% torchmatch bibliography. Single source of truth for all references in
% the documentation. Every citation key used in the docs corresponds to
% an entry below; the unified bibliography page (/references) renders
% these entries in a human-readable form.
%
% Convention for new citations, using docyard's citation system:
%   1. Add the entry here first.
%   2. Cite it in prose with the Pandoc/Quarto `@Key` syntax (or
%      `[@KeyA; @KeyB]` for multiple keys). This is sugar over the
%      `:docyard-cite{bib="Key"}` MDC component, which can also be used
%      directly. Do not use a plain `:Cite{...}` tag — that component
%      does not exist and silently fails to render.
%   3. Add `::Bibliography` / `::` at the bottom of the page to render
%      the bibliography for every key cited on that page (or
%      `::FullBibliography` for the site-wide list on /references).
%   4. Update /references if a new entry is introduced.
%
% Each entry below carries a short annotation in a comment block above
% it, explaining the paper's role in the LAP literature and (where
% applicable) its relation to a torchmatch implementation. These
% comments are for readers of the .bib file; the `note` fields inside
% each entry are intended for rendered bibliographies.


% Foundational result on bipartite matchings and minimum vertex covers
% (later named "König's theorem"). No algorithm, but the structural
% duality is the substrate that the Hungarian method later
% operationalizes. Original is in Hungarian; secondary literature
% provides English summaries.
@article{Konig1931,
  author = {K{\H o}nig, D{\'e}nes},
  title = {Gr{\'a}fok {\'e}s m{\'a}trixok},
  journal = {Matematikai {\'e}s Fizikai Lapok},
  year = {1931},
  volume = {38},
  pages = {116--119},
  note = {Hungarian. Origin of K{\H o}nig's theorem on bipartite matchings and
          covers.},
}


% Weighted-edge extension of König's theorem. Provides the
% dual-feasibility characterization that primal-dual LAP algorithms
% rely on. Translated to English by Kuhn in 1955 as "On Combinatorial
% Properties of Matrices", Logistics Papers Issue 11, George Washington
% University.
@article{Egervary1931,
  author = {Egerv{\'a}ry, Jen{\H o}},
  title = {Matrixok kombinatorius tulajdons{\'a}gair{\'o}l},
  journal = {Matematikai {\'e}s Fizikai Lapok},
  year = {1931},
  volume = {38},
  pages = {16--28},
  note = {Hungarian. Weighted extension of K{\H o}nig's theorem. Translated to
          English by H. W. Kuhn (1955) as ``On Combinatorial Properties of
          Matrices'', Logistics Papers Issue 11, George Washington University.},
}


% The paper that coined "Hungarian method" (in tribute to König and
% Egerváry) and first gave an explicit O(n^4) algorithm for the LAP.
% Built on Egerváry's 1931 weighted duality and reformulated it into a
% primal-dual procedure. The foundational reference for everything in
% torchmatch's Hungarian sub-family.
@article{Kuhn1955,
  author = {Kuhn, Harold W.},
  title = {The {H}ungarian method for the assignment problem},
  journal = {Naval Research Logistics Quarterly},
  year = {1955},
  volume = {2},
  number = {1--2},
  pages = {83--97},
  doi = {10.1002/nav.3800020109},
  note = {Coined the name ``Hungarian method'' in tribute to K{\H o}nig and
          Egerv{\'a}ry; first explicit $O(n^4)$ algorithm for the LAP.},
}


% The six-step primed/starred-zeros state machine. Mechanically clearer
% than Kuhn's original presentation and remains the canonical textbook
% description. Implemented in torchmatch as `munkres` (cuda/munkres.cu).
@article{Munkres1957,
  author = {Munkres, James},
  title = {Algorithms for the assignment and transportation problems},
  journal = {Journal of the Society for Industrial and Applied Mathematics},
  year = {1957},
  volume = {5},
  number = {1},
  pages = {32--38},
  doi = {10.1137/0105003},
  note = {Six-step state machine on primed and starred zeros under row/column
          covers; canonical textbook formulation of the Hungarian method.
          Implemented as \texttt{torchmatch.munkres}.},
}


