Paper Citation Record · LEDGER

Parallel Spectral Graph Sparsification via Low Diameter Decompositions

As of 15 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2607.25059.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2607.25059 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-31T02:32:38.540435Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

23 of 23 outbound references displayed

verified exact0
verified fuzzy0
unresolved22
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a7040d27-e05d-41ee-aeca-500e67f1c32b · outbound

This paper cites an unresolved cited work.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:37.383148Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dad2b911-d739-4c1a-8a54-85bdf12ec2be · outbound

This paper cites Spielman, and Nikhil Srivastava.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Spielman, and Nikhil Srivastava

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:37.446078Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e71a0f2-8d41-4204-99ee-d410ecc2017c · outbound

This paper cites A framework for parallelizing approximate gaussian elim- ination.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions A framework for parallelizing approximate gaussian elim- ination

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:37.507193Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b0d86c75-9462-4c19-a3ea-e748097af092 · outbound

This paper cites Blelloch, and Julian Shun.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Blelloch, and Julian Shun

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:37.545908Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d25c284-8ed9-43af-9cf5-c92a11c7a6df · outbound

This paper cites Blelloch, and Julian Shun.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Blelloch, and Julian Shun

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:37.580232Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8ef6e12-21e7-4f94-b87d-3bbafcd57a8b · outbound

This paper cites Dynamic low-stretch trees via dynamic low-diameter decompositions.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Dynamic low-stretch trees via dynamic low-diameter decompositions

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:37.620509Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c5b4629-6e2b-473c-b17b-63d96dacbc64 · outbound

This paper cites Robust and Practical Solution of Laplacian Equations by Approximate Elimination.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Robust and Practical Solution of Laplacian Equations by Approximate Elimination

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:37.671030Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 99dee200-2a64-45fc-a143-cbccd43e712b · outbound

This paper cites Spectral sparsification via random spanners.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Spectral sparsification via random spanners

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:37.724255Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d7868b67-a873-4fb6-9c08-43a63f6d41b4 · outbound

This paper cites Simple parallel and distributed algorithms for spectral graph sparsification,.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Simple parallel and distributed algorithms for spectral graph sparsification,

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:37.787352Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4156b5b-6532-4aaf-bcc6-91b795dce5ce · outbound

This paper cites Faster spectral sparsification and numerical algorithms for SDD matrices.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Faster spectral sparsification and numerical algorithms for SDD matrices

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:37.899730Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f28d21d6-4a03-4f67-91cd-cf8dff716036 · outbound

This paper cites Faster spectral sparsification and numerical algorithms for sdd matrices.ACM Trans.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Faster spectral sparsification and numerical algorithms for sdd matrices.ACM Trans

Reference 11

Resolution: malformed identifier; no resolver link, observed 2026-07-31T02:32:37.960759Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e521e73-2476-44b3-8ea2-88ce931967e7 · outbound

This paper cites Random-shift revisited: Tight approximations for tree embeddings andℓ 1-oblivious routings.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Random-shift revisited: Tight approximations for tree embeddings andℓ 1-oblivious routings

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:38.012214Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 269e1c70-e4b9-4caf-a13e-d98a018cb7fd · outbound

This paper cites A framework for an- alyzing resparsification algorithms.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions A framework for an- alyzing resparsification algorithms

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:38.061127Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9318c43c-dd0f-43dc-9702-8e9fba20c2b4 · outbound

This paper cites Approximate Gaussian Elimination for Laplacians: Fast, Sparse, and Simple.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Approximate Gaussian Elimination for Laplacians: Fast, Sparse, and Simple

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:38.118245Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8fcb41f4-181e-483f-af64-6964dd2b7f2e · outbound

This paper cites Miller, Richard Peng, Adrian Vladu, and Shen Chen Xu.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Miller, Richard Peng, Adrian Vladu, and Shen Chen Xu

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:38.178209Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 989fa28a-2f56-48be-8cc1-b057ffaec2da · outbound

This paper cites Miller, Richard Peng, and Shen Chen Xu.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Miller, Richard Peng, and Shen Chen Xu

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:38.209258Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d321dd8-b9f7-44cd-941d-814aae469029 · outbound

This paper cites Probability and computing: Randomized algorithms and probabilistic analysis, 2005.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Probability and computing: Randomized algorithms and probabilistic analysis, 2005

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:38.268266Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b6a17da6-db4d-41ef-807c-9f93eabc6946 · outbound

This paper cites Society for Industrial and Ap- plied Mathematics, second edition, 2003.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Society for Industrial and Ap- plied Mathematics, second edition, 2003

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:38.342373Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9cde2a8-00a7-48f9-97fd-42e792931ee1 · outbound

This paper cites A simple and efficient parallel laplacian solver.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions A simple and efficient parallel laplacian solver

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:38.398194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9aec081f-ca27-45f2-8655-b38f9f6732c3 · outbound

This paper cites Spielman and Nikhil Srivastava.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Spielman and Nikhil Srivastava

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:38.428788Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 10ce4e3d-d957-455c-a58f-56b99f7a70df · outbound

This paper cites Nearly-Linear Time Algorithms for Graph Partitioning, Graph Sparsification, and Solving Linear Systems.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Nearly-Linear Time Algorithms for Graph Partitioning, Graph Sparsification, and Solving Linear Systems

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:38.485275Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 890456eb-6075-4296-8e15-bcc4eadc5dec · outbound

This paper cites Approximate distance oracles.J.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Approximate distance oracles.J

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:38.540435Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af23b93c-2a49-4663-841c-c570b34254d5 · outbound

This paper cites Simple parallel and distributed algorithms for spectral graph sparsification.

Parallel Spectral Graph Sparsification via Low Diameter Decompositions Simple parallel and distributed algorithms for spectral graph sparsification

Reference 2014

Resolution: unresolved; no resolver link, observed 2026-07-31T02:32:37.844470Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.