@article{hoory_expander_2006,
  title    = {Expander graphs and their applications},
  volume   = {43},
  issn     = {0273-0979},
  url      = {http://www.ams.org/journal-getitem?pii=S0273-0979-06-01126-8},
  doi      = {10.1090/S0273-0979-06-01126-8},
  language = {en},
  number   = {04},
  urldate  = {2025-05-09},
  journal  = {Bulletin of the American Mathematical Society},
  author   = {Hoory, Shlomo and Linial, Nathan and Wigderson, Avi},
  month    = aug,
  year     = {2006},
  pages    = {439--562}
}

@article{arora_osqrtlogn_2010,
  title    = { {$O(\sqrt{\log n})$} {Approximation} to {SPARSEST} {CUT} in {$\tilde{O}(n^2)$} {Time}},
  volume   = {39},
  issn     = {0097-5397, 1095-7111},
  url      = {http://epubs.siam.org/doi/10.1137/080731049},
  doi      = {10.1137/080731049},
  language = {en},
  number   = {5},
  urldate  = {2025-05-09},
  journal  = {SIAM Journal on Computing},
  author   = {Arora, Sanjeev and Hazan, Elad and Kale, Satyen},
  month    = jan,
  year     = {2010},
  pages    = {1748--1771}
}

@misc{dorsi2024sparsestcuteigenvaluemultiplicities,
  title         = {Sparsest cut and eigenvalue multiplicities on low degree Abelian Cayley graphs},
  author        = {Tommaso d'Orsi and Chris Jones and Jake Ruotolo and Salil Vadhan and Jiyu Zhang},
  year          = {2024},
  eprint        = {2412.17115},
  archiveprefix = {arXiv},
  primaryclass  = {cs.DS},
  url           = {https://arxiv.org/abs/2412.17115}
}

@inproceedings{arora_expander_2004,
  address   = {New York, NY, USA},
  series    = {{STOC} '04},
  title     = {Expander flows, geometric embeddings and graph partitioning},
  isbn      = {978-1-58113-852-8},
  url       = {https://doi.org/10.1145/1007352.1007355},
  doi       = {10.1145/1007352.1007355},
  abstract  = {We give a O(√log n)-approximation algorithm for sparsest cut, balanced separator, and graph conductance problems. This improves the O(log n)-approximation of Leighton and Rao (1988). We use a well-known semidefinite relaxation with triangle inequality constraints. Central to our analysis is a geometric theorem about projections of point sets in Rd, whose proof makes essential use of a phenomenon called measure concentration. We also describe an interesting and natural "certificate" for a graph's expansion, by embedding an n-node expander in it with appropriate dilation and congestion. We call this an expander flow.},
  urldate   = {2025-05-09},
  booktitle = {Proceedings of the thirty-sixth annual {ACM} symposium on {Theory} of computing},
  publisher = {Association for Computing Machinery},
  author    = {Arora, Sanjeev and Rao, Satish and Vazirani, Umesh},
  month     = jun,
  year      = {2004},
  pages     = {222--231}
}

@article{leighton_multicommodity_1999,
  title   = {Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms},
  volume  = {46},
  issn    = {0004-5411},
  url     = {https://dl.acm.org/doi/10.1145/331524.331526},
  doi     = {10.1145/331524.331526},
  number  = {6},
  urldate = {2025-05-09},
  journal = {J. ACM},
  author  = {Leighton, Tom and Rao, Satish},
  month   = nov,
  year    = {1999},
  pages   = {787--832}
}
@INPROCEEDINGS{leighton_multicommodity_1988,
  author={Leighton, T. and Rao, S.},
  booktitle={[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science}, 
  title={An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms}, 
  year={1988},
  volume={},
  number={},
  pages={422-431},
  keywords={Application software;Approximation algorithms;Laboratories;Computer science;Particle separators;Linear programming;Contracts;Mathematics;Constraint theory;Bifurcation},
  doi={10.1109/SFCS.1988.21958}}

@article{garg_approximate_1996,
	title = {Approximate {Max}-{Flow} {Min}-({Multi}){Cut} {Theorems} and {Their} {Applications}},
	volume = {25},
	issn = {0097-5397},
	url = {https://epubs.siam.org/doi/10.1137/S0097539793243016},
	doi = {10.1137/S0097539793243016},
	number = {2},
	urldate = {2025-05-20},
	journal = {SIAM Journal on Computing},
	author = {Garg, Naveen and Vazirani, Vijay V. and Yannakakis, Mihalis},
	month = apr,
	year = {1996},
	note = {Publisher: Society for Industrial and Applied Mathematics},
	pages = {235--251},
}