% Independent SSP-style refinement bringing the Hungarian bound from
% O(n^4) to O(n^3). Less well known than Edmonds & Karp's 1972 paper
% but earlier; introduces the shortest-augmenting-path technique
% applied to the assignment problem specifically.
@article{Tomizawa1971,
  author = {Tomizawa, Nobuaki},
  title = {On some techniques useful for solution of transportation network
           problems},
  journal = {Networks},
  year = {1971},
  volume = {1},
  number = {2},
  pages = {173--194},
  doi = {10.1002/net.3230010206},
  note = {Independent reduction of the Hungarian method to $O(n^3)$ via shortest
          augmenting paths; predates Edmonds \& Karp (1972).},
}


% The other independent route to the O(n^3) bound for assignment and
% min-cost-flow problems. Wider scope than Tomizawa, since it covers
% general network flows; both reach the same asymptotic on the LAP.
@article{EdmondsKarp1972,
  author = {Edmonds, Jack and Karp, Richard M.},
  title = {Theoretical improvements in algorithmic efficiency for network flow
           problems},
  journal = {Journal of the ACM},
  year = {1972},
  volume = {19},
  number = {2},
  pages = {248--264},
  doi = {10.1145/321694.321699},
  note = {Independent $O(n^3)$ improvement to the Hungarian method via shortest
          augmenting paths in network flow; contemporary with [Tomizawa1971].},
}


% Textbook reformulation of the Hungarian inner loop as a BFS that
% discovers all vertex-disjoint augmenting paths per outer iteration.
% Same O(n^3) asymptotic, larger per-iteration work, much more exposed
% parallelism. Implemented in torchmatch as `lawler` (cuda/lawler.cu).
@book{Lawler1976,
  author = {Lawler, Eugene L.},
  title = {Combinatorial Optimization: Networks and Matroids},
  publisher = {Holt, Rinehart and Winston},
  year = {1976},
  address = {New York},
  isbn = {0-03-084866-0},
  note = {Tree-augmentation reformulation of the Hungarian inner loop; basis for
          the GPU-parallel BFS structure used in \texttt{torchmatch.lawler}.},
}


% The original auction algorithm, first circulated as an MIT LIDS
% working paper (May 1979). Available at
% web.mit.edu/dimitrib/www/Bertsekas_Auction_Distributed_1979.pdf.
% The widely cited follow-up is [Bertsekas1988] in Annals of Operations
% Research, which introduces ε-scaling. Not implemented in torchmatch.
@techreport{Bertsekas1979,
  author = {Bertsekas, Dimitri P.},
  title = {A distributed algorithm for the assignment problem},
  institution = {Laboratory for Information and Decision Systems, MIT},
  year = {1979},
  month = {May},
  type = {Working paper},
  url = {https://web.mit.edu/dimitrib/www/Bertsekas_Auction_Distributed_1979.pdf
         },
  note = {Original distributed-bidding (``auction'') algorithm for the LAP;
          precursor to the {$\varepsilon$}-scaling version in [Bertsekas1988].},
}


% The fast Dijkstra-based successive-shortest-path procedure. Defines
% the column-reduction warm start and the reduction-transfer step that
% give the JV constant factor its empirical edge. The de facto CPU
% reference for dense LAPs. Implemented in torchmatch as the
% jonker_scalar / jonker_dense / jonker_compact family
% (cpu/jonker_*.{h,cpp}).
@article{JonkerVolgenant1987,
  author = {Jonker, Roy and Volgenant, Anton},
  title = {A shortest augmenting path algorithm for dense and sparse linear
           assignment problems},
  journal = {Computing},
  year = {1987},
  volume = {38},
  number = {4},
  pages = {325--340},
  doi = {10.1007/BF02278710},
  note = {Dijkstra-based SSP with column-reduction warm start and reduction
          transfer; basis for \texttt{torchmatch.jonker\_*} on CPU.},
}


% Auction with ε-scaling: the more widely cited version of the auction
% algorithm, in Annals of Operations Research. Convergence proved under
% ε-scaling. Not implemented in torchmatch.
@article{Bertsekas1988,
  author = {Bertsekas, Dimitri P.},
  title = {The auction algorithm: a distributed relaxation method for the
           assignment problem},
  journal = {Annals of Operations Research},
  year = {1988},
  volume = {14},
  number = {1},
  pages = {105--123},
  doi = {10.1007/BF02186476},
  note = {Auction with {$\varepsilon$}-scaling; convergence guarantees. Widely
          cited follow-up to [Bertsekas1979].},
}


