{"paper":{"title":"Improved Algorithms for Computing $k$-Sink on Dynamic Path Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Binay Bhattacharya, Mordecai J. Golin, Naoki Katoh, Tsunehiko Kameda, Yuya Higashikawa","submitted_at":"2016-09-06T02:19:29Z","abstract_excerpt":"We present a novel approach to finding the $k$-sink on dynamic path networks with general edge capacities. Our first algorithm runs in $O(n \\log n + k^2 \\log^4 n)$ time, where $n$ is the number of vertices on the given path, and our second algorithm runs in $O(n \\log^3 n)$ time. Together, they improve upon the previously most efficient $O(kn \\log^2 n)$ time algorithm due to Arumugam et al. for all values of $k$. In the case where all the edges have the same capacity, we again present two algorithms that run in $O(n + k^2 \\log^2n)$ time and $O(n \\log n)$ time, respectively, and they together im"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01373","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"}