@inproceedings{lee_genus_2010,
  title      = {Genus and the geometry of the cut graph: [extended abstract]},
  isbn       = {978-0-89871-701-3 978-1-61197-307-5},
  shorttitle = {Genus and the geometry of the cut graph},
  url        = {https://epubs.siam.org/doi/10.1137/1.9781611973075.18},
  doi        = {10.1137/1.9781611973075.18},
  language   = {en},
  urldate    = {2025-05-07},
  booktitle  = {Proceedings of the {Twenty}-{First} {Annual} {ACM}-{SIAM} {Symposium} on {Discrete} {Algorithms}},
  publisher  = {Society for Industrial and Applied Mathematics},
  author     = {Lee, James R. and Sidiropoulos, Anastasios},
  month      = jan,
  year       = {2010},
  pages      = {193--201}
}
@misc{gupta2013sparsestcutboundedtreewidth,
  title         = {Sparsest Cut on Bounded Treewidth Graphs: Algorithms and Hardness Results},
  author        = {Anupam Gupta and Kunal Talwar and David Witmer},
  year          = {2013},
  eprint        = {1305.1347},
  archiveprefix = {arXiv},
  primaryclass  = {cs.DS},
  url           = {https://arxiv.org/abs/1305.1347}
}
@article{Chalermsook_2024,
  title     = {Approximating Sparsest Cut in Low-treewidth Graphs via Combinatorial Diameter},
  volume    = {20},
  issn      = {1549-6333},
  url       = {http://dx.doi.org/10.1145/3632623},
  doi       = {10.1145/3632623},
  number    = {1},
  journal   = {ACM Transactions on Algorithms},
  publisher = {Association for Computing Machinery (ACM)},
  author    = {Chalermsook, Parinya and Kaul, Matthias and Mnich, Matthias and Spoerhase, Joachim and Uniyal, Sumedha and Vaz, Daniel},
  year      = {2024},
  month     = jan,
  pages     = {1–20}
}
@article{juliaJACMapxhard,
  author     = {Chuzhoy, Julia and Khanna, Sanjeev},
  title      = {Polynomial flow-cut gaps and hardness of directed cut problems},
  year       = {2009},
  issue_date = {April 2009},
  publisher  = {Association for Computing Machinery},
  address    = {New York, NY, USA},
  volume     = {56},
  number     = {2},
  issn       = {0004-5411},
  url        = {https://doi.org/10.1145/1502793.1502795},
  doi        = {10.1145/1502793.1502795},
  journal    = {J. ACM},
  month      = apr,
  articleno  = {6},
  numpages   = {28},
  keywords   = {sparsest cut, hardness of approximation, Directed multicut}
}

@inproceedings{chawla_hardness_2005,
  title     = {On the hardness of approximating {MULTICUT} and {SPARSEST}-{CUT}},
  url       = {https://ieeexplore.ieee.org/document/1443081},
  doi       = {10.1109/CCC.2005.20},
  abstract  = {We show that the MULTICUT, SPARSEST-CUT, and MIN-2CNF/spl equiv/DELETION problems are NP-hard to approximate within every constant factor, assuming the unique games conjecture of Khot [STOC, 2002]. A quantitatively stronger version of the conjecture implies inapproximability factor of /spl Omega/(log log n).},
  urldate   = {2025-05-09},
  booktitle = {20th {Annual} {IEEE} {Conference} on {Computational} {Complexity} ({CCC}'05)},
  author    = {Chawla, S. and Krauthgamer, R. and Kumar, R. and Rabani, Y. and Sivakumar, D.},
  month     = jun,
  year      = {2005},
  note      = {ISSN: 1093-0159},
  keywords  = {Approximation algorithms, Computer science, Costs, Linear programming, Mathematics},
  pages     = {144--153}
}

@inproceedings{chlamtac_approximating_2010,
  address   = {Berlin, Heidelberg},
  title     = {Approximating {Sparsest} {Cut} in {Graphs} of {Bounded} {Treewidth}},
  isbn      = {978-3-642-15369-3},
  doi       = {10.1007/978-3-642-15369-3_10},
  language  = {en},
  booktitle = {Approximation, {Randomization}, and {Combinatorial} {Optimization}. {Algorithms} and {Techniques}},
  publisher = {Springer},
  author    = {Chlamtac, Eden and Krauthgamer, Robert and Raghavendra, Prasad},
  editor    = {Serna, Maria and Shaltiel, Ronen and Jansen, Klaus and Rolim, José},
  year      = {2010},
  keywords  = {General Demand, Linear Programming Relaxation, Linear Programming Solution, Tree Decomposition, Vertex Cover},
  pages     = {124--137}
}
@article{lognGapAumann98,
  author   = {Aumann, Yonatan and Rabani, Yuval},
  title    = {An {$O(\log k)$} Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm},
  journal  = {SIAM Journal on Computing},
  volume   = {27},
  number   = {1},
  pages    = {291-301},
  year     = {1998},
  doi      = {10.1137/S0097539794285983},
  url      = {https://doi.org/10.1137/S0097539794285983},
  eprint   = {https://doi.org/10.1137/S0097539794285983},
}
@article{Linial_London_Rabinovich_1995, title={The geometry of graphs and some of its algorithmic applications}, volume={15}, rights={http://www.springer.com/tdm}, ISSN={0209-9683, 1439-6912}, url={http://link.springer.com/10.1007/BF01200757}, DOI={10.1007/BF01200757}, number={2}, journal={Combinatorica}, author={Linial, Nathan and London, Eran and Rabinovich, Yuri}, year={1995}, month=jun, pages={215–245}, language={en} }

