{"paper":{"title":"Representation of ordered trees with a given degree distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Dekel Tsur","submitted_at":"2018-07-01T19:02:15Z","abstract_excerpt":"The degree distribution of an ordered tree $T$ with $n$ nodes is $\\vec{n} = (n_0,\\ldots,n_{n-1})$, where $n_i$ is the number of nodes in $T$ with $i$ children. Let $\\mathcal{N}(\\vec{n})$ be the number of trees with degree distribution $\\vec{n}$. We give a data structure that stores an ordered tree $T$ with $n$ nodes and degree distribution $\\vec{n}$ using $\\log \\mathcal{N}(\\vec{n})+O(n/\\log^t n)$ bits for every constant $t$. The data structure answers tree queries in constant time. This improves the current data structures with lowest space for ordered trees: The structure of Jansson et al.\\ ["},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00371","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"}