663 research outputs found
Recent progress in exact geometric computation
AbstractComputational geometry has produced an impressive wealth of efficient algorithms. The robust implementation of these algorithms remains a major issue. Among the many proposed approaches for solving numerical non-robustness, Exact Geometric Computation (EGC) has emerged as one of the most successful. This survey describes recent progress in EGC research in three key areas: constructive zero bounds, approximate expression evaluation and numerical filters
A view of Estimation of Distribution Algorithms through the lens of Expectation-Maximization
We show that a large class of Estimation of Distribution Algorithms,
including, but not limited to, Covariance Matrix Adaption, can be written as a
Monte Carlo Expectation-Maximization algorithm, and as exact EM in the limit of
infinite samples. Because EM sits on a rigorous statistical foundation and has
been thoroughly analyzed, this connection provides a new coherent framework
with which to reason about EDAs
Parallel Algorithms for Summing Floating-Point Numbers
The problem of exactly summing n floating-point numbers is a fundamental
problem that has many applications in large-scale simulations and computational
geometry. Unfortunately, due to the round-off error in standard floating-point
operations, this problem becomes very challenging. Moreover, all existing
solutions rely on sequential algorithms which cannot scale to the huge datasets
that need to be processed.
In this paper, we provide several efficient parallel algorithms for summing n
floating point numbers, so as to produce a faithfully rounded floating-point
representation of the sum. We present algorithms in PRAM, external-memory, and
MapReduce models, and we also provide an experimental analysis of our MapReduce
algorithms, due to their simplicity and practical efficiency.Comment: Conference version appears in SPAA 201
Evaluating Signs of Determinants Using Single-Precision Arithmetic
We propose a method of evaluating signs of 2×2 and 3×3 determinants with b-bit integer entries using only b and (b + 1)-bit arithmetic, respectively. This algorithm has numerous applications in geometric computation and provides a general and practical approach to robustness. The algorithm has been implemented and compared with other exact computation methods
Robustness and Randomness
Robustness problems of computational geometry algorithms is a topic that has been subject to intensive research efforts from both computer science and mathematics communities. Robustness problems are caused by the lack of precision in computations involving floating-point instead of real numbers. This paper reviews methods dealing with robustness and inaccuracy problems. It discussed approaches based on exact arithmetic, interval arithmetic and probabilistic methods. The paper investigates the possibility to use randomness at certain levels of reasoning to make geometric constructions more robust
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