[{"title":"On the computational complexity of betti numbers reductions from matrix rank","oa_version":"None","creator":{"id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","login":"apreinsp"},"month":"01","language":[{"iso":"eng"}],"year":"2014","doi":"10.1137/1.9781611973402.11","_id":"2177","publisher":"SIAM","day":"01","quality_controlled":"1","publication_status":"published","date_published":"2014-01-01T00:00:00Z","status":"public","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","publist_id":"4805","date_created":"2018-12-11T11:56:09Z","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Parsa","full_name":"Parsa, Salman","id":"4BDBD4F2-F248-11E8-B48F-1D18A9856A87","first_name":"Salman"}],"_version":11,"type":"conference","date_updated":"2019-08-02T12:37:39Z","publication":"Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms","conference":{"location":"Portland, USA","start_date":"2014-01-05","end_date":"2014-01-07","name":"SODA: Symposium on Discrete Algorithms"},"department":[{"_id":"HeEd","tree":[{"_id":"ResearchGroups"},{"_id":"IST"}]}],"abstract":[{"text":"We give evidence for the difficulty of computing Betti numbers of simplicial complexes over a finite field. We do this by reducing the rank computation for sparse matrices with to non-zero entries to computing Betti numbers of simplicial complexes consisting of at most a constant times to simplices. Together with the known reduction in the other direction, this implies that the two problems have the same computational complexity.","lang":"eng"}],"page":"152 - 160","citation":{"mla":"Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of Betti Numbers Reductions from Matrix Rank.” *Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*, SIAM, 2014, pp. 152–60, doi:10.1137/1.9781611973402.11.","ieee":"H. Edelsbrunner and S. Parsa, “On the computational complexity of betti numbers reductions from matrix rank,” in *Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*, Portland, USA, 2014, pp. 152–160.","ama":"Edelsbrunner H, Parsa S. On the computational complexity of betti numbers reductions from matrix rank. In: *Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*. SIAM; 2014:152-160. doi:10.1137/1.9781611973402.11","chicago":"Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of Betti Numbers Reductions from Matrix Rank.” In *Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*, 152–60. SIAM, 2014. https://doi.org/10.1137/1.9781611973402.11.","ista":"Edelsbrunner H, Parsa S. 2014. On the computational complexity of betti numbers reductions from matrix rank. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms 152–160.","short":"H. Edelsbrunner, S. Parsa, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–160.","apa":"Edelsbrunner, H., & Parsa, S. (2014). On the computational complexity of betti numbers reductions from matrix rank. In *Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms* (pp. 152–160). Portland, USA: SIAM. https://doi.org/10.1137/1.9781611973402.11"}}]