% Push-relabel cost-scaling for the LAP via its reduction to min-cost
% flow. Theoretically attractive worst case but rarely beats JV in
% practice on dense problems. Not implemented in torchmatch.
@article{GoldbergKennedy1995,
  author = {Goldberg, Andrew V. and Kennedy, Robert},
  title = {An efficient cost scaling algorithm for the assignment problem},
  journal = {Mathematical Programming},
  year = {1995},
  volume = {71},
  number = {2},
  pages = {153--177},
  doi = {10.1007/BF01585996},
  note = {Push-relabel cost-scaling for the LAP via min-cost flow reduction.},
}


% Kuhn's own retrospective; useful entry point for the historiography
% (clarifies the attribution chain König → Egerváry → Kuhn → Munkres).
@incollection{Kuhn2010Variants,
  author = {Kuhn, Harold W.},
  title = {The {H}ungarian method for the assignment problem},
  booktitle = {50 Years of Integer Programming 1958--2008},
  publisher = {Springer},
  editor = {J{\"u}nger, M. and Liebling, T. M. and Naddef, D. and Nemhauser, G.
            L. and Pulleyblank, W. R. and Reinelt, G. and Rinaldi, G. and Wolsey,
            L. A.},
  year = {2010},
  pages = {29--47},
  doi = {10.1007/978-3-540-68279-0_2},
  note = {Author's retrospective on the 1955 paper; clarifies the attribution
          chain to K{\H o}nig and Egerv{\'a}ry.},
}


% Comprehensive secondary treatment of the LAP and its variants
% (rectangular, bottleneck, k-cardinality, quadratic). Originally
% published in 2009 by SIAM; the 2012 revised reprint has corrections
% but the same chapter structure.
@book{BurkardDellAmicoMartello2012,
  author = {Burkard, Rainer E. and Dell'Amico, Mauro and Martello, Silvano},
  title = {Assignment Problems},
  publisher = {Society for Industrial and Applied Mathematics},
  year = {2012},
  edition = {Revised reprint},
  doi = {10.1137/1.9781611972238},
  isbn = {978-1-61197-222-1},
  note = {Comprehensive treatment of LAP variants, complexity bounds, and
          empirical comparisons. Original 2009; this is the 2012 revised reprint
          with corrections.},
}


% Rectangular-native reformulation of Jonker-Volgenant. Eliminates the
% pad-and-solve overhead for non-square cost matrices. Implemented in
% torchmatch as the rectangular-capable jonker_dense
% (cpu/jonker_dense_*.h) and as the basis for the tiled CUDA backend of
% jonker_dense_batch (cuda/jonker_tiled.cuh).
@article{Crouse2016,
  author = {Crouse, David F.},
  title = {On implementing {2D} rectangular assignment algorithms},
  journal = {IEEE Transactions on Aerospace and Electronic Systems},
  year = {2016},
  volume = {52},
  number = {4},
  pages = {1679--1696},
  doi = {10.1109/TAES.2016.140952},
  note = {Rectangular-native reformulation of Jonker-Volgenant; basis for
          \texttt{torchmatch.jonker\_dense} and the tiled CUDA backend of \texttt
          {torchmatch.jonker\_dense\_batch}.},
}


% ── Optimal transport ─────────────────────────────────────────────────────────

% Monge's original military-engineering formulation: find a bijective map from
% excavated soil (d{\'e}blais) to embankment sites (remblais) minimising total
% transport distance. Geometrically clean but lacks a convex relaxation.
@article{Monge1781,
  author = {Monge, Gaspard},
  title = {M{\'e}moire sur la th{\'e}orie des d{\'e}blais et des remblais},
  journal = {Histoire de l'Acad{\'e}mie Royale des Sciences},
  year = {1781},
  pages = {666--704},
  note = {Foundational deterministic mass-transport problem; no convex
          relaxation, making it hard to solve in general.},
}


% Kantorovich's LP relaxation: replace bijections with couplings (joint
% distributions whose marginals match source and target). Makes OT a linear
% program with strong duality; dual variables are "prices." Kantorovich shared
% the 1975 Nobel Prize in Economics with Koopmans for this and related work.
@article{Kantorovich1942,
  author = {Kantorovich, Leonid V.},
  title = {On the translocation of masses},
  journal = {Doklady Akademii Nauk USSR},
  year = {1942},
  volume = {37},
  number = {7--8},
  pages = {199--201},
  note = {LP relaxation of [Monge1781]: couplings instead of bijections;
          strong duality yields dual variables interpretable as prices.},
}


