Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T20:00:51.045225Z
Paper Citation Record · LEDGER
Fast Matrix Multiplication meets the Submodular Width
As of 23 August 2026, this Paper Citation Record lists 73 of 73 outbound references and 1 inbound Pith citation observation for arXiv:2412.06189.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-15T19:17:20.496742Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-16T12:16:17.039197Z
Reference resolution
73 of 73 outbound references displayed
- verified exact2
- verified fuzzy24
- unresolved45
- parse uncertain2
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 076eafca-4929-4c25-aca8-15809f9ea6ee · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.423665Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 387b8274-f0ca-4dcd-9ea2-544c025f53e3 · outbound
This paper cites Curtin, Benjamin Moseley, Hung Q.
Fast Matrix Multiplication meets the Submodular Width Curtin, Benjamin Moseley, Hung Q
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.526341Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fbbaa041-eef0-4f64-a1d7-5cbf0e696017 · outbound
This paper cites Ngo, and Atri Rudra.
Fast Matrix Multiplication meets the Submodular Width Ngo, and Atri Rudra
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.538045Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d955239c-d74b-40cf-b834-92299c633e99 · outbound
This paper cites Ngo, and Dan Suciu.
Fast Matrix Multiplication meets the Submodular Width Ngo, and Dan Suciu
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.546887Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 68241f88-a194-441c-aa7b-9d1cbfc5c181 · outbound
This paper cites PANDA: Query Evaluation in Submodular Width.
Fast Matrix Multiplication meets the Submodular Width PANDA: Query Evaluation in Submodular Width
Reference 5
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T20:00:51.297100Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4eaa87e6-1be4-490b-b34e-84db1bb4b9ea · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.567472Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a21bf7b6-10c4-4985-828a-9409495f9aa6 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.405842Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation f4174e5c-74d4-41b4-8d91-5ac6206e040f · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.586711Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 093b47a5-6fd0-4ef2-8835-0beb7ddb90ab · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.596069Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ce34da67-960e-4876-a6aa-25c2bd4f16b4 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.385005Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation d4030a23-ea3c-4254-9d49-95399facf0b9 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.361851Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation b24a29ec-b840-4f83-af98-514216a64d28 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.342381Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 229c531b-b3f2-48da-99ab-797e0d48826a · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.629046Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 25f1aa7f-5dc1-471b-abe2-f3fb74801cab · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 14
- Resolution
- verified exact
- doi, observed 2026-08-11T20:00:51.190255Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4d44e426-3d06-469d-a8cd-e375486d3f78 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.324356Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation af9a3f9e-243c-4502-94a4-b20c20fee263 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.299950Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 12cf8f11-e4a0-42aa-ab0c-c79dd41b9de0 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 17
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.656552Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation aadf09d2-3258-4b43-9c65-af3c009bf761 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.662999Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3d53f079-a83b-4398-a225-588e3c748196 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.669700Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 56395d05-67e3-4290-a657-645bbb9b5766 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.275832Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2b767378-d4d4-484c-9fb3-65d6f8561616 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.255141Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 092b48e8-e2b9-4331-b7e9-42b77478b282 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.234100Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation dd5f605b-8cda-4e5f-bc81-87ee1fd328b9 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.206235Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 7ebf7105-c349-4000-96cd-d5d3f9dbed8e · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 24
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.699672Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation dc08b13e-2e89-4e68-b037-7564cdfe4d97 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 25
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.707607Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 22460838-88f6-48fb-b481-cc84a66d0ca5 · outbound
This paper cites Ngo, Ely Porat, Christopher Ré, and Atri Rudra.
Fast Matrix Multiplication meets the Submodular Width Ngo, Ely Porat, Christopher Ré, and Atri Rudra
Reference 26
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.713571Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 75a01ef2-676c-42db-92d7-9cf214f28fa1 · outbound
This paper cites Ngo, Christopher Ré, and Atri Rudra.
