{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:A6CARZOQCNEJHSMSXUEBCZ26XD","short_pith_number":"pith:A6CARZOQ","schema_version":"1.0","canonical_sha256":"078408e5d0134893c992bd0811675eb8f08270ba0b1275b8fd43ebf3328e3834","source":{"kind":"arxiv","id":"1502.04533","version":1},"attestation_state":"computed","paper":{"title":"On the Minimum Cost Range Assignment Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Lilach Chaitman-Yerushalmi, Paz Carmi","submitted_at":"2015-02-16T13:47:05Z","abstract_excerpt":"We study the problem of assigning transmission ranges to radio stations placed arbitrarily in a $d$-dimensional ($d$-D) Euclidean space in order to achieve a strongly connected communication network with minimum total power consumption. The power required for transmitting in range $r$ is proportional to $r^\\alpha$, where $\\alpha$ is typically between $1$ and $6$, depending on various environmental factors. While this problem can be solved optimally in $1$D, in higher dimensions it is known to be $NP$-hard for any $\\alpha \\geq 1$.\n  For the $1$D version of the problem, i.e., radio stations loca"},"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":"1502.04533","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-02-16T13:47:05Z","cross_cats_sorted":[],"title_canon_sha256":"0fff5f00bc5042d8ea18610ec71ddd9f26da30d83995ddb07f910be58f074e64","abstract_canon_sha256":"e13a90a9d4cc115f0838281449e728842dc6a698920a4991f9554d97bb0b5d96"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:59.590037Z","signature_b64":"e3mPF2V3342Zr2e0jbVpJIqpVb9GQqaPbsrIGGulvWKF7UJjo/pAihHo+rlf4Ufb6IMe6ozkwEfbttdsAVe4CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"078408e5d0134893c992bd0811675eb8f08270ba0b1275b8fd43ebf3328e3834","last_reissued_at":"2026-05-18T02:26:59.589688Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:59.589688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Minimum Cost Range Assignment Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Lilach Chaitman-Yerushalmi, Paz Carmi","submitted_at":"2015-02-16T13:47:05Z","abstract_excerpt":"We study the problem of assigning transmission ranges to radio stations placed arbitrarily in a $d$-dimensional ($d$-D) Euclidean space in order to achieve a strongly connected communication network with minimum total power consumption. The power required for transmitting in range $r$ is proportional to $r^\\alpha$, where $\\alpha$ is typically between $1$ and $6$, depending on various environmental factors. While this problem can be solved optimally in $1$D, in higher dimensions it is known to be $NP$-hard for any $\\alpha \\geq 1$.\n  For the $1$D version of the problem, i.e., radio stations loca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04533","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.04533","created_at":"2026-05-18T02:26:59.589747+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.04533v1","created_at":"2026-05-18T02:26:59.589747+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04533","created_at":"2026-05-18T02:26:59.589747+00:00"},{"alias_kind":"pith_short_12","alias_value":"A6CARZOQCNEJ","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"A6CARZOQCNEJHSMS","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"A6CARZOQ","created_at":"2026-05-18T12:29:10.953037+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A6CARZOQCNEJHSMSXUEBCZ26XD","json":"https://pith.science/pith/A6CARZOQCNEJHSMSXUEBCZ26XD.json","graph_json":"https://pith.science/api/pith-number/A6CARZOQCNEJHSMSXUEBCZ26XD/graph.json","events_json":"https://pith.science/api/pith-number/A6CARZOQCNEJHSMSXUEBCZ26XD/events.json","paper":"https://pith.science/paper/A6CARZOQ"},"agent_actions":{"view_html":"https://pith.science/pith/A6CARZOQCNEJHSMSXUEBCZ26XD","download_json":"https://pith.science/pith/A6CARZOQCNEJHSMSXUEBCZ26XD.json","view_paper":"https://pith.science/paper/A6CARZOQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.04533&json=true","fetch_graph":"https://pith.science/api/pith-number/A6CARZOQCNEJHSMSXUEBCZ26XD/graph.json","fetch_events":"https://pith.science/api/pith-number/A6CARZOQCNEJHSMSXUEBCZ26XD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A6CARZOQCNEJHSMSXUEBCZ26XD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A6CARZOQCNEJHSMSXUEBCZ26XD/action/storage_attestation","attest_author":"https://pith.science/pith/A6CARZOQCNEJHSMSXUEBCZ26XD/action/author_attestation","sign_citation":"https://pith.science/pith/A6CARZOQCNEJHSMSXUEBCZ26XD/action/citation_signature","submit_replication":"https://pith.science/pith/A6CARZOQCNEJHSMSXUEBCZ26XD/action/replication_record"}},"created_at":"2026-05-18T02:26:59.589747+00:00","updated_at":"2026-05-18T02:26:59.589747+00:00"}