{"paper":{"title":"Parameterized Quantum Query Complexity of Graph Collision","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"quant-ph","authors_text":"Andris Ambainis, J\\=anis Iraids, Juris Smotrovs, Kaspars Balodis, Raitis Ozols","submitted_at":"2013-05-05T15:40:13Z","abstract_excerpt":"We present three new quantum algorithms in the quantum query model for \\textsc{graph-collision} problem: \\begin{itemize} \\item an algorithm based on tree decomposition that uses $O\\left(\\sqrt{n}t^{\\sfrac{1}{6}}\\right)$ queries where $t$ is the treewidth of the graph; \\item an algorithm constructed on a span program that improves a result by Gavinsky and Ito. The algorithm uses $O(\\sqrt{n}+\\sqrt{\\alpha^{**}})$ queries, where $\\alpha^{**}(G)$ is a graph parameter defined by \\[\\alpha^{**}(G):=\\min_{VC\\text{-- vertex cover of}G}{\\max_{\\substack{I\\subseteq VC\\\\I\\text{-- independent set}}}{\\sum_{v\\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1021","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"}