Fast Matrix Multiplication meets the Submodular Width Ngo, Christopher Ré, and Atri Rudra
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.719768Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fb55bbaa-2205-429a-a315-d1719f305d4b · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.180614Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 7d17f817-f3ab-4639-8a24-2237725d5fef · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.158523Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 09b53922-5379-4fc6-bc99-752531e39952 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.120088Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 19a16368-1111-4055-bf56-d4971cb7eedb · outbound
This paper cites Veldhuizen.
Fast Matrix Multiplication meets the Submodular Width Veldhuizen
Reference 31
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.747733Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5b0a676e-67b7-46fa-9686-11a1f01f73e8 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 32
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:00:50.759172Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e5d7f76b-2bbc-4f8c-a137-408577938e90 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 33
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.097943Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation dfafb13a-7a9e-4664-9102-0020c2aa99b7 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 34
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.077639Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 3d06f4bd-ee35-4e8c-9a18-1e0c2d7cf738 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.050151Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation b7d9ead8-823e-4b75-8471-933c1fd1e884 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:53.031534Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5f85a2a9-98f0-4a03-a464-6c3d9f8770b7 · outbound
This paper cites subsumes.
Fast Matrix Multiplication meets the Submodular Width subsumes
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:53.004853Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e035edb3-733b-4227-a595-e5c9b07a8f09 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 38
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:52.970967Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 633df375-7c32-44f6-a330-09342aaff28b · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 39
- Resolution
- parse uncertain
- raw_fallback, observed 2026-08-11T20:00:52.941362Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 1042d890-0ffe-4781-aa62-96d5207cddad · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 40
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:52.922631Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation ef8c6f9c-7b08-4cf9-99af-727fb9701a95 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 41
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:52.884547Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 41ef217d-3897-4227-b79f-362743ed600e · outbound
This paper cites We have EMM𝝈 1 ≤ MM(𝑌 ;𝑍 ;𝑋|𝑊) = 𝜔+1 2.
Fast Matrix Multiplication meets the Submodular Width We have EMM𝝈 1 ≤ MM(𝑌 ;𝑍 ;𝑋|𝑊) = 𝜔+1 2
Reference 42
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.856561Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c02a2da9-3cea-41fe-8926-950a33f300b0 · outbound
This paper cites From Proposition C.4, for an arbitrary generalized elimination ordering 𝝈∈𝜋(V) , EMM𝝈 1 = 𝜔+1 2.
Fast Matrix Multiplication meets the Submodular Width From Proposition C.4, for an arbitrary generalized elimination ordering 𝝈∈𝜋(V) , EMM𝝈 1 = 𝜔+1 2
Reference 43
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.828898Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation a355bf0d-6595-4153-8b4a-6120bd2ad6e3 · outbound
This paper cites By choosingA ={{𝑋,𝑊},{𝑌,𝑊},{𝑋,𝐿}} andB ={{𝑋,𝑊},{𝑍,𝑊}}, EMM𝝈 1 ≤ MM(𝑌𝑍,𝑊,𝑋 |𝐿) =ℎ(𝑌𝑍)+ 𝛾· min{ℎ(𝑊|𝐿),ℎ(𝑋|𝐿)}+ max{ℎ(𝑊|𝐿),ℎ(𝑋|𝐿)}+ ℎ(𝐿) ≤ 1+𝛾 2+ 1 = 𝜔 2+ 1.
Fast Matrix Multiplication meets the Submodular Width By choosingA ={{𝑋,𝑊},{𝑌,𝑊},{𝑋,𝐿}} andB ={{𝑋,𝑊},{𝑍,𝑊}}, EMM𝝈 1 ≤ MM(𝑌𝑍,𝑊,𝑋 |𝐿) =ℎ(𝑌𝑍)+ 𝛾· min{ℎ(𝑊|𝐿),ℎ(𝑋|𝐿)}+ max{ℎ(𝑊|𝐿),ℎ(𝑋|𝐿)}+ ℎ(𝐿) ≤ 1+𝛾 2+ 1 = 𝜔 2+ 1
Reference 44
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.798340Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation ef689844-a00b-4d3b-9d37-98ba02ef0b6a · outbound
This paper cites We have EMM𝝈 1 ≤ MM(𝑌𝑍 ;𝑊𝐿 ;𝑋)≤ 𝜔 2+ 1.