% Fluid-mechanics (dynamic) interpretation of the 2-Wasserstein distance as
% minimum kinetic energy. Connects OT to PDEs; gives a variational formulation
% amenable to gradient-based solvers.
@article{BenamouBrenier2000,
  author = {Benamou, Jean-David and Brenier, Yann},
  title = {A computational fluid mechanics solution to the {M}onge-{K}antorovich
           mass transfer problem},
  journal = {Numerische Mathematik},
  year = {2000},
  volume = {84},
  number = {3},
  pages = {375--393},
  doi = {10.1007/s002110050263},
  note = {Dynamic OT: $W_2^2$ equals the minimum kinetic energy to deform one
          distribution into the other; connects OT to PDEs.},
}


% Introduced EMD as a practical histogram similarity measure for computer
% vision. Established OT as a tool practitioners would actually use, not just a
% mathematical object. Also provided an efficient transportation-problem solver.
@article{Rubner2000,
  author = {Rubner, Yossi and Tomasi, Carlo and Guibas, Leonidas J.},
  title = {The earth mover's distance as a metric for image retrieval},
  journal = {International Journal of Computer Vision},
  year = {2000},
  volume = {40},
  number = {2},
  pages = {99--121},
  doi = {10.1023/A:1026543900054},
  note = {Introduced the Earth Mover's Distance (EMD) as a practical histogram
          similarity measure; established OT as a tool in computer vision.},
}


% Villani's first monograph: unifies OT geometry, analysis, and probability.
% Introduces displacement interpolation (geodesic paths between distributions)
% and establishes OT as a central object in modern mathematics.
@book{Villani2003,
  author = {Villani, C{\'e}dric},
  title = {Topics in Optimal Transportation},
  publisher = {American Mathematical Society},
  year = {2003},
  volume = {58},
  series = {Graduate Studies in Mathematics},
  doi = {10.1090/gsm/058},
  note = {First of Villani's two monographs on OT; introduces displacement
          interpolation and unifies geometry, analysis, and probability.},
}


% Villani's second monograph: comprehensive treatment of regularity theory,
% the Brenier map, curvature conditions (CD(K,N)), and probabilistic
% applications. Villani received the Fields Medal in 2010 partly for this work.
@book{Villani2008,
  author = {Villani, C{\'e}dric},
  title = {Optimal Transport: Old and New},
  publisher = {Springer},
  year = {2008},
  volume = {338},
  series = {Grundlehren der mathematischen Wissenschaften},
  doi = {10.1007/978-3-540-71050-9},
  note = {Second of Villani's monographs; comprehensive treatment including the
          Brenier map, regularity, and geometric applications. Fields Medal
          (2010) awarded partly for this body of work.},
}


% Convergence of the alternating row-and-column normalisation (Sinkhorn--Knopp
% iteration) to a doubly stochastic matrix with prescribed row and column sums.
% The foundational result behind all entropic OT solvers.
@article{Sinkhorn1967,
  author = {Sinkhorn, Richard},
  title = {Diagonal equivalence to matrices with prescribed row and column sums},
  journal = {The American Mathematical Monthly},
  year = {1967},
  volume = {74},
  number = {4},
  pages = {402--405},
  doi = {10.2307/2314570},
  note = {Proves convergence of the Sinkhorn--Knopp matrix-scaling iteration;
          foundational for all entropic OT solvers.},
}


% The computational breakthrough for OT in ML. Entropic regularisation
% turns OT into a Sinkhorn iteration, reducing $O(n^3)$ LP to $O(n^2)$ GPU-
% friendly matrix operations. Direct ancestor of the LOG_SINKHORN backend.
@inproceedings{Cuturi2013,
  author = {Cuturi, Marco},
  title = {Sinkhorn distances: lightspeed computation of optimal transportation
           distances},
  booktitle = {Advances in Neural Information Processing Systems},
  year = {2013},
  volume = {26},
  publisher = {Curran Associates},
  note = {Entropic regularisation of OT; reduction to Sinkhorn iteration
          enables large-scale batched OT on GPU. Direct ancestor of the
          \texttt{LOG\_SINKHORN} backend in torchmatch.},
}


