Given a set of numbers, the two-way partitioning problem is to divide them into two subsets, so that the sum of the numbers in each subset are as nearly equal as possible. The problem is NP-complete, and is contained in many scheduling applications. Based on a polynomial-time heuristic due to Karmarkar and Karp, we present a new algorithm, called Complete Karmarkar Karp (CKK), that optimally so...

A class of new solutions for Einstein’s field equations, by choosing the ansatz e?(r)=1+kr2R21+r2R2 metric potential, are obtained under Karmarkar condition. It is found that a number pulsars like 4U 1820-30, PSR J1903+327, 1608-52, Vela X-1, J1614-2230, Cen X-3 can be accomodated in this model. We have displayed nature physical parameters and energy conditions throughout distribution using num...

We describe an algorithm for linear and convex quadratic programming problems that uses power series approximation of the weighted barrier path that passes through the current iterate in order to find the next iterate. If r > 1 is the order of approximation used, we show that our algorithm has time complexity O(n t(+l/r)L(l+l/r)) iterations and O(n3 + n2r) arithmetic operations per iteration, w...

B. Qiu, F. Gao, T. K. Foo, P. Karmarkar, E. Atalar, and X. Yang Radiology, Image-guided bio-molecular intervention section, University of Washington Medical Center, Seattle, WA, United States, Radiology, Johns Hopkins University, Baltimore, MD, United States, Applied Science Laboratory, GE Healthcare, Baltimore, MD, United States, Electrical and Electronics Engineering, Bilkent University, Anka...

Let G = (U; V; E) be a bipartite graph with jUj = jV j = n. The factor size of G, f, is the maximum number of edge disjoint perfect matchings in G. We characterize the complexity of counting the number of perfect match-ings in classes of graphs parameterized by factor size. We describe the simple algorithm, which is an approximation algorithm for the permanent that is a natural simpliication of...