{"volume":4619,"publication_status":"published","_id":"3981","extern":1,"day":"21","date_updated":"2021-01-12T07:53:38Z","date_published":"2007-08-21T00:00:00Z","status":"public","conference":{"name":"WADS: International Workshop on Algrithms and Data Structures"},"date_created":"2018-12-11T12:06:15Z","intvolume":"      4619","citation":{"ieee":"D. Attali, H. Edelsbrunner, J. Harer, and Y. Mileyko, “Alpha-beta witness complexes,” presented at the WADS: International Workshop on Algrithms and Data Structures, 2007, vol. 4619, pp. 386–397.","ama":"Attali D, Edelsbrunner H, Harer J, Mileyko Y. Alpha-beta witness complexes. In: Vol 4619. Springer; 2007:386-397. doi:<a href=\"https://doi.org/10.1007/978-3-540-73951-7_34\">10.1007/978-3-540-73951-7_34</a>","ista":"Attali D, Edelsbrunner H, Harer J, Mileyko Y. 2007. Alpha-beta witness complexes. WADS: International Workshop on Algrithms and Data Structures, LNCS, vol. 4619, 386–397.","short":"D. Attali, H. Edelsbrunner, J. Harer, Y. Mileyko, in:, Springer, 2007, pp. 386–397.","apa":"Attali, D., Edelsbrunner, H., Harer, J., &#38; Mileyko, Y. (2007). Alpha-beta witness complexes (Vol. 4619, pp. 386–397). Presented at the WADS: International Workshop on Algrithms and Data Structures, Springer. <a href=\"https://doi.org/10.1007/978-3-540-73951-7_34\">https://doi.org/10.1007/978-3-540-73951-7_34</a>","chicago":"Attali, Dominique, Herbert Edelsbrunner, John Harer, and Yuriy Mileyko. “Alpha-Beta Witness Complexes,” 4619:386–97. Springer, 2007. <a href=\"https://doi.org/10.1007/978-3-540-73951-7_34\">https://doi.org/10.1007/978-3-540-73951-7_34</a>.","mla":"Attali, Dominique, et al. <i>Alpha-Beta Witness Complexes</i>. Vol. 4619, Springer, 2007, pp. 386–97, doi:<a href=\"https://doi.org/10.1007/978-3-540-73951-7_34\">10.1007/978-3-540-73951-7_34</a>."},"title":"Alpha-beta witness complexes","quality_controlled":0,"publist_id":"2149","alternative_title":["LNCS"],"publisher":"Springer","month":"08","type":"conference","page":"386 - 397","acknowledgement":"Research by the authors is partially supported by DARPA under grant HR0011-05-1-0007, by CNRS under grant PICS-3416 and by IST Program of the EU under Contract IST-2002-506766.","author":[{"first_name":"Dominique","last_name":"Attali","full_name":"Attali, Dominique"},{"orcid":"0000-0002-9823-6833","full_name":"Herbert Edelsbrunner","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Harer, John","first_name":"John","last_name":"Harer"},{"last_name":"Mileyko","first_name":"Yuriy","full_name":"Mileyko, Yuriy"}],"year":"2007","doi":"10.1007/978-3-540-73951-7_34","abstract":[{"text":"Building on the work of Martinetz, Schulten and de Silva, Carlsson, we introduce a 2-parameter family of witness complexes and algorithms for constructing them. This family can be used to determine the gross topology of point cloud data in R-d or other metric spaces. The 2-parameter family is sensitive to differences in sampling density and thus amenable to detecting patterns within the data set. It also lends itself to theoretical analysis. For example, we can prove that in the limit, when the witnesses cover the entire domain, witness complexes in the family that share the first, scale parameter have the same homotopy type.","lang":"eng"}]}