{"paper":{"title":"Width, depth and space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Felix Reidl, Fernando S\\'anchez Villaamil, Li-Hsuan Chen, Peter Rossmanith","submitted_at":"2016-07-04T16:06:41Z","abstract_excerpt":"The width measure treedepth, also known as vertex ranking, centered coloring and elimination tree height, is a well-established notion which has recently seen a resurgence of interest. Since graphs of bounded treedepth are more restricted than graphs of bounded tree- or pathwidth, we are interested in the algorithmic utility of this additional structure.\n  On the negative side, we show that every dynamic programming algorithm on treedepth decompositions of depth~$t$ cannot solve Dominating Set with $O((3-\\epsilon)^t \\cdot \\log n)$ space for any $\\epsilon > 0$. This result implies the same spac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00945","kind":"arxiv","version":2},"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"}