Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps
Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps
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用于计算复数和映射同调性的离散莫尔斯理论算法
DOI：
10.1007/s10208-013-9145-0
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发表时间：
2013
影响因子：
3
通讯作者：
Vidit Nanda
中科院分区：
文献类型：
--
作者：
S. Harker;K. Mischaikow;M. Mrozek;Vidit Nanda
我们给出了基于离散Morse理论的显式高效约简算法，以简化一类非常一般的复数的同调计算。这种复合体之间的顶维单元的集值映射是潜在的(可能是未知的)连续函数的自然离散近似，特别是当该函数的评估受到测量误差的影响时。我们引入了一种新的Morse理论前处理框架，用于从这类集值映射导出链映射，从而为计算由逼近连续函数诱导的同调上的态射提供了一种有效的方案。
We provide explicit and efficient reduction algorithms based on discrete Morse theory to simplify homology computation for a very general class of complexes. A set-valued map of top-dimensional cells between such complexes is a natural discrete approximation of an underlying (and possibly unknown) continuous function, especially when the evaluation of that function is subject to measurement errors. We introduce a new Morse theoretic preprocessing framework for deriving chain maps from such set-valued maps, and hence provide an effective scheme for computing the morphism induced on homology by the approximated continuous function.