{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5BIEOVZIRCX7DJHPCS2RR3CLYP","short_pith_number":"pith:5BIEOVZI","schema_version":"1.0","canonical_sha256":"e85047572888aff1a4ef14b518ec4bc3c9ef5725b8329f36f98723eb7ca8aa95","source":{"kind":"arxiv","id":"1702.06969","version":5},"attestation_state":"computed","paper":{"title":"Approximating Unique Games Using Low Diameter Graph Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Lap Chi Lau, Vedat Levi Alev","submitted_at":"2017-02-22T19:08:25Z","abstract_excerpt":"We design approximation algorithms for Unique Games when the constraint graph admits good low diameter graph decomposition. For the ${\\sf Max2Lin}_k$ problem in $K_r$-minor free graphs, when there is an assignment satisfying $1-\\varepsilon$ fraction of constraints, we present an algorithm that produces an assignment satisfying $1-O(r\\varepsilon)$ fraction of constraints, with the approximation ratio independent of the alphabet size. A corollary is an improved approximation algorithm for the ${\\sf MaxCut}$ problem for $K_r$-minor free graphs. For general Unique Games in $K_r$-minor free graphs,"},"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":"1702.06969","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-22T19:08:25Z","cross_cats_sorted":[],"title_canon_sha256":"934a5c1bea37c338a7760617db7a385fba4b4465d63ed53c0ab05ce4b79e7dba","abstract_canon_sha256":"70c5d5eb0e0924469e56eb8bb9245164c723c01b10879e1f1412f641222730cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:15.377775Z","signature_b64":"Ogb6bCaBvKRDR7tv7//JopuADWJuaNvlXdbqQyU1wbL5GJT/ptuPIxCcjSQkw4nOEhIc2Ep/EG4fzTuqFBOuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e85047572888aff1a4ef14b518ec4bc3c9ef5725b8329f36f98723eb7ca8aa95","last_reissued_at":"2026-05-18T00:29:15.377327Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:15.377327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximating Unique Games Using Low Diameter Graph Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Lap Chi Lau, Vedat Levi Alev","submitted_at":"2017-02-22T19:08:25Z","abstract_excerpt":"We design approximation algorithms for Unique Games when the constraint graph admits good low diameter graph decomposition. For the ${\\sf Max2Lin}_k$ problem in $K_r$-minor free graphs, when there is an assignment satisfying $1-\\varepsilon$ fraction of constraints, we present an algorithm that produces an assignment satisfying $1-O(r\\varepsilon)$ fraction of constraints, with the approximation ratio independent of the alphabet size. A corollary is an improved approximation algorithm for the ${\\sf MaxCut}$ problem for $K_r$-minor free graphs. For general Unique Games in $K_r$-minor free graphs,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06969","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":"1702.06969","created_at":"2026-05-18T00:29:15.377395+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.06969v5","created_at":"2026-05-18T00:29:15.377395+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06969","created_at":"2026-05-18T00:29:15.377395+00:00"},{"alias_kind":"pith_short_12","alias_value":"5BIEOVZIRCX7","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5BIEOVZIRCX7DJHP","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5BIEOVZI","created_at":"2026-05-18T12:31:00.734936+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.10479","citing_title":"Public Key Encryption from High-Corruption Constraint Satisfaction Problems","ref_index":61,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5BIEOVZIRCX7DJHPCS2RR3CLYP","json":"https://pith.science/pith/5BIEOVZIRCX7DJHPCS2RR3CLYP.json","graph_json":"https://pith.science/api/pith-number/5BIEOVZIRCX7DJHPCS2RR3CLYP/graph.json","events_json":"https://pith.science/api/pith-number/5BIEOVZIRCX7DJHPCS2RR3CLYP/events.json","paper":"https://pith.science/paper/5BIEOVZI"},"agent_actions":{"view_html":"https://pith.science/pith/5BIEOVZIRCX7DJHPCS2RR3CLYP","download_json":"https://pith.science/pith/5BIEOVZIRCX7DJHPCS2RR3CLYP.json","view_paper":"https://pith.science/paper/5BIEOVZI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.06969&json=true","fetch_graph":"https://pith.science/api/pith-number/5BIEOVZIRCX7DJHPCS2RR3CLYP/graph.json","fetch_events":"https://pith.science/api/pith-number/5BIEOVZIRCX7DJHPCS2RR3CLYP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5BIEOVZIRCX7DJHPCS2RR3CLYP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5BIEOVZIRCX7DJHPCS2RR3CLYP/action/storage_attestation","attest_author":"https://pith.science/pith/5BIEOVZIRCX7DJHPCS2RR3CLYP/action/author_attestation","sign_citation":"https://pith.science/pith/5BIEOVZIRCX7DJHPCS2RR3CLYP/action/citation_signature","submit_replication":"https://pith.science/pith/5BIEOVZIRCX7DJHPCS2RR3CLYP/action/replication_record"}},"created_at":"2026-05-18T00:29:15.377395+00:00","updated_at":"2026-05-18T00:29:15.377395+00:00"}