Piecewise Parabolic Approximate Computation Based on an Error-Flattened Segmenter and a Novel Quantizer

This paper proposes a novel Piecewise Parabolic Approximate Computation method for hardware function evaluation, which mainly incorporates an error-flattened segmenter and an implementation quantizer. Under a required software maximum absolute error (MAE), the segmenter adaptively selects a minimum number of parabolas to approximate the objective function. By completely imitating the circuit’s behavior before actual implementation, the quantizer calculates the minimum quantization bit width to ensure a non-redundant fixed-point hardware architecture with an MAE of 1 unit of least precision (ulp), eliminating the iterative design time for the circuits. The method causes the number of segments to reach the theoretical limit, and has great advantages in the number of segments and the size of the look-up table (LUT). To prove the superiority of the proposed method, six common functions were implemented by the proposed method under TSMC-90 nm technology. Compared to the state-of-the-art piecewise quadratic approximation methods, the proposed method has advantages in the area with roughly the same delay. Furthermore, a unified function-evaluation unit was also implemented under TSMC-90 nm technology.

Approximate computation for big data analytics

Over the past a few years, research and development has made significant progresses on big data analytics. A fundamental issue for big data analytics is the efficiency. If the optimal solution is unable to attain or unnecessary or has a price to high to pay, it is reasonable to sacrifice optimality with a "good" feasible solution that can be computed efficiently. Existing approximation techniques can be in general classified into approximation algorithms, approximate query processing for aggregate SQL queries and approximation computing for multiple layers of the system stack. In this article, we systematically introduce approximate computation, i.e. , query approximation and data approximation, for efficient and effective big data analytics. We explain the ideas and rationales behind query and data approximation, and show efficiency can be obtained with high effectiveness, and even without sacrificing for effectiveness, for certain data analytic tasks.

A Review of and Some Results for Ollivier–Ricci Network Curvature

Characterizing topological properties and anomalous behaviors of higher-dimensional topological spaces via notions of curvatures is by now quite common in mainstream physics and mathematics, and it is therefore natural to try to extend these notions from the non-network domains in a suitable way to the network science domain. In this article we discuss one such extension, namely Ollivier’s discretization of Ricci curvature. We first motivate, define and illustrate the Ollivier–Ricci Curvature. In the next section we provide some “not-previously-published” bounds on the exact and approximate computation of the curvature measure. In the penultimate section we review a method based on the linear sketching technique for efficient approximate computation of the Ollivier–Ricci network curvature. Finally in the last section we provide concluding remarks with pointers for further reading.