{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ULG3OU3DJLTUXI7DI5HOH6NNSI","short_pith_number":"pith:ULG3OU3D","schema_version":"1.0","canonical_sha256":"a2cdb753634ae74ba3e3474ee3f9ad921aea7f3802455b70e45acf8e86c9ebc4","source":{"kind":"arxiv","id":"1708.09314","version":2},"attestation_state":"computed","paper":{"title":"A Note on Approximating Weighted Independence on Intersection Graphs of Paths on a Grid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Saeed Mehrabi","submitted_at":"2017-08-30T15:06:28Z","abstract_excerpt":"A graph $G$ is called $B_k$-VPG, for some constant $k\\geq 0$, if it has a string representation on an axis-parallel grid such that each vertex is a path with at most $k$ bends and two vertices are adjacent in $G$ if and only if the corresponding paths intersect each other. The part of a path that is between two consecutive bends is called a segment of the path. In this paper, we study the Maximum-Weighted Independent Set problem on $B_k$-VPG graphs. The problem is known to be NP-complete on $B_1$-VPG graphs, even when the two segments of every path have unit length [12], and $O(\\log n)$-approx"},"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":"1708.09314","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-08-30T15:06:28Z","cross_cats_sorted":[],"title_canon_sha256":"40f4ebca8b137c0bc5384511237f21a3336f2e3a260631bf169e7f4672f3c168","abstract_canon_sha256":"c1a73d3c11057ba0defc06a2230e38b9b1187dde72434760f80ec987210ca56f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:20.832236Z","signature_b64":"NdVcuW7sJ42WKbZcKOA90bdbrWfwwaM6TpRaoG2gSVPWlzq3ScTnGHlmqdLhmy4Mzj8z7yuw9eTpeM6gMqdEDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2cdb753634ae74ba3e3474ee3f9ad921aea7f3802455b70e45acf8e86c9ebc4","last_reissued_at":"2026-05-18T00:06:20.831752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:20.831752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on Approximating Weighted Independence on Intersection Graphs of Paths on a Grid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Saeed Mehrabi","submitted_at":"2017-08-30T15:06:28Z","abstract_excerpt":"A graph $G$ is called $B_k$-VPG, for some constant $k\\geq 0$, if it has a string representation on an axis-parallel grid such that each vertex is a path with at most $k$ bends and two vertices are adjacent in $G$ if and only if the corresponding paths intersect each other. The part of a path that is between two consecutive bends is called a segment of the path. In this paper, we study the Maximum-Weighted Independent Set problem on $B_k$-VPG graphs. The problem is known to be NP-complete on $B_1$-VPG graphs, even when the two segments of every path have unit length [12], and $O(\\log n)$-approx"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09314","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":"1708.09314","created_at":"2026-05-18T00:06:20.831833+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.09314v2","created_at":"2026-05-18T00:06:20.831833+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09314","created_at":"2026-05-18T00:06:20.831833+00:00"},{"alias_kind":"pith_short_12","alias_value":"ULG3OU3DJLTU","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"ULG3OU3DJLTUXI7D","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"ULG3OU3D","created_at":"2026-05-18T12:31:46.661854+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/ULG3OU3DJLTUXI7DI5HOH6NNSI","json":"https://pith.science/pith/ULG3OU3DJLTUXI7DI5HOH6NNSI.json","graph_json":"https://pith.science/api/pith-number/ULG3OU3DJLTUXI7DI5HOH6NNSI/graph.json","events_json":"https://pith.science/api/pith-number/ULG3OU3DJLTUXI7DI5HOH6NNSI/events.json","paper":"https://pith.science/paper/ULG3OU3D"},"agent_actions":{"view_html":"https://pith.science/pith/ULG3OU3DJLTUXI7DI5HOH6NNSI","download_json":"https://pith.science/pith/ULG3OU3DJLTUXI7DI5HOH6NNSI.json","view_paper":"https://pith.science/paper/ULG3OU3D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.09314&json=true","fetch_graph":"https://pith.science/api/pith-number/ULG3OU3DJLTUXI7DI5HOH6NNSI/graph.json","fetch_events":"https://pith.science/api/pith-number/ULG3OU3DJLTUXI7DI5HOH6NNSI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ULG3OU3DJLTUXI7DI5HOH6NNSI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ULG3OU3DJLTUXI7DI5HOH6NNSI/action/storage_attestation","attest_author":"https://pith.science/pith/ULG3OU3DJLTUXI7DI5HOH6NNSI/action/author_attestation","sign_citation":"https://pith.science/pith/ULG3OU3DJLTUXI7DI5HOH6NNSI/action/citation_signature","submit_replication":"https://pith.science/pith/ULG3OU3DJLTUXI7DI5HOH6NNSI/action/replication_record"}},"created_at":"2026-05-18T00:06:20.831833+00:00","updated_at":"2026-05-18T00:06:20.831833+00:00"}