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Paper Citation Record · LEDGER

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front

As of 16 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:1908.09648.

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

pith.paper-citation-record.v1
1908.09648 v1

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T12:35:07.782475Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

47 of 47 outbound references displayed

  • verified exact2
  • verified fuzzy37
  • unresolved8
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a4b0ae4a-c3ca-45e9-b6a2-7610ea5d010d · outbound

This paper cites Agarwal and C.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Agarwal and C

Reference 1

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.378538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 489d3f07-f820-42ab-9b52-719f5a60d0d7 · outbound

This paper cites Agarwal, M.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Agarwal, M

Reference 2

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.367650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation c6e40562-22c1-43dd-a31d-ca1b21ce9c00 · outbound

This paper cites Auger, J.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Auger, J

Reference 3

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.355945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 581dabb3-4953-451a-8706-9b1aef963dd4 · outbound

This paper cites Computing k-Centers On a Line.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Computing k-Centers On a Line

Reference 4

Resolution
verified exact
local_arxiv, observed 2026-08-14T12:35:07.859638Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation add8c2a2-d879-42cb-a42d-be36aacda006 · outbound

This paper cites Maximum Volume Subset Selection for Anchored Boxes.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Maximum Volume Subset Selection for Anchored Boxes

Reference 5

Resolution
unresolved
no resolver link, observed 2026-08-14T12:35:07.616439Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:35:07.616439Z digest=sha256:d83f03925e416e6fee81a47e3d1efa7bf514a78cedccc897987cd2e9b3957248

Observation 123848b9-d223-4e50-b439-1a08e0f20dbd · outbound

This paper cites Bringmann, T.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Bringmann, T

Reference 6

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.342930Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.620612Z digest=sha256:9c32fe70030b4718f090dedad94a1c028e9c68ffdb82e995f1542be6dbfa811d

Observation 8af57929-d641-478b-88a3-fe4251fdc9c2 · outbound

This paper cites Calik, M.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Calik, M

Reference 7

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.329994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.624991Z digest=sha256:463a30ce6ae98dcf8362c75e151e4b260743b76519099a19167453e2b54ee270

Observation 8f1ca6ac-6787-41c0-914c-f24596aab4a8 · outbound

This paper cites Calik and B.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Calik and B

Reference 8

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.317660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 28dab5f1-6129-4727-965a-1f9921496ada · outbound

This paper cites Callaghan, S.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Callaghan, S

Reference 9

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.306216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 326df8e3-bd26-416d-8bf6-e38468bfd4f8 · outbound

This paper cites Network and discrete location: models, algorithms and appl ications.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Network and discrete location: models, algorithms and appl ications

Reference 10

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.294893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 29603b8e-4dcc-40ae-b8f7-63b130c8f7a3 · outbound

This paper cites The p-centre problemheuristic and optima l algorithms.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front The p-centre problemheuristic and optima l algorithms

Reference 11

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation dadaabe8-e414-422c-8246-b48e3e98ff5b · outbound

This paper cites On the rectangular p-center problem.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front On the rectangular p-center problem

Reference 12

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.270369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.644934Z digest=sha256:03c631f144d0f030cbbdf66a141e5ee982d38d21ed006b66c068e52c12a428ee

Observation cb7e0e56-e1bf-44c5-9f9f-10ffcb729060 · outbound

This paper cites an unresolved cited work.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Unresolved cited work

Reference 13

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.257659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation e000bc61-1dff-45b6-93a5-5a54f5765d29 · outbound

This paper cites Dupin, F.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Dupin, F

Reference 14

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.245053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 64768f23-a0d9-45e9-8a2c-4b151e777ac8 · outbound

This paper cites Dupin, F.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Dupin, F

Reference 15

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.233059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 53a28478-1559-4592-9296-ac8caa421ce9 · outbound

This paper cites k-medoids and p-median clustering are solvable in polynomial time for a 2d Pareto front.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front k-medoids and p-median clustering are solvable in polynomial time for a 2d Pareto front

