{"paper":{"title":"Succinct Indexable Dictionaries with Applications to Encoding $k$-ary Trees, Prefix Sums and Multisets","license":"","headline":"","cross_cats":["cs.DM","cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"Rajeev Raman, Srinivasa Rao Satti, Venkatesh Raman","submitted_at":"2007-05-04T07:47:05Z","abstract_excerpt":"We consider the {\\it indexable dictionary} problem, which consists of storing a set $S \\subseteq \\{0,...,m-1\\}$ for some integer $m$, while supporting the operations of $\\Rank(x)$, which returns the number of elements in $S$ that are less than $x$ if $x \\in S$, and -1 otherwise; and $\\Select(i)$ which returns the $i$-th smallest element in $S$. We give a data structure that supports both operations in O(1) time on the RAM model and requires ${\\cal B}(n,m) + o(n) + O(\\lg \\lg m)$ bits to store a set of size $n$, where ${\\cal B}(n,m) = \\ceil{\\lg {m \\choose n}}$ is the minimum number of bits requi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.0552","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}