{"paper":{"title":"On the Computational Complexity of Minimal Cumulative Cost Graph Pebbling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.CR","authors_text":"Jeremiah Blocki, Samson Zhou","submitted_at":"2016-09-14T21:22:51Z","abstract_excerpt":"We consider the computational complexity of finding a legal black pebbling of a DAG $G=(V,E)$ with minimum cumulative cost. A black pebbling is a sequence $P_0,\\ldots, P_t \\subseteq V$ of sets of nodes which must satisfy the following properties: $P_0 = \\emptyset$ (we start off with no pebbles on $G$), $\\mathsf{sinks}(G) \\subseteq \\bigcup_{j \\leq t} P_j$ (every sink node was pebbled at some point) and $\\mathsf{parents}\\big(P_{i+1}\\backslash P_i\\big) \\subseteq P_i$ (we can only place a new pebble on a node $v$ if all of $v$'s parents had a pebble during the last round). The cumulative cost of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04449","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"}