Paper Citation Record · LEDGER

Proportionally Fair Makespan Approximation

As of 19 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2412.08572.

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

pith.paper-citation-record.v1
2412.08572 v2

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T18:00:27.019346Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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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

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verified fuzzy41
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 16cb43d2-ff89-4068-855d-0c55f51fee7a · outbound

This paper cites Approximation schemes for scheduling on parallel machines.

Proportionally Fair Makespan Approximation Approximation schemes for scheduling on parallel machines

Reference 1

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Observation df2ba643-2857-4ba6-9bcd-20ce32fb7e61 · outbound

This paper cites Fair division of indivisib le goods: Recent progress and open questions.

Proportionally Fair Makespan Approximation Fair division of indivisib le goods: Recent progress and open questions

Reference 2

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Observation b25dde8b-0356-491c-b467-6ef9a80ecfed · outbound

This paper cites A derivation of the money rawlsian s olution.

Proportionally Fair Makespan Approximation A derivation of the money rawlsian s olution

Reference 3

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Observation 9e82cee0-0b33-4f37-994c-3acf7997341a · outbound

This paper cites Aslam, April Rasala, Cliﬀord Stein, and Neal E.

Proportionally Fair Makespan Approximation Aslam, April Rasala, Cliﬀord Stein, and Neal E

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.733194Z

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Observation e788e187-0997-4a25-8a80-a86c04cc4802 · outbound

This paper cites Optim al bounds on the price of fairness for indivisible goods.

Proportionally Fair Makespan Approximation Optim al bounds on the price of fairness for indivisible goods

Reference 5

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Observation da6bf4a9-d16c-4a9d-a8ea-141195156084 · outbound

This paper cites Achieving envy- freeness with limited subsidies under dichotomous valuati ons.

Proportionally Fair Makespan Approximation Achieving envy- freeness with limited subsidies under dichotomous valuati ons

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.702560Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation da0a61a8-b128-4d17-b056-b17ff35f2934 · outbound

This paper cites The price of fairness for indivis- ible goods.

Proportionally Fair Makespan Approximation The price of fairness for indivis- ible goods

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.687263Z

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Observation 5b78708c-6c17-4a52-a4d4-9d99db460ff4 · outbound

This paper cites The price of fairness.

Proportionally Fair Makespan Approximation The price of fairness

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.671039Z

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Observation d9274603-97db-4553-8901-2d55394120a8 · outbound

This paper cites The price of envy-freeness in machine scheduling.

Proportionally Fair Makespan Approximation The price of envy-freeness in machine scheduling

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.654392Z

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Observation 6b0171ba-a750-49de-a4a6-60943b2055ee · outbound

This paper cites Narayan, Mash bat Suzuki, and Adrian Vetta.

Proportionally Fair Makespan Approximation Narayan, Mash bat Suzuki, and Adrian Vetta

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.639188Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 189dfbe1-a389-4bb0-b7ec-5c4857a77964 · outbound

This paper cites Approximability Landscape of Welfare Maximization within Fair Allocations.

Proportionally Fair Makespan Approximation Approximability Landscape of Welfare Maximization within Fair Allocations

Reference 11

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Source-reported events for the cited work

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Observation e03ebd8c-bc73-4791-aea2-7effe3886005 · outbound

This paper cites The combinatorial assignment problem: Ap proximate competitive equilibrium from equal incomes.

Proportionally Fair Makespan Approximation The combinatorial assignment problem: Ap proximate competitive equilibrium from equal incomes

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.623335Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3d74b3af-d632-43b1-9174-adafa1efa256 · outbound

This paper cites Computin g envy-freeable allocations with limited subsi- dies.

Proportionally Fair Makespan Approximation Computin g envy-freeable allocations with limited subsi- dies

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.608232Z

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Observation 26dc3e21-e09f-4a16-9e06-76508dcccefb · outbound

This paper cites The eﬃciency of fair division.

Proportionally Fair Makespan Approximation The eﬃciency of fair division

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.594218Z

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Observation 50906343-75dd-4a59-b3ee-f745a1f8ccf9 · outbound

This paper cites Envy- freeness up to any item with high nash welfare: The virtue of donating items.

