An efficient computer algorithm is described for the perspective drawing of a wide class of surfaces. The class includes surfaces corresponding lo single-valued, continuous functions which are defined over rectangular domains. The algorithm automatically computes and eliminates “hidden lines.” The number of computations in the algorithm grows linearly with the number of sample points on the sur...

Let X and Y be two run-length encoded strings, of encoded lengths k and l, respectively. We present a simple O(|X|l+|Y |k) time algorithm that computes their edit distance.  2002 Elsevier Science B.V. All rights reserved.

A new fast addition algorithm on an elliptic curve over GF(2n) using the projective coordinates with x =X/Z and y = Y/Z2 is proposed.  2000 Elsevier Science B.V. All rights reserved.

A Schur-type algorithm is presented for computing recursively the triangular factorization R = LU of a strongly nonsingular n n matrix satisfying a displacement equation RY V R = GH with Hessenberg matrices Y and V and n matrices G, H. If is small compared with n and the matrices Y and V admit fast matrix-vector multiplication, the new algorithm is fast in the sense that it will require less th...

Given an rc-graph R of permutation w and an rc-graph Y of permutation v, we provide an insertion algorithm, which defines an rc-graph R ← Y in the case when v is a shuffle with the descent at r and w has no descents greater than r or in the case when v is a shuffle, whose shape is a hook. This algorithm gives a combinatorial rule for computing the generalized Littlewood-Richardson coefficients ...

We present algorithm qHyper for nding all solutions y(x) of a linear homogeneous q-diierence equation such that y(qx) = r(x)y(x) where r(x) is a rational function of x. Applications include construction of basic hypergeometric series solutions, and deenite q-hypergeometric summation in closed form.

The multi-path algorithm for finding hamilton cycles in a graph G is described in the book by Christofides. It is an intelligent exhaustive search for a hamilton cycle. In this paper we describe how the algorithm can be improved in two ways: (1) by detecting small separating sets M for which G–M has more than |M| components; and (2) by detecting bipartitions (X,Y), where |X|<|Y|.

Require: Algorithm parameters γ > 1 and η < 1, an auxiliary scalar vk, iteration counter iter = 0, and the maximum number of iterations maxiter. Ensure: A critical point 1: Initiate y0 and σ0. 2: repeat 3: Given yk and σk, solve (1.1) to find the minimizer Rk via the LBFGS algorithm. 4: Compute v = ∑ i ( tr(DiRkR T k )− bi )2 . 5: if v < ηvk then 6: y i = y k i − σk · ( tr(DiRkR T k )− bi ) for...

is known as a linear complementarity problem. Under the assumption that M is positive semidefinite, this paper presents an algorithm that solves the problem in O(n 3 L) arithmetic operations by tracing the path of centers, {(x, y) E S: x~y~ = I.* (i = 1, 2 , . . . , n) for some/~ > 0} of the feasible region S = {(x, y) >~ 0: y = Mx + q}, where L denotes the size of the input data of the problem.

where J (t, y) = {i : Ti = t, Yi = y} represents the set of respondents with Ti = t and Yi = y. However, this likelihood function is difficult to maximize because it consists of many mixture components. Thus, following Imai (2011), we develop an EM algorithm by treating Z∗ i,J+t as partially missing data for each t = 1, . . . ,K. This leads to the following complete-data likelihood function, Lc...