In *Proceedings of the Twenty-Fifth Annual Symposium on Computational Geometry*, of *SCG '09*, pages 247–256. ACM.

Paper doi abstract bibtex

Paper doi abstract bibtex

We study the problem of computing zigzag persistence of a sequence of homology groups and study a particular sequence derived from the levelsets of a real-valued function on a topological space. The result is a local, symmetric interval descriptor of the function. Our structural results establish a connection between the zigzag pairs in this sequence and extended persistence, and in the process resolve an open question associated with the latter. Our algorithmic results not only provide a way to compute zigzag persistence for any sequence of homology groups, but combined with our structural results give a novel algorithm for computing extended persistence. This algorithm is easily parallelizable and uses (asymptotically) less memory.

@inproceedings{carlssonZigzagPersistentHomology2009, location = {{New York, NY, USA}}, title = {Zigzag {{Persistent Homology}} and {{Real}}-Valued {{Functions}}}, isbn = {978-1-60558-501-7}, url = {http://doi.acm.org/10.1145/1542362.1542408}, doi = {10.1145/1542362.1542408}, abstract = {We study the problem of computing zigzag persistence of a sequence of homology groups and study a particular sequence derived from the levelsets of a real-valued function on a topological space. The result is a local, symmetric interval descriptor of the function. Our structural results establish a connection between the zigzag pairs in this sequence and extended persistence, and in the process resolve an open question associated with the latter. Our algorithmic results not only provide a way to compute zigzag persistence for any sequence of homology groups, but combined with our structural results give a novel algorithm for computing extended persistence. This algorithm is easily parallelizable and uses (asymptotically) less memory.}, booktitle = {Proceedings of the {{Twenty}}-Fifth {{Annual Symposium}} on {{Computational Geometry}}}, series = {{{SCG}} '09}, publisher = {{ACM}}, urldate = {2018-04-20}, date = {2009}, pages = {247--256}, keywords = {algorithms,extended persistence,levelset zigzag,Mayer-Vietoris pyramid,zigzag persistent homology}, author = {Carlsson, Gunnar and family=Silva, given=Vin, prefix=de, useprefix=true and Morozov, Dmitriy}, file = {/home/dimitri/Nextcloud/Zotero/storage/WNIUXA7Y/Carlsson et al. - 2009 - Zigzag Persistent Homology and Real-valued Functio.pdf} }

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