Paper Citation Record · LEDGER

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition

As of 8 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2507.01873.

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

pith.paper-citation-record.v1
2507.01873 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:02:19.438055Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

35 of 35 outbound references displayed

verified exact3
verified fuzzy24
unresolved8
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 293d446c-ed4b-49c3-b6c9-c12723541970 · outbound

This paper cites write newline.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition write newline

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T21:02:19.318049Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bfa9b34a-c163-4aef-8b7b-235c5e5f285b · outbound

This paper cites Better balance by being biased: A 0.8776-approximation for max bisection.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Better balance by being biased: A 0.8776-approximation for max bisection

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T21:02:19.323508Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bf4a0e40-4aac-4282-b573-a156fd635a48 · outbound

This paper cites Differentially Private Gomory-Hu Trees.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Differentially Private Gomory-Hu Trees

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-06T21:02:19.530289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6941a2a5-d995-4cad-9f7d-25305de7e123 · outbound

This paper cites Approximating the cut-norm via grothendieck's inequality.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Approximating the cut-norm via grothendieck's inequality

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.887238Z

Source-reported events for the cited work

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Observation cb5551a4-53d2-4c77-9b62-527c17158739 · outbound

This paper cites On differentially private graph sparsification and applications.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition On differentially private graph sparsification and applications

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.875474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation deaedd8e-e78d-407e-a343-bcb9962f55cf · outbound

This paper cites Wherefore art thou R3579X? anonymized social networks, hidden patterns, and structural steganography.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Wherefore art thou R3579X? anonymized social networks, hidden patterns, and structural steganography

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.861718Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e9de831d-b789-4d36-8b2e-55d57bd20792 · outbound

This paper cites Bencz\' u r and David R.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Bencz\' u r and David R

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.848561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 99016054-cfa5-475d-a30d-fab0a926297f · outbound

This paper cites Differentially Private Algorithms for Graph Cuts: A Shifting Mechanism Approach and More.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Differentially Private Algorithms for Graph Cuts: A Shifting Mechanism Approach and More

Reference 8

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Source-reported events for the cited work

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Observation bff4a0e2-3114-484e-83a4-e0fe5b504cef · outbound

This paper cites A deterministic algorithm for balanced cut with applications to dynamic connectivity, flows, and beyond.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition A deterministic algorithm for balanced cut with applications to dynamic connectivity, flows, and beyond

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.835276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0ba2a0dc-37c8-48b0-b357-0952cc8dd158 · outbound

This paper cites Stop the Open Data Bus, We Want to Get Off.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Stop the Open Data Bus, We Want to Get Off

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-06T21:02:19.495560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c027b86a-c3c8-4ea5-bf81-4ac1b0993819 · outbound

This paper cites On approximate graph colouring and max-k-cut algorithms based on the -function.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition On approximate graph colouring and max-k-cut algorithms based on the -function

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.822731Z

Source-reported events for the cited work

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Observation ff0f9f69-e0f3-41d6-8868-e16bafbf4dbc · outbound

This paper cites Differential privacy and robust statistics.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Differential privacy and robust statistics

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.809563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c0db5ce0-4675-4e30-ad44-d9db86c812a0 · outbound

This paper cites Nearly tight bounds for differentially private multiway cut.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Nearly tight bounds for differentially private multiway cut

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.796807Z

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Observation cb1a6d01-c285-4b2d-ad1f-027e3cef6c58 · outbound

This paper cites an unresolved cited work.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:02:19.784961Z

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Observation 2348fecb-45c1-45ed-bbac-84b2c78af77a · outbound

This paper cites Differential privacy.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Differential privacy

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.773258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1350a6ee-db51-42dd-8109-c71e4301acdb · outbound

This paper cites Differentially private release of synthetic graphs.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Differentially private release of synthetic graphs

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.761228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a6711943-6748-4baf-87ff-131898854f5f · outbound

This paper cites Improved approximation algorithms for MAX k -CUT and MAX BISECTION.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Improved approximation algorithms for MAX k -CUT and MAX BISECTION

Reference 17

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Source-reported events for the cited work