Proportionally Fair Makespan Approximation Envy- freeness up to any item with high nash welfare: The virtue of donating items

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.578536Z

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Observation 98b32bb8-91ce-4aed-b607-daad32e82673 · outbound

This paper cites The unreasonable fairness of maximum nash welfare.

Proportionally Fair Makespan Approximation The unreasonable fairness of maximum nash welfare

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.561367Z

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Observation b6eebdd9-bbb2-4685-8889-ef9368ce155f · outbound

This paper cites Egalitarian price of fairness for indivisible goods.

Proportionally Fair Makespan Approximation Egalitarian price of fairness for indivisible goods

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.546076Z

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Observation 0fc1ff90-284f-4db9-8ca8-a7f1f058e23e · outbound

This paper cites E fx exists for three agents.

Proportionally Fair Makespan Approximation E fx exists for three agents

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.530765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ab31dd4c-5870-49ce-b412-c56fc8056825 · outbound

This paper cites A lower bound for scheduling mecha- nisms.

Proportionally Fair Makespan Approximation A lower bound for scheduling mecha- nisms

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.514240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4ab2b56f-9e81-43f5-8347-4e94234b36e9 · outbound

This paper cites On the nisan-ronen conjecture.

Proportionally Fair Makespan Approximation On the nisan-ronen conjecture

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.498073Z

Source-reported events for the cited work

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Observation ca2217d5-bc92-4566-86dd-6f6ba5b2f5bd · outbound

This paper cites A proof of the Nisan-Ronen con- jecture.

Proportionally Fair Makespan Approximation A proof of the Nisan-Ronen con- jecture

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.480067Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 216d2f08-a50b-4a35-99ef-c8cff8af0e56 · outbound

This paper cites An application of bin-packing to multiprocessor scheduling.

Proportionally Fair Makespan Approximation An application of bin-packing to multiprocessor scheduling

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.464232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation dd8ff53b-1744-4854-9a24-926eb3ff6466 · outbound

This paper cites Envy-free makespan approximation.

Proportionally Fair Makespan Approximation Envy-free makespan approximation

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.448193Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cdf7a915-5d2f-4d2e-9530-f02443762384 · outbound

This paper cites proportional chore-cut ting.

Proportionally Fair Makespan Approximation proportional chore-cut ting

Reference 24

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation bec0b281-0fd6-4455-8f55-d42a671ef068 · outbound

This paper cites Improved Lower Bounds for Truthful Scheduling.

Proportionally Fair Makespan Approximation Improved Lower Bounds for Truthful Scheduling

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-11T18:00:27.065658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1f8fe697-b320-42e5-8347-17bd53136ab4 · outbound

This paper cites Approximation schemes for scheduling on uniformly related and identical parallel machines.

Proportionally Fair Makespan Approximation Approximation schemes for scheduling on uniformly related and identical parallel machines

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.418019Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5f09d894-d2b7-441f-b746-24ab309ae969 · outbound

This paper cites On the c omplexity of chore division.

Proportionally Fair Makespan Approximation On the c omplexity of chore division

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.404373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 817376f9-c1c6-4b49-9af0-4a2002713506 · outbound

This paper cites On op timal tradeoﬀs between EFX and nash welfare.

Proportionally Fair Makespan Approximation On op timal tradeoﬀs between EFX and nash welfare

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.390342Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d9a314ca-c6d3-446a-b156-05798ebbe753 · outbound

This paper cites Tight lower bounds on envy-f ree makespan approximation.

Proportionally Fair Makespan Approximation Tight lower bounds on envy-f ree makespan approximation

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.375110Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 395b6cde-4476-4169-8065-71f2c6f5c7d1 · outbound

This paper cites an unresolved cited work.

Proportionally Fair Makespan Approximation Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:00:27.359955Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation db4094e1-3aad-4ad2-836c-576b1ce1ab36 · outbound

This paper cites Bounds for certain multiprocessing an omalies.

Proportionally Fair Makespan Approximation Bounds for certain multiprocessing an omalies

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.344722Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 278d3e14-89e8-45b7-bc0e-7b1f3c43b25a · outbound

This paper cites Fair division with subs idy.

