Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T18:00:27.019346Z
Paper Citation Record · LEDGER
Proportionally Fair Makespan Approximation
As of 16 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.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
47 of 47 outbound references displayed
- verified exact1
- verified fuzzy41
- unresolved5
- parse uncertain0
- malformed identifier0
- metadata mismatch0
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
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T18:00:27.773298Z
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.
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
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T18:00:26.810039Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
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
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T18:00:27.748251Z
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.
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
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.
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
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T18:00:27.718199Z
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.
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
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.
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
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.
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
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.
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
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.
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
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.
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
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T18:00:26.853567Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
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
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.
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
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.
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
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.
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
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.
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
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.
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
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.
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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
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
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.
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 2026-08-16T06:30:59.297886+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
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.
Observation cdf7a915-5d2f-4d2e-9530-f02443762384 · outbound
This paper cites proportional chore-cut ting.
Proportionally Fair Makespan Approximation proportional chore-cut ting
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T18:00:27.432963Z
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.
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 2026-08-16T06:30:59.297886+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
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.
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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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
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.
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
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.
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
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.
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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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
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.
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
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.
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
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.
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
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.
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 2026-08-16T06:30:59.297886+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
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T18:00:26.981573Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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
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.
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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
No inbound Pith citation observations are available.