Mateusz Juda

Distributed computation of coverage in sensor networks by homological methods

Recent work on algebraic-topological methods for verifying coverage in planar sensor networks relied exclusively on centralized computation: a limiting constraint for large networks. This paper presents a distributed algorithm for homology computation over a sensor network, for purposes of verifying coverage. The techniques involve reduction and coreduction of simplicial complexes, and are of independent interest. Verification of the ensuing algorithms is proved, and simulations detail the improved network efficiency and performance.

Computing fundamental groups from point clouds

We describe an algorithm for computing a finite, and typically small, presentation of the fundamental group of a finite regular CW-space. The algorithm is based on the construction of a discrete vector field on the

Topological Descriptors for 3D Surface Analysis

3

Fast, Simple and Separable Computation of Betti Numbers on Three-Dimensional Cubical Complexes

3-skeleton of the space. A variant yields the homomorphism of fundamental groups induced by a cellular map of spaces. We illustrate how the algorithm can be used to infer information about the fundamental group

Fundamental Group Algorithm for low dimensional tessellated CW complexes

\pi _1(K)

Persistent Homology of Morse Decompositions in Combinatorial Dynamics.

π1(K) of a metric space