[{"publication":"Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms","publist_id":"4805","date_updated":"2021-01-12T06:55:48Z","page":"152 - 160","_id":"2177","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","oa_version":"None","quality_controlled":"1","publication_status":"published","day":"01","citation":{"chicago":"Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of Betti Numbers Reductions from Matrix Rank.” In <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>, 152–60. SIAM, 2014. <a href=\"https://doi.org/10.1137/1.9781611973402.11\">https://doi.org/10.1137/1.9781611973402.11</a>.","apa":"Edelsbrunner, H., &#38; Parsa, S. (2014). On the computational complexity of betti numbers reductions from matrix rank. In <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i> (pp. 152–160). Portland, USA: SIAM. <a href=\"https://doi.org/10.1137/1.9781611973402.11\">https://doi.org/10.1137/1.9781611973402.11</a>","ieee":"H. Edelsbrunner and S. Parsa, “On the computational complexity of betti numbers reductions from matrix rank,” in <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>, Portland, USA, 2014, pp. 152–160.","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.","mla":"Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of Betti Numbers Reductions from Matrix Rank.” <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>, SIAM, 2014, pp. 152–60, doi:<a href=\"https://doi.org/10.1137/1.9781611973402.11\">10.1137/1.9781611973402.11</a>.","ama":"Edelsbrunner H, Parsa S. On the computational complexity of betti numbers reductions from matrix rank. In: <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>. SIAM; 2014:152-160. doi:<a href=\"https://doi.org/10.1137/1.9781611973402.11\">10.1137/1.9781611973402.11</a>"},"type":"conference","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"}],"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"last_name":"Parsa","full_name":"Parsa, Salman","first_name":"Salman","id":"4BDBD4F2-F248-11E8-B48F-1D18A9856A87"}],"status":"public","department":[{"_id":"HeEd"}],"conference":{"name":"SODA: Symposium on Discrete Algorithms","end_date":"2014-01-07","location":"Portland, USA","start_date":"2014-01-05"},"date_created":"2018-12-11T11:56:09Z","doi":"10.1137/1.9781611973402.11","year":"2014","month":"01","date_published":"2014-01-01T00:00:00Z","publisher":"SIAM","scopus_import":1,"title":"On the computational complexity of betti numbers reductions from matrix rank","language":[{"iso":"eng"}]}]