{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:6F6XMNDQUOBDCQRRHW2V63YL46","short_pith_number":"pith:6F6XMNDQ","schema_version":"1.0","canonical_sha256":"f17d763470a3823142313db55f6f0be7ad08cade60f5a3467d98c5b2ff97c194","source":{"kind":"arxiv","id":"1107.2256","version":5},"attestation_state":"computed","paper":{"title":"Complexity of Metric Dimension on Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Erik Jan van Leeuwen, Josep Diaz, Maria Serna, Olli Pottonen","submitted_at":"2011-07-12T12:07:33Z","abstract_excerpt":"The metric dimension of a graph $G$ is the size of a smallest subset $L \\subseteq V(G)$ such that for any $x,y \\in V(G)$ with $x\\not= y$ there is a $z \\in L$ such that the graph distance between $x$ and $z$ differs from the graph distance between $y$ and $z$. Even though this notion has been part of the literature for almost 40 years, prior to our work the computational complexity of determining the metric dimension of a graph was still very unclear. In this paper, we show tight complexity boundaries for the Metric Dimension problem. We achieve this by giving two complementary results. First, "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1107.2256","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-07-12T12:07:33Z","cross_cats_sorted":[],"title_canon_sha256":"a81121dee11335c1923e78af84ecc3ec1fb555e24e327ad9ee2b6b45a1b43f7d","abstract_canon_sha256":"f7c924190fc20a7932a9db5191c457da41fc9a9fedd73656abcfe586430b0611"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:13.917953Z","signature_b64":"6MKvey/Xr//EWHs6gFK2K4ZDhJ0Vn2i7V1qpwwAV1PxUdi3wmLsGjjOTpC8PKAsCyWaB0aOxkl1jkjo+g3CTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f17d763470a3823142313db55f6f0be7ad08cade60f5a3467d98c5b2ff97c194","last_reissued_at":"2026-05-18T01:11:13.917389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:13.917389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complexity of Metric Dimension on Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Erik Jan van Leeuwen, Josep Diaz, Maria Serna, Olli Pottonen","submitted_at":"2011-07-12T12:07:33Z","abstract_excerpt":"The metric dimension of a graph $G$ is the size of a smallest subset $L \\subseteq V(G)$ such that for any $x,y \\in V(G)$ with $x\\not= y$ there is a $z \\in L$ such that the graph distance between $x$ and $z$ differs from the graph distance between $y$ and $z$. Even though this notion has been part of the literature for almost 40 years, prior to our work the computational complexity of determining the metric dimension of a graph was still very unclear. In this paper, we show tight complexity boundaries for the Metric Dimension problem. We achieve this by giving two complementary results. First, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2256","kind":"arxiv","version":5},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1107.2256","created_at":"2026-05-18T01:11:13.917475+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.2256v5","created_at":"2026-05-18T01:11:13.917475+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2256","created_at":"2026-05-18T01:11:13.917475+00:00"},{"alias_kind":"pith_short_12","alias_value":"6F6XMNDQUOBD","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"6F6XMNDQUOBDCQRR","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"6F6XMNDQ","created_at":"2026-05-18T12:26:22.705136+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2409.12199","citing_title":"Fault Tolerant Metric Dimensions of Leafless Cacti Graphs with Application in Supply Chain Management","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6F6XMNDQUOBDCQRRHW2V63YL46","json":"https://pith.science/pith/6F6XMNDQUOBDCQRRHW2V63YL46.json","graph_json":"https://pith.science/api/pith-number/6F6XMNDQUOBDCQRRHW2V63YL46/graph.json","events_json":"https://pith.science/api/pith-number/6F6XMNDQUOBDCQRRHW2V63YL46/events.json","paper":"https://pith.science/paper/6F6XMNDQ"},"agent_actions":{"view_html":"https://pith.science/pith/6F6XMNDQUOBDCQRRHW2V63YL46","download_json":"https://pith.science/pith/6F6XMNDQUOBDCQRRHW2V63YL46.json","view_paper":"https://pith.science/paper/6F6XMNDQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.2256&json=true","fetch_graph":"https://pith.science/api/pith-number/6F6XMNDQUOBDCQRRHW2V63YL46/graph.json","fetch_events":"https://pith.science/api/pith-number/6F6XMNDQUOBDCQRRHW2V63YL46/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6F6XMNDQUOBDCQRRHW2V63YL46/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6F6XMNDQUOBDCQRRHW2V63YL46/action/storage_attestation","attest_author":"https://pith.science/pith/6F6XMNDQUOBDCQRRHW2V63YL46/action/author_attestation","sign_citation":"https://pith.science/pith/6F6XMNDQUOBDCQRRHW2V63YL46/action/citation_signature","submit_replication":"https://pith.science/pith/6F6XMNDQUOBDCQRRHW2V63YL46/action/replication_record"}},"created_at":"2026-05-18T01:11:13.917475+00:00","updated_at":"2026-05-18T01:11:13.917475+00:00"}