We give fast new approximation algorithms for the problem of choosing k planar points out of n to minimize the length of their minimum spanning tree (equivalently, of their traveling salesman tour or Steiner tree). For any x ≤ k, we can find an approximation achieving approximation ratio O(log k/ log x) in time O(n log n+ 2kn log k). In particular, we get an approximation with ratio O(log k/ lo...

Properties of software failure times modelled as realizations of order statistics generated by independent but non-identically distributed exponential random variables are developed. Edgeworth and saddle point approximations to central order statistic densities so generated are developed using an exact integral representation of these densities. A comparison of Edgeworth and saddle point approx...

In this paper the properties of Rédei rational functions are used to derive rational approximations for square roots and both Newton and Padé approximations are given as particular cases. As a consequence, such approximations can be derived directly by power matrices. Moreover, Rédei rational functions are introduced as convergents of particular periodic continued fractions and are applied for ...

Two methods of discrete images are proposed to approximate the reaction field from ionic solvent for a point charge inside a dielectric spherical cavity. Fast and accurate calculation of such a reaction field is needed in hybrid explicit/implicit solvation models of biomolecules. A firstand a second-order image approximation methods, in the order of u = λa (λ – the inverse Debye screening lengt...

Identifying the common 3-D substructure between two drug or protein molecules is an important problem in synthetic drug design and molecular biology. This problem can be represented as the following geometric pattern matching problem: given two point sets A and B in three-dimensions, and a real number > 0, nd the maximum cardinality subset S A for which there is an isometry I, such that each po...

Rough set theory places great importance on approximation accuracy, which is used to gauge how well a rough model describes target concept. However, traditional accuracy has limitations since it varies with changes in the concept and cannot evaluate overall descriptive ability of model. To overcome this, two types average that objectively assess model’s approximate all information granules prop...