Fast Matrix Multiplication meets the Submodular Width We have EMM𝝈 1 ≤ MM(𝑌𝑍 ;𝑊𝐿 ;𝑋)≤ 𝜔 2+ 1
Reference 45
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.773112Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 6c0ee6df-2c9d-4937-be14-e20bbe518e07 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 46
- Resolution
- parse uncertain
- raw_fallback, observed 2026-08-11T20:00:52.748779Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5fc042bf-cc8f-4c35-b517-338ef6a06d88 · outbound
This paper cites □ Lemma C.8.
Fast Matrix Multiplication meets the Submodular Width □ Lemma C.8
Reference 47
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.728392Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4bc3b114-d9e7-4c66-a021-aed4a7860750 · outbound
This paper cites As𝑈 𝝈 3 ,𝑈 𝝈 4 ⊆𝑈 𝝈 1 , we have: max 𝑖∈[| 𝝈|] min ℎ(𝑈 𝝈 𝑖), EMM𝝈 𝑖 ≤ max{min{𝜔(1− Δ), 2− Δ}, 1+ Δ}.
Fast Matrix Multiplication meets the Submodular Width As𝑈 𝝈 3 ,𝑈 𝝈 4 ⊆𝑈 𝝈 1 , we have: max 𝑖∈[| 𝝈|] min ℎ(𝑈 𝝈 𝑖), EMM𝝈 𝑖 ≤ max{min{𝜔(1− Δ), 2− Δ}, 1+ Δ}
Reference 48
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.705515Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 82650af9-79a7-41b0-b6a2-79aa4c15b5f4 · outbound
This paper cites Similarly, ℎ(𝑈 𝝈.
Fast Matrix Multiplication meets the Submodular Width Similarly, ℎ(𝑈 𝝈
Reference 49
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.684006Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4d899803-0744-4410-b336-efe2741b001b · outbound
This paper cites As𝑈 𝝈 3 ,𝑈 𝝈 4 ⊆𝑈 𝝈 1 , we have max 𝑖∈[| 𝝈|] min ℎ(𝑈 𝝈 𝑖), EMM𝝈 𝑖 ≤ 1+ Δ.
Fast Matrix Multiplication meets the Submodular Width As𝑈 𝝈 3 ,𝑈 𝝈 4 ⊆𝑈 𝝈 1 , we have max 𝑖∈[| 𝝈|] min ℎ(𝑈 𝝈 𝑖), EMM𝝈 𝑖 ≤ 1+ Δ
Reference 50
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.640223Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation f611daae-1711-4c04-8ea6-07391c28a552 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 51
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:52.616136Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 22089e0a-f283-44ab-ad34-f6d80ae4d2e2 · outbound
This paper cites As 𝑈 𝝈 3 ,𝑈 𝝈 4 ⊆𝑈 𝝈 1 , we have max 𝑖∈[| 𝝈|] min ℎ(𝑈 𝝈 𝑖), EMM𝝈 𝑖 ≤ 2− Δ.
Fast Matrix Multiplication meets the Submodular Width As 𝑈 𝝈 3 ,𝑈 𝝈 4 ⊆𝑈 𝝈 1 , we have max 𝑖∈[| 𝝈|] min ℎ(𝑈 𝝈 𝑖), EMM𝝈 𝑖 ≤ 2− Δ
Reference 52
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.584311Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation a725c695-1f54-43f4-9753-4b148dde96de · outbound
This paper cites Moreover,ℎ(𝑈 𝝈.
