
@misc{di_montesano_persistent_2022,
	title = {Persistent Homology of Chromatic Alpha Complexes},
	url = {http://arxiv.org/abs/2212.03128},
	doi = {10.48550/arXiv.2212.03128},
	abstract = {Motivated by applications in medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on persistent homology for images, kernels and cokernels, we design provably stable homological quantifiers that describe the geometric micro- and macro-structure of how the color classes mingle. These can be efficiently computed using chromatic variants of Delaunay mosaics and Alpha complexes.},
	number = {{arXiv}:2212.03128},
	publisher = {{arXiv}},
	author = {di Montesano, Sebastiano Cultrera and Draganov, Ondřej and Edelsbrunner, Herbert and Saghafian, Morteza},
	urldate = {2023-02-28},
	date = {2022-12-06},
	eprinttype = {arxiv},
	eprint = {2212.03128 [cs, math]},
	keywords = {Mathematics - Algebraic Topology, Computer Science - Computational Geometry},
	file = {arXiv.org Snapshot:C\:\\Users\\Abhinav\\Zotero\\storage\\AC99V9LM\\2212.html:text/html;di Montesano et al_2022_Persistent Homology of Chromatic Alpha Complexes.pdf:C\:\\Users\\Abhinav\\OneDrive\\zotero\\di Montesano et al_2022_Persistent Homology of Chromatic Alpha Complexes.pdf:application/pdf},
}


@inproceedings{welzl_smallest_1991,
	location = {Berlin, Heidelberg},
	title = {Smallest enclosing disks (balls and ellipsoids)},
	isbn = {978-3-540-46457-0},
	doi = {10.1007/BFb0038202},
	series = {Lecture Notes in Computer Science},
	abstract = {A simple randomized algorithm is developed which computes the smallest enclosing disk of a finite set of points in the plane in expected linear time. The algorithm is based on Seidel's recent Linear Programming algorithm, and it can be generalized to computing smallest enclosing balls or ellipsoids of point sets in higher dimensions in a straightforward way. Experimental results of an implementation are presented.},
	pages = {359--370},
	booktitle = {New Results and New Trends in Computer Science},
	publisher = {Springer},
	author = {Welzl, Emo},
	editor = {Maurer, Hermann},
	date = {1991},
	langid = {english},
	keywords = {Average Runtime, Closed Disk, Expected Running Time, Random Permutation, Small Disk},
	file = {Welzl_1991_Smallest enclosing disks (balls and ellipsoids).pdf:C\:\\Users\\Abhinav\\OneDrive\\zotero\\Welzl_1991_Smallest enclosing disks (balls and ellipsoids).pdf:application/pdf},
}
