{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:35XU5JBFFNCGBI2PBHU73KDBI4","short_pith_number":"pith:35XU5JBF","schema_version":"1.0","canonical_sha256":"df6f4ea4252b4460a34f09e9fda861472afcd31a0e30d2d5ae77ab9934f93ab8","source":{"kind":"arxiv","id":"2411.13334","version":2},"attestation_state":"computed","paper":{"title":"Sublinear-Time Sampling of Spanning Trees in the Congested Clique","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Joshua Z. Sobel, Sourya Roy, Sriram V. Pemmaraju","submitted_at":"2024-11-20T14:07:23Z","abstract_excerpt":"We present the first sublinear-in-$n$ round algorithm for sampling an approximately uniform spanning tree of an $n$-vertex graph in the CongestedClique model of distributed computing. In particular, our algorithm requires $\\Tilde{O}(n^{0.657})$ rounds for sampling a spanning tree within total variation distance $1/n^c$, for arbitrary constant $c > 0$, from the uniform distribution. More precisely, our algorithm requires $\\Tilde{O}(n^{1/2 + \\alpha})$ rounds, where $O(n^\\alpha)$ is the running time of matrix multiplication in the CongestedClique model (currently $\\alpha = 1 - 2/\\omega = 0.157$, "},"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":"2411.13334","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DC","submitted_at":"2024-11-20T14:07:23Z","cross_cats_sorted":[],"title_canon_sha256":"cd81256e775b462c01c34c5d560ea0f853f876be478e9518080d23ef7ff0549e","abstract_canon_sha256":"c3876ebb129cf216a39719992a20a7c3cf9e166bb49861aaf57513ab7432ac2d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:00:40.372950Z","signature_b64":"SVtM/riVcYEGOxRgRyvlR2dfFXfq0PRISw3RXtQrPoh3vwuvsa5PPQ7x/0i180F08gc6Y85NrdbBaPpdHo1NCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df6f4ea4252b4460a34f09e9fda861472afcd31a0e30d2d5ae77ab9934f93ab8","last_reissued_at":"2026-07-05T11:00:40.372376Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:00:40.372376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sublinear-Time Sampling of Spanning Trees in the Congested Clique","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Joshua Z. Sobel, Sourya Roy, Sriram V. Pemmaraju","submitted_at":"2024-11-20T14:07:23Z","abstract_excerpt":"We present the first sublinear-in-$n$ round algorithm for sampling an approximately uniform spanning tree of an $n$-vertex graph in the CongestedClique model of distributed computing. In particular, our algorithm requires $\\Tilde{O}(n^{0.657})$ rounds for sampling a spanning tree within total variation distance $1/n^c$, for arbitrary constant $c > 0$, from the uniform distribution. More precisely, our algorithm requires $\\Tilde{O}(n^{1/2 + \\alpha})$ rounds, where $O(n^\\alpha)$ is the running time of matrix multiplication in the CongestedClique model (currently $\\alpha = 1 - 2/\\omega = 0.157$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13334","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.13334/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2411.13334","created_at":"2026-07-05T11:00:40.372456+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.13334v2","created_at":"2026-07-05T11:00:40.372456+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13334","created_at":"2026-07-05T11:00:40.372456+00:00"},{"alias_kind":"pith_short_12","alias_value":"35XU5JBFFNCG","created_at":"2026-07-05T11:00:40.372456+00:00"},{"alias_kind":"pith_short_16","alias_value":"35XU5JBFFNCGBI2P","created_at":"2026-07-05T11:00:40.372456+00:00"},{"alias_kind":"pith_short_8","alias_value":"35XU5JBF","created_at":"2026-07-05T11:00:40.372456+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/35XU5JBFFNCGBI2PBHU73KDBI4","json":"https://pith.science/pith/35XU5JBFFNCGBI2PBHU73KDBI4.json","graph_json":"https://pith.science/api/pith-number/35XU5JBFFNCGBI2PBHU73KDBI4/graph.json","events_json":"https://pith.science/api/pith-number/35XU5JBFFNCGBI2PBHU73KDBI4/events.json","paper":"https://pith.science/paper/35XU5JBF"},"agent_actions":{"view_html":"https://pith.science/pith/35XU5JBFFNCGBI2PBHU73KDBI4","download_json":"https://pith.science/pith/35XU5JBFFNCGBI2PBHU73KDBI4.json","view_paper":"https://pith.science/paper/35XU5JBF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.13334&json=true","fetch_graph":"https://pith.science/api/pith-number/35XU5JBFFNCGBI2PBHU73KDBI4/graph.json","fetch_events":"https://pith.science/api/pith-number/35XU5JBFFNCGBI2PBHU73KDBI4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/35XU5JBFFNCGBI2PBHU73KDBI4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/35XU5JBFFNCGBI2PBHU73KDBI4/action/storage_attestation","attest_author":"https://pith.science/pith/35XU5JBFFNCGBI2PBHU73KDBI4/action/author_attestation","sign_citation":"https://pith.science/pith/35XU5JBFFNCGBI2PBHU73KDBI4/action/citation_signature","submit_replication":"https://pith.science/pith/35XU5JBFFNCGBI2PBHU73KDBI4/action/replication_record"}},"created_at":"2026-07-05T11:00:40.372456+00:00","updated_at":"2026-07-05T11:00:40.372456+00:00"}