Proportionally Fair Makespan Approximation Fair division with subs idy

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.329613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5601a750-aec4-4c4e-a50c-18ed33fce4a0 · outbound

This paper cites Multi-dimensional envy-free scheduling mechanisms.

Proportionally Fair Makespan Approximation Multi-dimensional envy-free scheduling mechanisms

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.314251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f8c1ed55-e14d-49ef-9ae5-4e3d15658c42 · outbound

This paper cites Mertzios, Hend rik Molter, Rolf Niedermeier, and Dvir Shab- tay.

Proportionally Fair Makespan Approximation Mertzios, Hend rik Molter, Rolf Niedermeier, and Dvir Shab- tay

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.296769Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation bf368e06-15a9-4f15-bdec-d89d06ea570b · outbound

This paper cites Exact and approximate algorithms for scheduling nonidentical proces- sors.

Proportionally Fair Makespan Approximation Exact and approximate algorithms for scheduling nonidentical proces- sors

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.281724Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8193a8a2-414c-4488-8b5b-aee0a060cd4d · outbound

This paper cites A lower bound of 1+phi for truthful scheduling mechanisms.

Proportionally Fair Makespan Approximation A lower bound of 1+phi for truthful scheduling mechanisms

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.266158Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ca42f303-f43e-4ae6-b25c-978a0ca6f33a · outbound

This paper cites Appro ximation algorithms for scheduling unre- lated parallel machines.

Proportionally Fair Makespan Approximation Appro ximation algorithms for scheduling unre- lated parallel machines

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.250016Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8ba0c69b-525b-4b12-8abd-c6961d79dbed · outbound

This paper cites A complete landscape for the price of envy-freeness.

Proportionally Fair Makespan Approximation A complete landscape for the price of envy-freeness

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.233053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8239a25c-6550-4f21-a333-05817246253f · outbound

This paper cites Mixed fair division: A survey.

Proportionally Fair Makespan Approximation Mixed fair division: A survey

Reference 39

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Source-reported events for the cited work

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Observation ddf66cc6-cafb-4ed6-9433-ca0e189a0ed3 · outbound

This paper cites On the fair allocation of indivisible goo ds.

Proportionally Fair Makespan Approximation On the fair allocation of indivisible goo ds

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.205511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3bd79d3d-1e92-4911-8e85-f1930ad23785 · outbound

This paper cites Algorithmic mechanism desig n.

Proportionally Fair Makespan Approximation Algorithmic mechanism desig n

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.189973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 65469a6d-8116-4964-84dd-d727305924b5 · outbound

This paper cites Existence theorems, lower bounds and algorithms for scheduling to meet two objectives.

Proportionally Fair Makespan Approximation Existence theorems, lower bounds and algorithms for scheduling to meet two objectives

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.173500Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d8c01083-5792-4cc1-bdc6-0b7bbb589261 · outbound

This paper cites Algorithms for scheduling independent tasks.

Proportionally Fair Makespan Approximation Algorithms for scheduling independent tasks

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.155884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 39353e89-a42f-4883-bd0a-f296b42df674 · outbound

This paper cites On the existence of schedul es that are near-optimal for both makespan and total weighted completion time.

Proportionally Fair Makespan Approximation On the existence of schedul es that are near-optimal for both makespan and total weighted completion time

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.141557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3ca386a8-97ae-4de7-90e2-53ee2e0bf9d1 · outbound

This paper cites The problem of fair division.

Proportionally Fair Makespan Approximation The problem of fair division

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-11T18:00:27.009424Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a915702-5232-49bf-89cd-56fba79a7a51 · outbound

This paper cites One quarter e ach (on average) ensures proportionality.

Proportionally Fair Makespan Approximation One quarter e ach (on average) ensures proportionality

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.115559Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f7a94efe-8b28-4085-812c-74a6d073504c · outbound

This paper cites On the exact upper bound for the multiﬁt proce ssor scheduling algorithm.

Proportionally Fair Makespan Approximation On the exact upper bound for the multiﬁt proce ssor scheduling algorithm

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:00:27.099868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

No inbound Pith citation observations are available.