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Observation 6d15bc03-3097-45d6-a6ae-dd530295f7fc · outbound

This paper cites On graph problems in a semi-streaming model.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition On graph problems in a semi-streaming model

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.739586Z

Source-reported events for the cited work

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Observation a36865e6-2e45-4e19-bc7b-ec287f0e136a · outbound

This paper cites Garey, David S.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Garey, David S

Reference 19

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Source-reported events for the cited work

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Observation c354f324-9936-45f1-be46-f4465df4040e · outbound

This paper cites Differentially private combinatorial optimization.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Differentially private combinatorial optimization

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.718090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d4123b6e-cb59-42ee-b222-63bdf2197014 · outbound

This paper cites an unresolved cited work.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:02:19.705363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a649115e-8b32-4171-a3bd-f90af228715b · outbound

This paper cites Goemans and David P.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Goemans and David P

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.692547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b57cb1e2-76d6-403d-a57b-1a4933898e6d · outbound

This paper cites Accurate estimation of the degree distribution of private networks.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Accurate estimation of the degree distribution of private networks

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.680769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 69260466-129d-4743-9620-652403e35391 · outbound

This paper cites Random sampling in cut, flow, and network design problems.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Random sampling in cut, flow, and network design problems

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.667947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 75f04974-6801-4ff6-adbf-0be4cc8efb1e · outbound

This paper cites Optimal inapproximability results for MAX-CUT and other 2-variable CSP s? SIAM Journal on Computing , 37(1):319--357, 2007.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Optimal inapproximability results for MAX-CUT and other 2-variable CSP s? SIAM Journal on Computing , 37(1):319--357, 2007

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.653681Z

Source-reported events for the cited work

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Observation f59c88c2-1f3a-4e16-87d7-59c9cfc17501 · outbound

This paper cites Private graph data release: A survey.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Private graph data release: A survey

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.641029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 799f7b8f-7968-4927-829d-fd9012675fe5 · outbound

This paper cites Deterministic Weighted Expander Decomposition in Almost-linear Time.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Deterministic Weighted Expander Decomposition in Almost-linear Time

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-06T21:02:19.478057Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c05affc6-3385-46b5-a3b3-d365f23f7002 · outbound

This paper cites Optimal bounds on private graph approximation.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Optimal bounds on private graph approximation

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.628359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 212dd172-9530-4ba1-8bcc-2eb4525f8ba6 · outbound

This paper cites Robust de-anonymization of large sparse datasets.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Robust de-anonymization of large sparse datasets

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.615723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d9981575-4fa4-4154-ba59-17f630df5bcd · outbound

This paper cites Dynamic spanning forest with worst-case update time: adaptive, Las Vegas , and O(n$ ^ 1/2 - \( $ \)) -time.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Dynamic spanning forest with worst-case update time: adaptive, Las Vegas , and O(n$ ^ 1/2 - \( $ \)) -time

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.602969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 349a92a7-3b87-43f6-b1bb-13fabf7dcb50 · outbound

This paper cites Optimal hierarchical decompositions for congestion minimization in networks.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Optimal hierarchical decompositions for congestion minimization in networks

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-06T21:02:19.424194Z

Source-reported events for the cited work

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Observation 369f7d07-c541-416f-b5d8-0d0c84a7554a · outbound

This paper cites Approximating CSP s with global cardinality constraints using SDP hierarchies.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Approximating CSP s with global cardinality constraints using SDP hierarchies

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.580208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4899417c-6ea5-4514-ae9b-1922bba790ba · outbound

This paper cites Expander decomposition and pruning: Faster, stronger, and simpler.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Expander decomposition and pruning: Faster, stronger, and simpler

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.567716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 93fbbd91-4f09-4ed5-a791-f8964d1cd19a · outbound

This paper cites Differentially private analysis on graph streams.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Differentially private analysis on graph streams

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.555401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f60a845a-a12a-444c-a9f3-93384c5db513 · outbound

This paper cites Fully-dynamic minimum spanning forest with improved worst-case update time.

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition Fully-dynamic minimum spanning forest with improved worst-case update time

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:02:19.543296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

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