Reference 16

Resolution
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local_arxiv, observed 2026-08-14T12:35:07.833087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.661608Z digest=sha256:01976f360ccc4ae932347e2bd3a4ae9a82bba7466492c48c04909b0dbb0c1868

Observation c5b2f03e-d1e1-484c-9451-595bb595941c · outbound

This paper cites Ehrgott and X.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Ehrgott and X

Reference 17

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.220631Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation aae4ce70-3fc6-4b64-b4c8-9f81f8c71d47 · outbound

This paper cites Elloumi, M.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Elloumi, M

Reference 18

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raw_fallback, observed 2026-08-14T12:35:08.208695Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 73298cbe-2687-4548-882f-c57d0dec2c0f · outbound

This paper cites Elshaikh, S.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Elshaikh, S

Reference 19

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.196842Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation f756fe19-8d9d-481e-bded-76c3cfc55eb8 · outbound

This paper cites Eppstein.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Eppstein

Reference 20

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.184134Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation b702453a-6a8c-4090-93b0-a36034f94f58 · outbound

This paper cites Ferone, P.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Ferone, P

Reference 21

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.172352Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 9f942540-5711-4457-a7cb-790bb5ae09ba · outbound

This paper cites Gonzalez.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Gonzalez

Reference 22

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation c64ae6c3-0fa8-43d8-984d-c1884cf1089f · outbound

This paper cites Fast Exact k-Means, k-Medians and Bregman Divergence Clustering in 1D.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Fast Exact k-Means, k-Medians and Bregman Divergence Clustering in 1D

Reference 23

Resolution
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no resolver link, observed 2026-08-14T12:35:07.687885Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation c6f4a0f3-1a18-4733-9508-a75dbdc6271f · outbound

This paper cites Guo-Hui and G.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Guo-Hui and G

Reference 24

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.147491Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 0f67fba2-30ec-43d4-a352-8ea27ea1e1d7 · outbound

This paper cites Hochbaum.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Hochbaum

Reference 25

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raw_fallback, observed 2026-08-14T12:35:08.136033Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation ae76354e-8abb-4d16-b2c7-88b429ebcf3b · outbound

This paper cites Hochbaum and D.B.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Hochbaum and D.B

Reference 26

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raw_fallback, observed 2026-08-14T12:35:08.124378Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 948f2348-4513-4006-a851-b6ab3dc4a0a5 · outbound

This paper cites Hsu and G.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Hsu and G

Reference 27

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.111438Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation ea4c4fda-2c64-423d-b8b9-3eb4097961e6 · outbound

This paper cites Hwang, R.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Hwang, R

Reference 28

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.098539Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 5ca540ea-901c-460a-945e-327e646c23ee · outbound

This paper cites Karmakar, S.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Karmakar, S

Reference 29

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.086683Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 66677d2b-9f00-4671-bc45-2bd493dc1945 · outbound

This paper cites an unresolved cited work.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Unresolved cited work

Reference 30

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raw_fallback, observed 2026-08-14T12:35:08.075096Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 19d1607b-1f74-49d5-9e29-246fccfa45df · outbound

This paper cites Mahajan, P.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Mahajan, P

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:35:08.062091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation a1f95124-b0a1-4f83-90cc-ad58e4e551b1 · outbound

This paper cites an unresolved cited work.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:35:08.050389Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 38fed393-ab33-43e9-a788-b0caf5a56ee0 · outbound

This paper cites Megiddo and K.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Megiddo and K

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:35:08.039657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation b596a23d-8a15-4183-b8cb-372dae2dc0a8 · outbound

This paper cites Megiddo and A.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Megiddo and A

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:35:08.028047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation daace1c1-957d-4caf-aedd-b2783adf5c46 · outbound

This paper cites Mladenovi´ c, M.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Mladenovi´ c, M

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:35:08.016645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.738184Z digest=sha256:6f1b1ad2e0d6022d61ce3e851417f7acae10fbda912c3d2d5963a4738627a3ef

