{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QHVXSCTYQ55OYHADQVQZ3IQKGZ","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":"14e0b9bbee06c6b9584e9d2ae0f183d608f9105b9c12c2651071d44d2fa1d5bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-07-06T15:46:23Z","title_canon_sha256":"b2fefbad3340a1ae106d38ccba53ad29ed722dc1c7f8fd9dfb4fdba1dc365f2e"},"schema_version":"1.0","source":{"id":"1207.1668","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1668","created_at":"2026-05-18T03:51:36Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1668v1","created_at":"2026-05-18T03:51:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1668","created_at":"2026-05-18T03:51:36Z"},{"alias_kind":"pith_short_12","alias_value":"QHVXSCTYQ55O","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QHVXSCTYQ55OYHAD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QHVXSCTY","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:664df8ab5cdb6718cb3d1a83fd0d8e208efb3c5c8dc8bd21ce0b67b0940c31db","target":"graph","created_at":"2026-05-18T03:51:36Z","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":"To our knowledge, there are only two known algorithms for constructing sparse and light spanners for general graphs. One of them is the greedy algorithm of Alth$\\ddot{o}$fer et al. \\cite{ADDJS93}, analyzed by Chandra et al. in SoCG'92. The greedy algorithm consructs, for every \\emph{weighted} undirected $n$-vertex $m$-edge graph $G = (V,E)$ and any integer $k \\ge 1$, a $(2k-1)$-spanner with $O(n^{1 + 1/k})$ edges and weight $O(k \\cdot n^{(1+\\eps)/k}) \\cdot \\omega(MST(G))$, for any $\\eps > 0$. The drawback of the greedy algorithm is that it requires $O(m \\cdot (n^{1 + 1/k} + n \\cdot \\log n))$ t","authors_text":"Michael Elkin, Shay Solomon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-07-06T15:46:23Z","title":"Fast Constructions of Light-Weight Spanners for General Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1668","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":"sha256:0753154953f8cb320464e0c29875eb2e9407932a8d44148232d06547e474d7c1","target":"record","created_at":"2026-05-18T03:51:36Z","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":"14e0b9bbee06c6b9584e9d2ae0f183d608f9105b9c12c2651071d44d2fa1d5bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-07-06T15:46:23Z","title_canon_sha256":"b2fefbad3340a1ae106d38ccba53ad29ed722dc1c7f8fd9dfb4fdba1dc365f2e"},"schema_version":"1.0","source":{"id":"1207.1668","kind":"arxiv","version":1}},"canonical_sha256":"81eb790a78877aec1c0385619da20a3675bb9550268617777b3fe532325b7f8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81eb790a78877aec1c0385619da20a3675bb9550268617777b3fe532325b7f8e","first_computed_at":"2026-05-18T03:51:36.504981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:36.504981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sOtwrkNnr/W8FkEmFlJngsSYsMGeHo2DAnhuJEzxKox4hahseKT1Puw3w3b8sGI0LMl2ZpKU5OLKjvWHhPrnAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:36.505552Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1668","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0753154953f8cb320464e0c29875eb2e9407932a8d44148232d06547e474d7c1","sha256:664df8ab5cdb6718cb3d1a83fd0d8e208efb3c5c8dc8bd21ce0b67b0940c31db"],"state_sha256":"176af2f165892c7d246bd1bfdd0f9cc69816d3f26211465d962c06ebf6488e09"}