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Algorithms"],"published-print":{"date-parts":[[2017,7,31]]},"abstract":"<jats:p>\n            We introduce the\n            <jats:italic>hollow heap<\/jats:italic>\n            , a very simple data structure with the same amortized efficiency as the classical Fibonacci heap. All heap operations except\n            <jats:italic>delete<\/jats:italic>\n            and\n            <jats:italic>delete<\/jats:italic>\n            -\n            <jats:italic>min<\/jats:italic>\n            take\n            <jats:italic>O<\/jats:italic>\n            (1) time, worst case as well as amortized;\n            <jats:italic>delete<\/jats:italic>\n            and\n            <jats:italic>delete<\/jats:italic>\n            -\n            <jats:italic>min<\/jats:italic>\n            take\n            <jats:italic>O<\/jats:italic>\n            (log\n            <jats:italic>n<\/jats:italic>\n            ) amortized time on a heap of\n            <jats:italic>n<\/jats:italic>\n            items. Hollow heaps are the simplest structure to achieve these bounds. Hollow heaps combine two novel ideas: the use of lazy deletion and re-insertion to do\n            <jats:italic>decrease<\/jats:italic>\n            -\n            <jats:italic>key<\/jats:italic>\n            operations and the use of a dag (directed acyclic graph) instead of a tree or set of trees to represent a heap. Lazy deletion produces hollow nodes (nodes without items), giving the data structure its name.\n          <\/jats:p>","DOI":"10.1145\/3093240","type":"journal-article","created":{"date-parts":[[2017,7,28]],"date-time":"2017-07-28T12:19:47Z","timestamp":1501244387000},"page":"1-27","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Hollow Heaps"],"prefix":"10.1145","volume":"13","author":[{"given":"Thomas Dueholm","family":"Hansen","sequence":"first","affiliation":[{"name":"Aarhus University, Aarhus N., Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haim","family":"Kaplan","sequence":"additional","affiliation":[{"name":"Tel Aviv University, Tel Aviv, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert E.","family":"Tarjan","sequence":"additional","affiliation":[{"name":"Princeton University and Intertrust Technologies, Sunnyvale, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7638-7710","authenticated-orcid":false,"given":"Uri","family":"Zwick","sequence":"additional","affiliation":[{"name":"Tel Aviv University, Tel Aviv, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,7,27]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Proceedings of the 7th ACM-SIAM Symposium on Discrete Algorithms (SODA\u201996)","author":"Brodal G. 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In Proceedings of the 7th ACM-SIAM Symposium on Discrete Algorithms (SODA\u201996). 52--58."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2213977.2214082"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/0207026"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-40273-9_3"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386390"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/50087.50096"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.6028\/jres.071B.032"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830910000838"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/320211.320214"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/28869.28874"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579168"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1137\/100785351"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/ISTCS.1995.377045"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-43948-7_53"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/509907.509990"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/1328911.1328914"},{"key":"e_1_2_1_17_1","unstructured":"H. Kaplan R. E. Tarjan and U. Zwick. 2014. Fibonacci heaps revisited. CoRR abs\/1407.5750 (2014). http:\/\/arxiv.org\/abs\/1407.5750  H. Kaplan R. E. Tarjan and U. Zwick. 2014. Fibonacci heaps revisited. CoRR abs\/1407.5750 (2014). http:\/\/arxiv.org\/abs\/1407.5750"},{"key":"e_1_2_1_18_1","volume-title":"Sorting and Searching","author":"Knuth D. E.","unstructured":"D. E. Knuth . 1998. Sorting and Searching ( 2 nd ed.). The art of computer programming, Vol. 3 . Addison-Wesley . D. E. Knuth. 1998. Sorting and Searching (2nd ed.). The art of computer programming, Vol. 3. 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