% Wasserstein GAN: uses the 1-Wasserstein distance as a GAN training
% objective. Gives meaningful gradients even when generated and real
% distributions have disjoint support (where Jensen-Shannon divergence
% saturates). Opened the door to OT losses in generative modelling.
@inproceedings{Arjovsky2017,
  author = {Arjovsky, Martin and Chintala, Soumith and Bottou, L{\'e}on},
  title = {Wasserstein generative adversarial networks},
  booktitle = {International Conference on Machine Learning},
  year = {2017},
  volume = {70},
  pages = {214--223},
  publisher = {PMLR},
  note = {1-Wasserstein GAN objective; meaningful gradient signal even under
          disjoint support, where Jensen-Shannon divergence saturates.},
}


% Sinkhorn divergence: debiases the entropic OT loss to recover a proper
% divergence that is positive, symmetric, and zero iff the two distributions
% coincide. Achieved by subtracting the self-transport terms.
@inproceedings{Genevay2018,
  author = {Genevay, Aude and Peyr{\'e}, Gabriel and Cuturi, Marco},
  title = {Learning generative models with {S}inkhorn divergences},
  booktitle = {International Conference on Artificial Intelligence and
               Statistics},
  year = {2018},
  volume = {84},
  pages = {1608--1617},
  publisher = {PMLR},
  note = {Defines the Sinkhorn divergence by debiasing the entropic OT loss;
          recovers a proper symmetric divergence zero iff distributions match.},
}


% Unbalanced OT: replaces the hard marginal constraints with KL divergence
% penalties. Handles distributions with different total mass; robust to
% outliers. Scaling iteration analogous to balanced Sinkhorn.
@article{Chizat2018,
  author = {Chizat, Lena{\"i}c and Peyr{\'e}, Gabriel and Vialard,
            Fran{\c{c}}ois-Xavier and Schmitzer, Bernhard},
  title = {Scaling algorithms for unbalanced optimal transport problems},
  journal = {Mathematics of Computation},
  year = {2018},
  volume = {87},
  number = {314},
  pages = {2563--2609},
  doi = {10.1090/mcom/3303},
  note = {KL-relaxed marginals for unbalanced OT; softened Sinkhorn iteration
          handles mass differences and is robust to outliers.},
}


% Combines unbalanced marginals with the debiasing from [Genevay2018] to yield
% the Sinkhorn divergence for unbalanced OT. Convergence analysis in the
% unbalanced setting. arXiv:1910.12958.
@article{Sejourne2019,
  author = {S{\'e}journ{\'e}, Thibault and Feydy, Jean and Vialard,
            Fran{\c{c}}ois-Xavier and Trouv{\'e}, Alain and Peyr{\'e},
            Gabriel},
  title = {Sinkhorn divergences for unbalanced optimal transport},
  journal = {arXiv preprint arXiv:1910.12958},
  year = {2019},
  note = {Extends the Sinkhorn divergence to unbalanced marginals; convergence
          analysis in the unbalanced setting.},
}


% Log-domain (Gibbs-potential) formulation of the Sinkhorn iteration for
% numerical stability at small regularisation or large costs. Used in
% torchmatch's LOG_SINKHORN, SINKHORN_DIVERGENCE, and UNBALANCED_SINKHORN.
@article{Schmitzer2019,
  author = {Schmitzer, Bernhard},
  title = {Stabilized sparse scaling algorithms for entropy regularized
           transport problems},
  journal = {SIAM Journal on Scientific Computing},
  year = {2019},
  volume = {41},
  number = {3},
  pages = {A1443--A1481},
  doi = {10.1137/16M1106018},
  note = {Log-domain (Gibbs-potential) Sinkhorn; numerically stable for all
          regularisation strengths and cost magnitudes.},
}


% Polynomial-time primal network simplex for min-cost flow; the standard exact
% EMD solver. CPU-only in torchmatch (EXACT_EMD backend). O((n+m)^3 log(n+m))
% worst-case, typically much faster in practice.
@article{Orlin1997,
  author = {Orlin, James B.},
  title = {A polynomial time primal network simplex algorithm for minimum
           cost flows},
  journal = {Mathematical Programming},
  year = {1997},
  volume = {78},
  number = {2},
  pages = {109--129},
  doi = {10.1007/BF02614374},
  note = {Network simplex with polynomial worst-case guarantee; basis for the
          \texttt{EXACT\_EMD} backend in torchmatch.},
}


