Tight Interval Inclusions with Compensated Algorithms

Projection Algorithms for Variational Inclusions

Numerical Validation of Compensated Summation Algorithms with Stochastic Arithmetic

Compensated summation algorithms are designed to improve the accuracy of ill-conditioned sums. They are based on algorithms, such as FastTwoSum, which are proved to provide, with rounding to nearest, the sum of two floating-point numbers and the associated rounding error. Discrete stochastic arithmetic enables one to estimate rounding error propagation in numerical codes. It requires a random r...

Scalability of Selectorecombinative Genetic Algorithms for Problems with Tight Linkage

Ensuring building-block (BB) mixing is critical to the success of genetic and evolutionary algorithms. This study develops facetwise models to predict the BB mixing time and the population sizing dictated by BB mixing for single-point crossover. The population-sizing model suggests that for moderate-to-large problems, BB mixing – instead of BB decision making and BB supply – bounds the populati...

INTERVAL ANALYSIS-BASED HYPERBOX GRANULAR COMPUTING CLASSIFICATION ALGORITHMS

Representation of a granule, relation and operation between two granules are mainly researched in granular computing. Hyperbox granular computing classification algorithms (HBGrC) are proposed based on interval analysis. Firstly, a granule is represented as the hyperbox which is the Cartesian product of $N$ intervals for classification in the $N$-dimensional space. Secondly, the relation betwee...

Almost-Tight Distributed Minimum Cut Algorithms

We study the problem of computing the minimum cut in a weighted distributed messagepassing networks (the CONGEST model). Let λ be the minimum cut, n be the number of nodes (processors) in the network, and D be the network diameter. Our algorithm can compute λ exactly in O(( √ n log∗ n+D)λ log n) time. To the best of our knowledge, this is the first paper that explicitly studies computing the ex...