{"paper":{"title":"Nearly Optimal Deterministic Algorithm for Sparse Walsh-Hadamard Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.LG","math.FA","math.IT"],"primary_cat":"cs.IT","authors_text":"Mahdi Cheraghchi, Piotr Indyk","submitted_at":"2015-04-28T20:22:27Z","abstract_excerpt":"For every fixed constant $\\alpha > 0$, we design an algorithm for computing the $k$-sparse Walsh-Hadamard transform of an $N$-dimensional vector $x \\in \\mathbb{R}^N$ in time $k^{1+\\alpha} (\\log N)^{O(1)}$. Specifically, the algorithm is given query access to $x$ and computes a $k$-sparse $\\tilde{x} \\in \\mathbb{R}^N$ satisfying $\\|\\tilde{x} - \\hat{x}\\|_1 \\leq c \\|\\hat{x} - H_k(\\hat{x})\\|_1$, for an absolute constant $c > 0$, where $\\hat{x}$ is the transform of $x$ and $H_k(\\hat{x})$ is its best $k$-sparse approximation. Our algorithm is fully deterministic and only uses non-adaptive queries to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07648","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"}