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Throughout this paper, a persistence diagram ${cal P}$ is composed of a set $P$ of planar points (each corresponding to a topological feature) above the line $Y=X$, as well as the line $Y=X$ itself, i.e., ${cal P}=Pcup{(x,y)|y=x}$. Given a set of persistence diagrams ${cal P}_1,...,{cal P}_m$, for the data reduction purpose, one way to summarize their topological features is to compute the {em center} ${cal C}$ of them first under the bottleneck distance. We consider two discre
Graphs model real-world circumstances in many applications where they may constantly change to capture the dynamic behavior of the phenomena. Topological persistence which provides a set of birth and death pairs for the topological features is one in
Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under $mathbb{Z}_2
Given a simple polygon $P$ and a set $Q$ of points contained in $P$, we consider the geodesic $k$-center problem where we want to find $k$ points, called emph{centers}, in $P$ to minimize the maximum geodesic distance of any point of $Q$ to its close
For a polygonal domain with $h$ holes and a total of $n$ vertices, we present algorithms that compute the $L_1$ geodesic diameter in $O(n^2+h^4)$ time and the $L_1$ geodesic center in $O((n^4+n^2 h^4)alpha(n))$ time, respectively, where $alpha(cdot)$
An algorithm is presented that constructs an acyclic partial matching on the cells of a given simplicial complex from a vector-valued function defined on the vertices and extended to each simplex by taking the least common upper bound of the values o