Observation 4b4b3628-e027-49d1-8785-ccc8374d0f28 · outbound

This paper cites Peugeot, N.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Peugeot, N

Reference 36

Resolution
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raw_fallback, observed 2026-08-14T12:35:08.004544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.741508Z digest=sha256:4d0a22968df36b0503a82d2e63a6c7e3c8f40e6fcba97271dd270a7ff01f51c1

Observation d864f706-d3c6-4f5a-9ff7-1e6db82255ab · outbound

This paper cites Pulido and C.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Pulido and C

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:35:07.991827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.744896Z digest=sha256:5d9ff5e3691e6c64d7b2c7ae861601ee1630f9ec1fe24133e1998d3e99032f41

Observation 829e5222-d208-4bcd-8c5a-f9ed2fb7fda2 · outbound

This paper cites Ramirez-Atencia, S.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Ramirez-Atencia, S

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:35:07.979840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.748217Z digest=sha256:4ec191f70259ec15e2501321364d7b4696b6839d8b41ed3d8cb48010e6bab980

Observation d022ae77-5b40-4c96-8838-7ab3a6ce8505 · outbound

This paper cites Kubushishi.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Kubushishi

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:35:07.968010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.751678Z digest=sha256:d74fc9d8d1251b241b4c0d283349ec90aacd04dd3fde1f7cf3fa1e0fbfef235a

Observation b975a63d-c299-48be-8590-325eab5008d8 · outbound

This paper cites Samorani, Y.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Samorani, Y

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:35:07.956918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.755095Z digest=sha256:24094dc2ef6500241f436dcde085a7847ecf642269f8822f3c39ea3582104877

Observation 6db0b622-8983-4466-ab0d-c46888716fed · outbound

This paper cites an unresolved cited work.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:35:07.945890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.758836Z digest=sha256:673e19b8575d77040bd796ba51ba16cabf588200d3d323889c6a5a0a9960c895

Observation d75f5694-45cb-44a0-8613-bcfd7fdf394e · outbound

This paper cites an unresolved cited work.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Unresolved cited work

Reference 42

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:35:07.934727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.762533Z digest=sha256:4e15df9cde381c64d4d3bb90f87c75ae2a902df54a1ab515f5d9f77d99aab8c5

Observation 3452f2be-f3ea-47b1-8788-3f72963432bd · outbound

This paper cites Sintorn and U.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Sintorn and U

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:35:07.922151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.766201Z digest=sha256:de9cb857c987f0a959b2f91100b94a1ea3eec00cf9688656f996fffd1a652f0c

Observation 327e0dc9-0961-4476-8923-ea44eb9f4eca · outbound

This paper cites an unresolved cited work.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:35:07.909945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.770018Z digest=sha256:ab0b17f3620782c1aee0b9fb034d32d2fc8ef3d085abc7453e3ddaebb14a669f

Observation 6281723e-cbd1-4e2e-8b2a-769a2bd7096f · outbound

This paper cites W ang and M.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front W ang and M

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:35:07.897122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.773752Z digest=sha256:eaa70f96a12ce99274683876054fb89b6bd0c542f9c5a3bde1e078a84061764b

Observation ce22c41c-1dae-42d5-b212-15a7732d48b8 · outbound

This paper cites Zio and R.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front Zio and R

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:35:07.884048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.778428Z digest=sha256:09bff0813f130850422f4ab86141a7ad11ff69f0675e00b63ab94469d92bcbb0

Observation 7da712eb-6122-4a19-b0cc-68a309745f01 · outbound

This paper cites □ Lemma 10.

Planar p-center problems are solvable in polynomial time when clustering a Pareto Front □ Lemma 10

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:35:07.872451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:35:07.782475Z digest=sha256:ff80b01e75feef250e3016173ad757ea586717fc1cd5da65e1c6daed750d8339

Pith citing papers

No inbound Pith citation observations are available.