Fast Matrix Multiplication meets the Submodular Width Moreover,ℎ(𝑈 𝝈
Reference 53
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.544991Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 89a1ae14-3be1-4522-93b2-20cb3650958d · outbound
This paper cites As 𝑈 𝝈 3 ,𝑈 𝝈 4 ⊆𝑈 𝝈 1 , we have: max 𝑖∈[| 𝝈|] min ℎ(𝑈 𝝈 𝑖), EMM𝝈 𝑖 ≤ max 1+ Δ, min (𝜔− 1)( 1− Δ)+ 1− Δ 2 , 2− Δ.
Fast Matrix Multiplication meets the Submodular Width As 𝑈 𝝈 3 ,𝑈 𝝈 4 ⊆𝑈 𝝈 1 , we have: max 𝑖∈[| 𝝈|] min ℎ(𝑈 𝝈 𝑖), EMM𝝈 𝑖 ≤ max 1+ Δ, min (𝜔− 1)( 1− Δ)+ 1− Δ 2 , 2− Δ
Reference 54
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.516147Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 02d06bc5-12f4-4d59-a5d7-cc815a7f0909 · outbound
This paper cites Putting two cases together, we obtain the desired upper bound.
Fast Matrix Multiplication meets the Submodular Width Putting two cases together, we obtain the desired upper bound
Reference 55
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.487858Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation de189c8d-8e06-46e4-ba2c-4e599764cf9c · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 56
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:52.454811Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 21faf27a-4dfe-4079-bec1-202248d3834f · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 57
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:52.429751Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 848c85ab-c030-4001-84a6-f709b73817ed · outbound
This paper cites • 𝝈[1] ={𝑊}.ℎ(𝑈 𝝈.
Fast Matrix Multiplication meets the Submodular Width • 𝝈[1] ={𝑊}.ℎ(𝑈 𝝈
Reference 58
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.400813Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9629e0e0-1de6-405e-a32d-10855e4a36a3 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 59
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:52.374307Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 8a9ab6c9-50bd-47f8-9875-d6ede39d5064 · outbound
This paper cites • |𝝈[1]| = 2.ℎ(𝑈 𝝈.
Fast Matrix Multiplication meets the Submodular Width • |𝝈[1]| = 2.ℎ(𝑈 𝝈
Reference 60
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.349382Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c198a38e-053c-4198-8147-518ccc45f96a · outbound
This paper cites Case 2:𝜔 < 5.
Fast Matrix Multiplication meets the Submodular Width Case 2:𝜔 < 5
Reference 61
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.321704Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 976470b7-53cf-46a8-9e4b-71e1d6235ee2 · outbound
This paper cites Let𝑋 =(𝑏𝑐𝑓),𝑌 =(𝑑𝑒𝑓),𝑍 =(𝑎𝑒𝑓),𝑊 =(𝑎𝑏𝑓).
Fast Matrix Multiplication meets the Submodular Width Let𝑋 =(𝑏𝑐𝑓),𝑌 =(𝑑𝑒𝑓),𝑍 =(𝑎𝑒𝑓),𝑊 =(𝑎𝑏𝑓)
Reference 62
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.299044Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e93fb51c-219e-42af-8131-b7924b487838 · outbound
This paper cites The case with 𝝈[1] ={𝑌} is the same.
Fast Matrix Multiplication meets the Submodular Width The case with 𝝈[1] ={𝑌} is the same
Reference 63
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.276124Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 176cec1a-637b-4c62-88ec-55e150c75147 · outbound
This paper cites The case with 𝝈[1] ={𝑍} is the same.
Fast Matrix Multiplication meets the Submodular Width The case with 𝝈[1] ={𝑍} is the same
Reference 64
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.240186Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation a65d3388-8687-49b2-b873-be4df17a1268 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 65
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:52.214590Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 0b7aa64d-84ba-452a-8788-2c3cf8f32fad · outbound
This paper cites We define below an upper bound,𝑐□ 𝑘 , on𝑐𝑘 that uses only square matrix multiplication and show that 𝜔-subw(H) ≤𝑐□ 𝑘 for any 𝑘-cycle graphH.