% Proves that Maximum Mean Discrepancy (MMD) with energy-distance kernels is
% equivalent to an OT-based test statistic. The connection is cited when the
% Sinkhorn divergence converges to the unregularised OT cost and MMD.
@article{Sejdinovic2013,
  author = {Sejdinovic, Dino and Sriperumbudur, Bharath and Gretton, Arthur
            and Fukumizu, Kenji},
  title = {Equivalence of distance-based and {RKHS}-based statistics in
           hypothesis testing},
  journal = {The Annals of Statistics},
  year = {2013},
  volume = {41},
  number = {5},
  pages = {2263--2291},
  doi = {10.1214/13-AOS1140},
  note = {Proves that MMD with energy-distance kernels equals an OT-based
          statistic; the connection between Sinkhorn divergence, OT, and MMD.},
}


% ── Assignment applications (blog) ──────────────────────────────────────────

% SORT: linear motion prediction via a Kalman filter, IoU cost matrix,
% Hungarian assignment. Established the template that the later
% tracker family below all extend.
@inproceedings{Bewley2016,
  author = {Bewley, Alex and Ge, Zongyuan and Ott, Lionel and Ramos, Fabio
            and Upcroft, Ben},
  title = {Simple online and realtime tracking},
  booktitle = {IEEE International Conference on Image Processing (ICIP)},
  year = {2016},
  pages = {3464--3468},
  doi = {10.1109/ICIP.2016.7533003},
  note = {SORT; Kalman-filter motion prediction plus IoU cost and Hungarian
          assignment. Establishes the tracking-by-detection template extended
          by [Wojke2017], [Zhang2022], [Aharon2022], and [Cao2023].},
}


% DeepSORT: adds an appearance (re-identification) embedding distance
% to the SORT cost matrix.
@inproceedings{Wojke2017,
  author = {Wojke, Nicolai and Bewley, Alex and Paulus, Dietrich},
  title = {Simple online and realtime tracking with a deep association metric},
  booktitle = {IEEE International Conference on Image Processing (ICIP)},
  year = {2017},
  pages = {3645--3649},
  doi = {10.1109/ICIP.2017.8296962},
  note = {DeepSORT; adds an appearance re-identification embedding distance to
          the SORT cost matrix in [Bewley2016].},
}


% ByteTrack: extends SORT-style tracking to also associate
% low-confidence detections via a second assignment pass.
@inproceedings{Zhang2022,
  author = {Zhang, Yifu and Sun, Peize and Jiang, Yi and Yu, Dongdong
            and Weng, Fucheng and Yuan, Zehuan and Luo, Ping and Liu, Wenyu
            and Wang, Xinggang},
  title = {{ByteTrack}: Multi-object tracking by associating every detection box},
  booktitle = {European Conference on Computer Vision (ECCV)},
  year = {2022},
  series = {Lecture Notes in Computer Science},
  volume = {13682},
  pages = {1--21},
  doi = {10.1007/978-3-031-20047-2_1},
  note = {Associates low-confidence detections through a second Hungarian
          assignment pass on top of the SORT template.},
}


% BoT-SORT: refines the SORT motion model with camera-motion
% compensation and adds appearance embeddings; assignment step
% unchanged. arXiv-only.
@article{Aharon2022,
  author = {Aharon, Nir and Orfaig, Roy and Bobrovsky, Ben-Zion},
  title = {{BoT-SORT}: Robust associations multi-pedestrian tracking},
  journal = {arXiv preprint arXiv:2206.14651},
  year = {2022},
  note = {Camera-motion compensation and appearance embeddings on top of the
          SORT template; the Hungarian assignment step is unchanged.},
}


% OC-SORT: observation-centric re-update reducing the motion-model
% drift that pure Kalman-filter prediction accumulates during
% occlusions.
@inproceedings{Cao2023,
  author = {Cao, Jinkun and Pang, Jiangmiao and Weng, Xinshuo
            and Khirodkar, Rawal and Kitani, Kris},
  title = {Observation-centric {SORT}: Rethinking {SORT} for robust
           multi-object tracking},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition
               (CVPR)},
  year = {2023},
  pages = {9686--9696},
  doi = {10.1109/CVPR52729.2023.00934},
  note = {Observation-centric re-update reduces motion-model drift under
          occlusion; same Hungarian assignment core as [Bewley2016].},
}


