{"oa_version":"None","abstract":[{"lang":"eng","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."}],"publication_status":"published","publication":"Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms","quality_controlled":"1","scopus_import":1,"title":"On the computational complexity of betti numbers reductions from matrix rank","_id":"2177","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Salman","full_name":"Parsa, Salman","last_name":"Parsa","id":"4BDBD4F2-F248-11E8-B48F-1D18A9856A87"}],"doi":"10.1137/1.9781611973402.11","conference":{"start_date":"2014-01-05","end_date":"2014-01-07","name":"SODA: Symposium on Discrete Algorithms","location":"Portland, USA"},"language":[{"iso":"eng"}],"type":"conference","date_updated":"2021-01-12T06:55:48Z","publist_id":"4805","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_published":"2014-01-01T00:00:00Z","day":"01","year":"2014","publisher":"SIAM","status":"public","page":"152 - 160","month":"01","date_created":"2018-12-11T11:56:09Z","citation":{"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>","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.","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>.","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.","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>","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>.","short":"H. Edelsbrunner, S. Parsa, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–160."},"department":[{"_id":"HeEd"}]}