Fast Matrix Multiplication meets the Submodular Width We define below an upper bound,𝑐□ 𝑘 , on𝑐𝑘 that uses only square matrix multiplication and show that 𝜔-subw(H) ≤𝑐□ 𝑘 for any 𝑘-cycle graphH
Reference 66
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.179508Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 326f26dc-41db-4e4c-95aa-1dc19012c9a6 · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 67
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:52.150772Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e9c86495-613b-4eb2-aab3-a2f823fa77dc · outbound
This paper cites EMM𝝈 1 = min{MM(𝑋1,𝑋 2,𝑌 ;𝑋3), MM(𝑋1,𝑋 2𝑋3,𝑌)} = 2− 1 𝜔 ; Fast Matrix Multiplication meets the Submodular Width 31 • 𝝈[1] ={𝑋1}.ℎ(𝑈 𝝈.
Fast Matrix Multiplication meets the Submodular Width EMM𝝈 1 = min{MM(𝑋1,𝑋 2,𝑌 ;𝑋3), MM(𝑋1,𝑋 2𝑋3,𝑌)} = 2− 1 𝜔 ; Fast Matrix Multiplication meets the Submodular Width 31 • 𝝈[1] ={𝑋1}.ℎ(𝑈 𝝈
Reference 68
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.124916Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 914dad85-c75e-43b4-a047-123cc52a9999 · outbound
This paper cites EMM𝝈 1 = min{MM(𝑋2,𝑌,𝑋 1|𝑋3), MM(𝑋2𝑋3,𝑌,𝑋 1), MM(𝑋2,𝑋 3𝑌,𝑋 1)} = The case with 𝝈[1] ={𝑋2} or 𝝈[1] ={𝑋3} is the same.
Fast Matrix Multiplication meets the Submodular Width EMM𝝈 1 = min{MM(𝑋2,𝑌,𝑋 1|𝑋3), MM(𝑋2𝑋3,𝑌,𝑋 1), MM(𝑋2,𝑋 3𝑌,𝑋 1)} = The case with 𝝈[1] ={𝑋2} or 𝝈[1] ={𝑋3} is the same
Reference 69
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.083993Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e4d7f861-97ad-46bf-9bcb-90ba56b89eed · outbound
This paper cites EMM𝝈 1 = MM(𝑋2,𝑋 3,𝑋 1𝑌) = 2− 1 𝜔.
Fast Matrix Multiplication meets the Submodular Width EMM𝝈 1 = MM(𝑋2,𝑋 3,𝑋 1𝑌) = 2− 1 𝜔
Reference 70
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.053116Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 00412fa1-b95e-49a7-95f8-0425ed0682c0 · outbound
This paper cites EMM𝝈 1 = MM(𝑋3,𝑌,𝑋 1𝑋2) = 2− 1 𝜔.
Fast Matrix Multiplication meets the Submodular Width EMM𝝈 1 = MM(𝑋3,𝑌,𝑋 1𝑋2) = 2− 1 𝜔
Reference 71
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:00:52.024546Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 3bd496f2-c06a-4044-9bdf-98f1fa059b9f · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 72
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:51.999685Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation fe90528c-93c8-4ae1-91d0-e1174be2a56d · outbound
This paper cites an unresolved cited work.
Fast Matrix Multiplication meets the Submodular Width Unresolved cited work
Reference 73
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:00:51.962617Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Pith citing papers
Observation 838fae22-7d05-4de7-bf91-ae453d006935 · inbound
Lower Bounds for Conjunctive Query Evaluation cites this paper.
Lower Bounds for Conjunctive Query Evaluation Fast Matrix Multiplication meets the Submodular Width
Reference 58
- Resolution
- verified exact
- local_arxiv, observed 2026-08-15T19:17:20.730611Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.