A common approach to deal with NP-hard problems is to deploy polynomial-time -approximation algorithms. These algorithms often resort to rounding and scaling to guarantee a solution that is within a factor (1 + ) of the optimal solution. Usually, researchers either only round up or only down. In this paper we will evaluate the gain in accuracy when rounding up and down. The main application of ...

The usual procedure to compute the determinant is the so-called Gaussian elimination. We can view this as the transformation of the matrix into a lower triangular matrix with column operations. These transformations do not change the determinant but in the triangular matrix, the computation of the determinant is more convenient: we must only multiply the diagonal elements to obtain it. (It is a...

The analysis of longitudinal income data is often made challenging for several reasons. For example, in a national Australian survey on over time, non-negligible proportion responses are missing, and it believed the missingness mechanism non-ignorable. Also, there large number reported zero incomes, some which may be true zeros (corresponding to individuals who legitimately do not earn an incom...

The purpose of this paper is to treat digit set conversions and digit recodings in terms of primitive recoding operations that have elementary implementations. The partial compressions and roundings are each associated with borrow-save or carry-save recodings implementable in one level of logic. Iterative utilization of recoding have application for: i) reducing the range of truncated lower ord...

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid the excessive rounding error propagation of conventional floating-point arithmetic. Unlike interval arithmetic, its uncertainty tracking is based on statistics and the central limit theorem, with a much tighter bounding r...

We combine the pipage rounding technique of Ageev & Sviridenko witha recent rounding method developed by Srinivasan, to develop a new randomized rounding approach for fractional vectors defined on the edge-sets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to the following applications: richer random-graph models for graphs with a given degree-s...