{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:AL3IPAM2NTWWH3KXEC5LPUK5QU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"26cc0c69dcf79ae43376f18644c29115275ef7b440de352e2d1c82fc677a0c97","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-01-08T21:23:37Z","title_canon_sha256":"264b98a11de33f59180e194f7417e0c71aa8dd7d566bb8428b9d38b9778ab227"},"schema_version":"1.0","source":{"id":"0901.1140","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.1140","created_at":"2026-05-18T02:15:02Z"},{"alias_kind":"arxiv_version","alias_value":"0901.1140v3","created_at":"2026-05-18T02:15:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1140","created_at":"2026-05-18T02:15:02Z"},{"alias_kind":"pith_short_12","alias_value":"AL3IPAM2NTWW","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"AL3IPAM2NTWWH3KX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"AL3IPAM2","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:247111c00f809a9b317ddbfe10bde2503a2e61bae8f84aa27ad4244e17cf436c","target":"graph","created_at":"2026-05-18T02:15:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In the \\emph{tollbooth problem}, we are given a tree $\\bT=(V,E)$ with $n$ edges, and a set of $m$ customers, each of whom is interested in purchasing a path on the tree. Each customer has a fixed budget, and the objective is to price the edges of $\\bT$ such that the total revenue made by selling the paths to the customers that can afford them is maximized. An important special case of this problem, known as the \\emph{highway problem}, is when $\\bT$ is restricted to be a line.\n  For the tollbooth problem, we present a randomized $O(\\log n)$-approximation, improving on the current best $O(\\log m","authors_text":"Khaled Elbassioni, Rajiv Raman, Rene Sitters, Saurabh Ray","cross_cats":["cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-01-08T21:23:37Z","title":"On Profit-Maximizing Pricing for the Highway and Tollbooth Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1140","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fb35a6f13147d1cc9341a355a04fb46cc5bd77a574dafb691969722e1b9ce2d0","target":"record","created_at":"2026-05-18T02:15:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"26cc0c69dcf79ae43376f18644c29115275ef7b440de352e2d1c82fc677a0c97","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-01-08T21:23:37Z","title_canon_sha256":"264b98a11de33f59180e194f7417e0c71aa8dd7d566bb8428b9d38b9778ab227"},"schema_version":"1.0","source":{"id":"0901.1140","kind":"arxiv","version":3}},"canonical_sha256":"02f687819a6ced63ed5720bab7d15d853c4e383a3599dd74a943e214c6112693","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02f687819a6ced63ed5720bab7d15d853c4e383a3599dd74a943e214c6112693","first_computed_at":"2026-05-18T02:15:02.854472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:02.854472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n6t7H+/p8bq+88R/ixn7PM+QunrslO3qU5sQDmP7sxNhEMPELtfKB5U2qVfZtrNiF6pkuHYior887xd8cgG4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:02.854894Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.1140","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb35a6f13147d1cc9341a355a04fb46cc5bd77a574dafb691969722e1b9ce2d0","sha256:247111c00f809a9b317ddbfe10bde2503a2e61bae8f84aa27ad4244e17cf436c"],"state_sha256":"dde8466ad8d26b725edc402bb796a2a70a3fce6cbfe0ce513d75556b21020b02"}