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Persistent homology has become one of the most popular tools used in topological data analysis for analyzing big data sets. In an effort to minimize the computational complexity of finding the persistent homology of a data set, we develop a simplicial collapse algorithm called the selective collapse. This algorithm works by representing the previously developed strong collapse as a forest and uses...
Algebraic topology has been successfully applied to detect and localize sensor network coverage holes with minimal assumptions on sensor locations. These methods all use a computation of topological invariants called homology spaces. We develop a distributed algorithm for collapsing a sensor network, hence simplifying its analysis. We prove that the collapse is equivalent to a previously developed...
There has recently been increased interest in applications of topology to areas ranging from control and sensing, to social network analysis, to high-dimensional point cloud data analysis. Here we use simplicial complexes to represent the group relationship structure in a network. We detail a novel algorithm for simplifying homology and “hole location” computations on a complex by reducing it to its...
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