWG of a given string y of length n over an integer alphabet of polynomial size in n. We also show that a straightforward modification to our DAWG construction algorithm leads to the f...

Let P (n) denote the largest prime divisor of n, and let Ψ(x, y) be the number of integers n ≤ x with P (n) ≤ y. In this paper we present improvements to Bernstein’s algorithm, which finds rigorous upper and lower bounds for Ψ(x, y). Bernstein’s original algorithm runs in time roughly linear in y. Our first, easy improvement runs in time roughly y. Then, assuming the Riemann Hypothesis, we show...

Let X and Y be sequences of integers. A common increasing subsequence of X and Y is an increasing subsequence common to X and Y . In this note, we propose an O(|X| · |Y |)-time and O(|X| + |Y |)-space algorithm for finding one of the longest common increasing subsequences of X and Y , which improves the space complexity of Yang et al. [I.H. Yang, C.P. Huang, K.M. Chao, A fast algorithm for comp...

in this paper, a new alternative method for order reduction of high order systems is presented based on optimization of multi objective fitness function by using harmony search algorithm. at first, step response of full order system is obtained as a vector, then, a suitable fixed structure considered for model order reduction which order of original system is bigger than fixed structure model. ...

A systematic algorithm for building integrating factors of the form μ(x, y), μ(x, y) or μ(y, y) for second order ODEs is presented. The algorithm can determine the existence and explicit form of the integrating factors themselves without solving any differential equations, except for a linear ODE in one subcase of the μ(x, y) problem. Examples of ODEs not having point symmetries are shown to be...

Theorem 1. Given a structured instance x and arbitrary candidate labeling set Y , no algorithm exists that can always find the most violated label (in Y or not in Y) in poly(|x|) time unless P = N P , where |x| is the length of x. Sketch of the Proof. We prove this theorem by first proving the following lemmas: Lemma 1. We prove that no algorithm exists that can always find the most violated la...

Due to a large number of applications, bicliques of graphs have been widely considered in the literature. This paper focuses on non-induced bicliques. Given a graph G = (V,E) on n vertices, a pair (X,Y ), with X,Y ⊆ V , X ∩ Y = ∅, is a non-induced biclique if {x, y} ∈ E for any x ∈ X and y ∈ Y . The NP-complete problem of finding a non-induced (k1, k2)-biclique asks to decide whether G contains...