{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:BEFAOW3DOBET62LTBRVLG335FP","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":"6604e32cc1b04cf93f05f97d0f490ce3bac74aaa05e9c6f00f8478d6e42d2949","cross_cats_sorted":["cs.DS"],"license":"","primary_cat":"cs.CC","submitted_at":"1998-09-24T17:48:18Z","title_canon_sha256":"350ad84cd4991b07a88c84bcf3096a4b312cb087a0cbfdabbb77984ecf754ed3"},"schema_version":"1.0","source":{"id":"cs/9809103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/9809103","created_at":"2026-07-04T23:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"cs/9809103v1","created_at":"2026-07-04T23:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/9809103","created_at":"2026-07-04T23:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"BEFAOW3DOBET","created_at":"2026-07-04T23:57:25Z"},{"alias_kind":"pith_short_16","alias_value":"BEFAOW3DOBET62LT","created_at":"2026-07-04T23:57:25Z"},{"alias_kind":"pith_short_8","alias_value":"BEFAOW3D","created_at":"2026-07-04T23:57:25Z"}],"graph_snapshots":[{"event_id":"sha256:5c5589bdbf06ab590a65e48abf17f8cc65ba00a1e321fdd5232f41ba3198e07e","target":"graph","created_at":"2026-07-04T23:57:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cs/9809103/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a <subgraph \\from a given subgraph-class that minimizes the second objective subject to the budget on the first. We consider three different criteria - the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for t","authors_text":"Daniel J. Rosenkrantz, Harry B. Hunt III, Madhav V. Marathe, Ravi Sundaram, R. Ravi, S. S. Ravi","cross_cats":["cs.DS"],"headline":"","license":"","primary_cat":"cs.CC","submitted_at":"1998-09-24T17:48:18Z","title":"Bicriteria Network Design Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/9809103","kind":"arxiv","version":1},"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:ce02675bc3ee159679285824b9b4df0ecab7f264545b5b8113bdcc1f50d2e6fd","target":"record","created_at":"2026-07-04T23:57:25Z","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":"6604e32cc1b04cf93f05f97d0f490ce3bac74aaa05e9c6f00f8478d6e42d2949","cross_cats_sorted":["cs.DS"],"license":"","primary_cat":"cs.CC","submitted_at":"1998-09-24T17:48:18Z","title_canon_sha256":"350ad84cd4991b07a88c84bcf3096a4b312cb087a0cbfdabbb77984ecf754ed3"},"schema_version":"1.0","source":{"id":"cs/9809103","kind":"arxiv","version":1}},"canonical_sha256":"090a075b6370493f69730c6ab36f7d2bde601d04e475014cb19a77ea7942d18e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"090a075b6370493f69730c6ab36f7d2bde601d04e475014cb19a77ea7942d18e","first_computed_at":"2026-07-04T23:57:25.774566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:57:25.774566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h60Va/WVfqv3+6xL9X2KZP3GOemC6QpReAiaqxeK/Kx8rBx5NJDREo6St/madNw2cF8fBlfkqzeQZo8dyA85Dg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:57:25.775166Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/9809103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce02675bc3ee159679285824b9b4df0ecab7f264545b5b8113bdcc1f50d2e6fd","sha256:5c5589bdbf06ab590a65e48abf17f8cc65ba00a1e321fdd5232f41ba3198e07e"],"state_sha256":"de638efcb81cda8f6e38ff4d95f1a8db8d90c2c8725fa956c3cce0b79d23350f"}