{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,11]],"date-time":"2026-10-11T03:11:08Z","timestamp":1791688268130,"version":"4.3.4"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1994,8]]},"abstract":"<jats:p>The dynamic dictionary problem is considered: provide an algorithm for storing a dynamic set, allowing the operations insert, delete, and lookup. A dynamic perfect hashing strategy is given: a randomized algorithm for the dynamic dictionary problem that takes $O(1)$ worst-case time for lookups and $O(1)$ amortized expected time for insertions and deletions; it uses space proportional to the size of the set stored. Furthermore, lower bounds for the time complexity of a class of deterministic algorithms for the dictionary problem are proved. This class encompasses realistic hashing-based schemes that use linear space. Such algorithms have amortized worst-case time complexity $\\Omega (\\log n)$ for a sequence of n insertions and lookups; if the worst-case lookup time is restricted to k, then the lower bound becomes $\\Omega (k \\cdot n^{{1 \/ k}} )$.<\/jats:p>","DOI":"10.1137\/s0097539791194094","type":"journal-article","created":{"date-parts":[[2005,2,24]],"date-time":"2005-02-24T06:39:46Z","timestamp":1109227186000},"page":"738-761","source":"Crossref","is-referenced-by-count":200,"title":["Dynamic Perfect Hashing: Upper and Lower Bounds"],"prefix":"10.1137","volume":"23","author":[{"given":"Martin","family":"Dietzfelbinger","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anna","family":"Karlin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kurt","family":"Mehlhorn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Friedhelm","family":"Meyer auf der Heide","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hans","family":"Rohnert","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert E.","family":"Tarjan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,13]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"H. V. Aho, D. Lee,  Storing a dynamic sparse table,  Proc. 27th IEEE Symp. on Foundations of Computer Science,  1986,  55\u201360","DOI":"10.1109\/SFCS.1986.50"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"H. Bast, T. Hagerup,  Fast and reliable parallel hashing,  Proc. 3rd Annual ACM Symp. on Parallel Algorithms and Architectures,  1991,  50\u201361","DOI":"10.1145\/113379.113384"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(88)90210-4"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(79)90044-8"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"M. Dietzfelbinger, A. Karlin, K. Mehlhorn, F. Meyer auf der heide, H. Rohnert, R. E. Tarjan,  Dynamic perfect hashing: Upper and lower bounds,  Proc. 29th IEEE Symp. on Foundations of Computer Science,  1988,  524\u2013531","DOI":"10.1109\/SFCS.1988.21968"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"M. Dietzfelbinger, F. 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