{"paper":{"title":"Binary Jumbled Pattern Matching via All-Pairs Shortest Paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Danny Hermelin, Gad M. Landau, Oren Weimann, Yuri Rabinovich","submitted_at":"2014-01-09T16:38:21Z","abstract_excerpt":"In binary jumbled pattern matching we wish to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of size $i$ and has exactly $j$ 1-bits. The problem naturally generalizes to node-labeled trees and graphs by replacing \"substring\" with \"connected subgraph\".\n  In this paper, we give an ${n^2}/{2^{\\Omega(\\log n/\\log \\log n)^{1/2}}}$ time solution for both strings and trees. This odd-looking time complexity improves the state of the art $O(n^2/\\log^2 n)$ solutions by more than any poly-logarithmic factor. It originates from the recent seminal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2065","kind":"arxiv","version":4},"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"}