{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZECDFU6ZGNFVV342NWCPV4VJKP","short_pith_number":"pith:ZECDFU6Z","schema_version":"1.0","canonical_sha256":"c90432d3d9334b5aef9a6d84faf2a953c804f985f613d3efb22ddd51338ffa20","source":{"kind":"arxiv","id":"1505.04918","version":2},"attestation_state":"computed","paper":{"title":"Sublinear Approximation Algorithms for Boxicity and Related Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Abhijin Adiga, Jasine Babu, L. Sunil Chandran","submitted_at":"2015-05-19T09:19:39Z","abstract_excerpt":"Boxicity of a graph G(V, E) is the minimum integer k such that G can be represented as the intersection graph of axis parallel boxes in $\\mathbb{R}^k$. Cubicity is a variant of boxicity, where the axis parallel boxes in the intersection representation are restricted to be of unit length sides. Deciding whether boxicity (resp. cubicity) of a graph is at most k is NP-hard, even for k=2 or 3. Computing these parameters is inapproximable within $O(n^{1 - \\epsilon})$-factor, for any $\\epsilon >0$ in polynomial time unless NP=ZPP, even for many simple graph classes.\n  In this paper, we give a polyno"},"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":"1505.04918","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-05-19T09:19:39Z","cross_cats_sorted":[],"title_canon_sha256":"f63380d66724774d97758e6a35259d265e38a370eeca49a4637780698f6db5da","abstract_canon_sha256":"75f0edd155a7f2b037915096cc7abbd132f9318742e769479194dab981b97574"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:52.344265Z","signature_b64":"+BZMAF8JHnS6LtReC4ncnjcDeDSJO4LbFxONenc7uQj34bKduiMm3A68vdCFw15Lx8ulUDexmCKbx8Le2g22Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c90432d3d9334b5aef9a6d84faf2a953c804f985f613d3efb22ddd51338ffa20","last_reissued_at":"2026-05-18T01:55:52.343591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:52.343591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sublinear Approximation Algorithms for Boxicity and Related Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Abhijin Adiga, Jasine Babu, L. Sunil Chandran","submitted_at":"2015-05-19T09:19:39Z","abstract_excerpt":"Boxicity of a graph G(V, E) is the minimum integer k such that G can be represented as the intersection graph of axis parallel boxes in $\\mathbb{R}^k$. Cubicity is a variant of boxicity, where the axis parallel boxes in the intersection representation are restricted to be of unit length sides. Deciding whether boxicity (resp. cubicity) of a graph is at most k is NP-hard, even for k=2 or 3. Computing these parameters is inapproximable within $O(n^{1 - \\epsilon})$-factor, for any $\\epsilon >0$ in polynomial time unless NP=ZPP, even for many simple graph classes.\n  In this paper, we give a polyno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04918","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.04918","created_at":"2026-05-18T01:55:52.343706+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.04918v2","created_at":"2026-05-18T01:55:52.343706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04918","created_at":"2026-05-18T01:55:52.343706+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZECDFU6ZGNFV","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZECDFU6ZGNFVV342","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZECDFU6Z","created_at":"2026-05-18T12:29:52.810259+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/ZECDFU6ZGNFVV342NWCPV4VJKP","json":"https://pith.science/pith/ZECDFU6ZGNFVV342NWCPV4VJKP.json","graph_json":"https://pith.science/api/pith-number/ZECDFU6ZGNFVV342NWCPV4VJKP/graph.json","events_json":"https://pith.science/api/pith-number/ZECDFU6ZGNFVV342NWCPV4VJKP/events.json","paper":"https://pith.science/paper/ZECDFU6Z"},"agent_actions":{"view_html":"https://pith.science/pith/ZECDFU6ZGNFVV342NWCPV4VJKP","download_json":"https://pith.science/pith/ZECDFU6ZGNFVV342NWCPV4VJKP.json","view_paper":"https://pith.science/paper/ZECDFU6Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.04918&json=true","fetch_graph":"https://pith.science/api/pith-number/ZECDFU6ZGNFVV342NWCPV4VJKP/graph.json","fetch_events":"https://pith.science/api/pith-number/ZECDFU6ZGNFVV342NWCPV4VJKP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZECDFU6ZGNFVV342NWCPV4VJKP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZECDFU6ZGNFVV342NWCPV4VJKP/action/storage_attestation","attest_author":"https://pith.science/pith/ZECDFU6ZGNFVV342NWCPV4VJKP/action/author_attestation","sign_citation":"https://pith.science/pith/ZECDFU6ZGNFVV342NWCPV4VJKP/action/citation_signature","submit_replication":"https://pith.science/pith/ZECDFU6ZGNFVV342NWCPV4VJKP/action/replication_record"}},"created_at":"2026-05-18T01:55:52.343706+00:00","updated_at":"2026-05-18T01:55:52.343706+00:00"}