% DETR: places the Hungarian matcher on the training-time critical
% path via a set-prediction loss over a fixed-size prediction set.
% torchmatch's batched LAP ops target exactly this training-time
% matching cost.
@inproceedings{Carion2020,
  author = {Carion, Nicolas and Massa, Francisco and Synnaeve, Gabriel
            and Usunier, Nicolas and Kirillov, Alexander and Zagoruyko, Sergey},
  title = {End-to-end object detection with transformers},
  booktitle = {European Conference on Computer Vision (ECCV)},
  year = {2020},
  series = {Lecture Notes in Computer Science},
  volume = {12346},
  pages = {213--229},
  doi = {10.1007/978-3-030-58452-8_13},
  note = {DETR; introduces the Hungarian-matching set-prediction training
          loss that the entire DETR lineage, including [Cheng2021], preserves.},
}


% MaskFormer: a DETR-lineage mask-classification model; preserves the
% Hungarian matching step for per-mask set prediction.
@inproceedings{Cheng2021,
  author = {Cheng, Bowen and Schwing, Alexander G. and Kirillov, Alexander},
  title = {Per-pixel classification is not all you need for semantic
           segmentation},
  booktitle = {Advances in Neural Information Processing Systems},
  year = {2021},
  volume = {34},
  pages = {17864--17875},
  note = {MaskFormer; recasts semantic segmentation as mask classification,
          preserving the Hungarian matching step from the DETR lineage
          ([Carion2020]).},
}


% ── Transport applications (blog) ───────────────────────────────────────────

% Formalises photo-realistic colour transfer as iterated 1D OT
% projections (sliced Wasserstein), scaling to full 3D colour
% histograms without materialising an n^3 cost.
@article{Pitie2007,
  author = {Piti{\'e}, Fran{\c{c}}ois and Kokaram, Anil C. and Dahyot, Rozenn},
  title = {Automated colour grading using colour distribution transfer},
  journal = {Computer Vision and Image Understanding},
  year = {2007},
  volume = {107},
  number = {1--2},
  pages = {123--137},
  doi = {10.1016/j.cviu.2006.11.011},
  note = {Iterated 1D OT projections (sliced Wasserstein) for colour transfer;
          scales to full 3D colour histograms.},
}


% Wasserstein autoencoder: replaces the VAE evidence lower bound with a
% Wasserstein distance between the aggregate posterior and the prior.
@inproceedings{Tolstikhin2018,
  author = {Tolstikhin, Ilya and Bousquet, Olivier and Gelly, Sylvain
            and Sch{\"o}lkopf, Bernhard},
  title = {Wasserstein auto-encoders},
  booktitle = {International Conference on Learning Representations},
  year = {2018},
  note = {WAE; replaces the VAE evidence lower bound with a Wasserstein
          distance between the aggregate posterior and the prior.},
}


% Flow matching: frames diffusion-model training as learning a vector
% field that transports a noise source distribution to the data target
% distribution.
@inproceedings{Lipman2022,
  author = {Lipman, Yaron and Chen, Ricky T. Q. and Ben-Hamu, Heli
            and Nickel, Maximilian and Le, Matt},
  title = {Flow matching for generative modeling},
  booktitle = {International Conference on Learning Representations},
  year = {2023},
  note = {Frames diffusion-model training as learning a vector field
          transporting a noise source distribution to the data target
          distribution; the OT-conditioned variant uses the OT displacement
          plan between individual samples.},
}


% Rectified flow: straightens flow-matching trajectories via an
% OT-conditioned reflow procedure, reducing the number of sampling
% steps needed at inference.
@inproceedings{Liu2022,
  author = {Liu, Xingchao and Gong, Chengyue and Liu, Qiang},
  title = {Flow straight and fast: Learning to generate and transfer data
           with rectified flow},
  booktitle = {International Conference on Learning Representations},
  year = {2023},
  note = {Straightens [Lipman2022]-style flow-matching trajectories via an
          OT-conditioned reflow procedure, reducing inference sampling steps.},
}


% OTDA: transports labelled source features toward an unlabelled target
% domain using the regularised OT plan between the two feature
% distributions, then trains a target-domain classifier on the result.
@article{Courty2017,
  author = {Courty, Nicolas and Flamary, R{\'e}mi and Tuia, Devis
            and Rakotomamonjy, Alain},
  title = {Optimal transport for domain adaptation},
  journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
  year = {2017},
  volume = {39},
  number = {9},
  pages = {1853--1865},
  doi = {10.1109/TPAMI.2016.2615921},
  note = {OTDA; transports labelled source features toward an unlabelled
          target domain via the regularised OT plan, then trains a
          target-domain classifier on the result.},
}


