Bahman Kalantari

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Given an undirected edge-weighted graph and a natural number m, we consider the problem of finding a minimum-weight spanning forest such that each of its trees spans at least m vertices. For m ___ 4, the problem is shown to be NP-hard. We describe a simple 2-approximate greedy heuristic that runs within the time needed to compute a minimum spanning tree. If(More)
Given a set P with n points in R , its diameter, dP , is the maximum of the Euclidean distances between its points. We describe an algorithm that in m ≤ n iterations obtains r1 < r2 < . . . < rm ≤ dP ≤ min { √3 r1 , √  5 − 2 √3 rm } . For k fixed, the cost of each iteration is O(n) . In particular in the first iteration, the algorithm produces an(More)
Smale’s analysis of Newton’s iteration function induce a lower bound on the gap between two distinct zeros of a given complex-valued analytic function f(z). In this paper we make use of a fundamental family of iteration functions Bm(z), m ≥ 2, to derive an infinite family of lower bounds on the above gap. However, even for m = 2, where B2(z) coincides with(More)
Let p(x) be a polynomial of degree n 2 with coe cients in a sub eld K of the complex numbers. For each natural number m 2, let L m (x) be the m m lower triangular matrix whose diagonal entries are p(x) and for each j = 1; : : : ; m 1, its j-th subdiagonal entries are p (j) (x)=j!. For i = 1; 2, let L (i) m (x) be the matrix obtained from L m (x) by deleting(More)
The z e r o o n e in teger p rog ramming prob lem in min imiza t ion form can be fo rmula ted as fol lows: (P 1 ) min imize z (x) = c Tx, sub jec t to x E F where F = { x E R " [ A x b , x ~ = O o r 1, f o r a l l i = l , 2 . . . . ,n} , C T = ( C 1 . . . . . Cn) , X T = (X, . . . . . Xn), b T = (bl . . . . , bin), and A is an m × n matr ix. Wi thou t loss(More)
A new formula for the approximation of root of polynomials with complex coefficients is presented. For each simple root there exists a neighborhood such that given any input within this neighborhood, the formula generates a convergent sequence, computed via elementary operations on the input and the corresponding derivative values. Each element of the(More)