{"paper":{"title":"On-the-Fly Array Initialization in Less Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Frank Kammer, Torben Hagerup","submitted_at":"2017-09-29T16:13:52Z","abstract_excerpt":"We show that for all given $n,t,w \\in \\{1,2,...\\}$ with $n<2^w$, an array of $n$ entries of $w$ bits each can be represented on a word RAM with a word length of $w$ bits in at most $nw+\\lceil n(t/(2 w))^t\\rceil$ bits of uninitialized memory to support constant-time initialization of the whole array and $O(t)$-time reading and writing of individual array entries. At one end of this tradeoff, we achieve initialization and access (i.e., reading and writing) in constant time with $nw+\\lceil n/w^t\\rceil$ bits for arbitrary fixed $t$, to be compared with $nw+\\Theta(n)$ bits for the best previous sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10477","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"}