% DeepJDOT: integrates OT domain-adaptation alignment into end-to-end
% training, recomputing the OT plan between source/target minibatches
% each iteration.
@inproceedings{Damodaran2018,
  author = {Damodaran, Bharath Bhushan and Kellenberger, Benjamin
            and Flamary, R{\'e}mi and Tuia, Devis and Courty, Nicolas},
  title = {{DeepJDOT}: Deep joint distribution optimal transport for
           unsupervised domain adaptation},
  booktitle = {European Conference on Computer Vision (ECCV)},
  year = {2018},
  series = {Lecture Notes in Computer Science},
  volume = {11208},
  pages = {467--483},
  doi = {10.1007/978-3-030-01225-0_28},
  note = {Integrates [Courty2017]-style OT alignment into end-to-end training;
          the OT plan between minibatches is recomputed every iteration and
          reweights the classification loss.},
}


% Wasserstein barycenters: weighted averages of distributions in
% Wasserstein space that respect the geometry of the ground metric.
@article{Agueh2011,
  author = {Agueh, Martial and Carlier, Guillaume},
  title = {Barycenters in the {W}asserstein space},
  journal = {SIAM Journal on Mathematical Analysis},
  year = {2011},
  volume = {43},
  number = {2},
  pages = {904--924},
  doi = {10.1137/100805741},
  note = {Defines Wasserstein barycenters; weighted averages of distributions
          that respect the geometry of the ground metric, unlike Euclidean
          averaging.},
}


% Word Mover's Distance: OT between word-embedding distributions of
% two documents, using pretrained embeddings as the ground metric.
@inproceedings{Kusner2015,
  author = {Kusner, Matt J. and Sun, Yu and Kolkin, Nicholas I.
            and Weinberger, Kilian Q.},
  title = {From word embeddings to document distances},
  booktitle = {International Conference on Machine Learning},
  year = {2015},
  volume = {37},
  pages = {957--966},
  publisher = {PMLR},
  note = {Word Mover's Distance; OT between word-embedding distributions of
          two documents, insensitive to synonymy and paraphrase.},
}


% Waddington-OT: models cellular differentiation as an OT problem
% between adjacent-timepoint scRNA-seq profiles, recovering
% developmental trajectories without paired data.
@article{Schiebinger2019,
  author = {Schiebinger, Geoffrey and Shu, Jian and Tabaka, Marcin
            and Cleary, Brian and Subramanian, Vidya and Solomon, Aryeh
            and Gould, Joshua and Liu, Siyan and Lin, Stacie and Berube, Peter
            and Lee, Lia and Chen, Jenny and Brumbaugh, Justin
            and Rigollet, Philippe and Hochedlinger, Konrad
            and Jaenisch, Rudolf and Regev, Aviv and Lander, Eric S.},
  title = {Optimal-transport analysis of single-cell gene expression
           identifies developmental trajectories in reprogramming},
  journal = {Cell},
  year = {2019},
  volume = {176},
  number = {4},
  pages = {928--943},
  doi = {10.1016/j.cell.2019.01.006},
  note = {Waddington-OT; the OT plan between adjacent-timepoint scRNA-seq
          profiles recovers developmental trajectories without paired data.},
}


% Moscot: scales Waddington-OT-style trajectory inference to
% million-cell datasets and extends it to spatial and multi-omics
% single-cell data. Cited as the bioRxiv preprint (2023); later
% published in Nature (2025).
@article{Klein2023,
  author = {Klein, Dominik and Palla, Giovanni and Lange, Marius
            and Klein, Michal and Piran, Zoe and Gander, Manuel
            and Meng-Papaxanthos, Laetitia and Sterr, Michael
            and Treutlein, Barbara and Lickert, Heiko and Theis, Fabian J.},
  title = {Mapping cells through time and space with moscot},
  journal = {bioRxiv},
  year = {2023},
  doi = {10.1101/2023.05.11.540374},
  note = {Moscot; scales OT-based single-cell trajectory inference in
          [Schiebinger2019] to million-cell, multi-omics, and spatial
          datasets. Later published in Nature (2025).},
}