{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T12:46:27Z","timestamp":1788871587349,"version":"build-2803163510"},"reference-count":14,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2015,1,13]],"date-time":"2015-01-13T00:00:00Z","timestamp":1421107200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"NSF","award":["CCF-1116892, CAREER CCF-0845701, CDI-0941553, CMMI-1024554"],"award-info":[{"award-number":["CCF-1116892, CAREER CCF-0845701, CDI-0941553, CMMI-1024554"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Theory"],"published-print":{"date-parts":[[2015,1,13]]},"abstract":"\n We study local filters for two properties of functions of the form\n f<\/jats:italic>\n : {0,1}d \u2192 R: the Lipschitz property and monotonicity. A local filter with additive error\n a<\/jats:italic>\n is a randomized algorithm that is given black-box access to a function\n f<\/jats:italic>\n and a query point\n x<\/jats:italic>\n in the domain of\n f<\/jats:italic>\n . It outputs a value\n F<\/jats:italic>\n (x) such that (i) the\n reconstructed function<\/jats:italic>\n F<\/jats:italic>\n (x) satisfies the property (in our case, is Lipschitz or monotone) and (ii) if the input function\n f<\/jats:italic>\n satisfies the property, then for every point\n x<\/jats:italic>\n in the domain (with high constant probability) the reconstructed value\n F<\/jats:italic>\n (x) differs from\n f<\/jats:italic>\n (x) by at most\n a<\/jats:italic>\n . Local filters were introduced by Saks and Seshadhri [2010]. The relaxed definition we study is due to Bhattacharyya et al. [2012], except that we further relax it by allowing additive error. Local filters for Lipschitz and monotone functions have applications to areas such as data privacy.\n <\/jats:p>\n \n We show that every local filter for Lipschitz or monotone functions runs in time exponential in the dimension\n d<\/jats:italic>\n , even when the filter is allowed significant additive error. Prior lower bounds (for local filters with no additive error, that is, with\n a<\/jats:italic>\n =0) applied only to a more restrictive class of filters, for example,\n nonadaptive<\/jats:italic>\n filters. To prove our lower bounds, we construct families of hard functions and show that lookups of a local filter on these functions are captured by a combinatorial object that we call a\n c<\/jats:italic>\n -connector. Then we present a lower bound on the maximum outdegree of a\n c<\/jats:italic>\n -connector and show that it implies the desired bounds on the running time of local filters. Our lower bounds, in particular, imply the same bound on the running time for a class of privacy mechanisms.\n <\/jats:p>","DOI":"10.1145\/2692372.2692373","type":"journal-article","created":{"date-parts":[[2015,1,16]],"date-time":"2015-01-16T09:29:58Z","timestamp":1421400598000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Limitations of Local Filters of Lipschitz and Monotone Functions"],"prefix":"10.1145","volume":"7","author":[{"given":"Pranjal","family":"Awasthi","sequence":"first","affiliation":[{"name":"Carnegie Mellon University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Madhav","family":"Jha","sequence":"additional","affiliation":[{"name":"Pennsylvania State University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marco","family":"Molinaro","sequence":"additional","affiliation":[{"name":"Carnegie Mellon University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sofya","family":"Raskhodnikova","sequence":"additional","affiliation":[{"name":"Pennsylvania State University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2015,1,13]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-007-9075-9"},{"key":"e_1_2_1_2_1","volume-title":"Proceedings of SODA","author":"Alon Noga","unstructured":"Noga Alon , Ronitt Rubinfeld , Shai Vardi , and Ning Xie . 2012. Space-efficient local computation algorithms . In Proceedings of SODA , Yuval Rabani (Ed.), SIAM , 1132--1139. Noga Alon, Ronitt Rubinfeld, Shai Vardi, and Ning Xie. 2012. Space-efficient local computation algorithms. In Proceedings of SODA, Yuval Rabani (Ed.), SIAM, 1132--1139."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/100808186"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/110826655"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(93)90044-W"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/11761679_29"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/11681878_14"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/285055.285060"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1137\/110840741"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/335305.335315"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.5555\/1980617.1980629"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539793255151"},{"key":"e_1_2_1_13_1","volume-title":"Proceedings of ICS. 223--238","author":"Rubinfeld Ronitt","year":"2011","unstructured":"Ronitt Rubinfeld , Gil Tamir , Shai Vardi , and Ning Xie . 2011 . Fast local computation algorithms . In Proceedings of ICS. 223--238 . Ronitt Rubinfeld, Gil Tamir, Shai Vardi, and Ning Xie. 2011. Fast local computation algorithms. In Proceedings of ICS. 223--238."},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1137\/080728561"}],"container-title":["ACM Transactions on Computation Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2692372.2692373","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2692372.2692373","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T03:19:40Z","timestamp":1750216780000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2692372.2692373"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,13]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,1,13]]}},"alternative-id":["10.1145\/2692372.2692373"],"URL":"https:\/\/doi.org\/10.1145\/2692372.2692373","relation":{},"ISSN":["1942-3454","1942-3462"],"issn-type":[{"value":"1942-3454","type":"print"},{"value":"1942-3462","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1,13]]},"assertion":[{"value":"2013-04-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2014-05-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-01-13","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}