@article{Cohen-Addad_Mömke_Verdugo_2024, title={A 2-approximation for the bounded treewidth sparsest cut problem in $\textsf{FPT}$Time}, volume={206}, ISSN={1436-4646}, url={https://doi.org/10.1007/s10107-023-02044-1}, DOI={10.1007/s10107-023-02044-1}, number={1}, journal={Mathematical Programming}, author={Cohen-Addad, Vincent and Mömke, Tobias and Verdugo, Victor}, year={2024}, month=jul, pages={479–495}, language={en} }
@INPROCEEDINGS{uniformhardnessFocs07,
  author={Ambuhl, Christoph and Mastrolilli, Monaldo and Svensson, Ola},
  booktitle={48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)},
  title={Inapproximability Results for Sparsest Cut, Optimal Linear Arrangement, and Precedence Constrained Scheduling},
  year={2007},
  volume={},
  number={},
  pages={329-337},
  keywords={Cost function;Processor scheduling;Polynomials;NP-complete problem;Approximation algorithms;Single machine scheduling;Computer science},
  doi={10.1109/FOCS.2007.40}}

@article{bonsma_complexity_2012,
	title = {The complexity of finding uniform sparsest cuts in various graph classes},
	volume = {14},
	copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
	issn = {15708667},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S1570866711001110},
	doi = {10.1016/j.jda.2011.12.008},
	language = {en},
	urldate = {2025-05-10},
	journal = {Journal of Discrete Algorithms},
	author = {Bonsma, Paul and Broersma, Hajo and Patel, Viresh and Pyatkin, Artem},
	month = jul,
	year = {2012},
	pages = {136--149},
}

@inproceedings{rao_small_1999,
	address = {Miami Beach Florida USA},
	title = {Small distortion and volume preserving embeddings for planar and {Euclidean} metrics},
	isbn = {978-1-58113-068-3},
	url = {https://dl.acm.org/doi/10.1145/304893.304983},
	doi = {10.1145/304893.304983},
	language = {en},
	urldate = {2025-05-10},
	booktitle = {Proceedings of the fifteenth annual symposium on {Computational} geometry},
	publisher = {ACM},
	author = {Rao, Satish},
	month = jun,
	year = {1999},
	pages = {300--306},
}

@article{Ford_Fulkerson_1956, title={Maximal Flow Through a Network}, volume={8}, rights={https://www.cambridge.org/core/terms}, ISSN={0008-414X, 1496-4279}, url={https://www.cambridge.org/core/product/identifier/S0008414X00036890/type/journal_article}, DOI={10.4153/CJM-1956-045-5}, journal={Canadian Journal of Mathematics}, author={Ford, L. R. and Fulkerson, D. R.}, year={1956}, pages={399–404}, language={en} }

@article{Hu_1963, title={Multi-Commodity Network Flows}, volume={11}, ISSN={0030-364X, 1526-5463}, url={https://pubsonline.informs.org/doi/10.1287/opre.11.3.344}, DOI={10.1287/opre.11.3.344}, number={3}, journal={Operations Research}, author={Hu, T. C.}, year={1963}, month=jun, pages={344–360}, language={en} }

@article{schrijver_homotopic_1990,
	title = {Homotopic {Routing} {Methods}},
	language = {en},
	journal = {Paths, Flows, and VLSI-Layout},
	author = {Schrijver, Alexander},
	year = {1990},
	pages = {329 --371},
}
@inproceedings{aumann_rabani_1995,
author = {Aumann, Yonatan and Rabani, Yuval},
title = {Improved bounds for all optical routing},
year = {1995},
isbn = {0898713498},
publisher = {Society for Industrial and Applied Mathematics},
address = {USA},
booktitle = {Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms},
pages = {567–576},
numpages = {10},
location = {San Francisco, California, USA},
series = {SODA '95}
}

@article{arora_frechet_2007,
	title = {Fréchet {Embeddings} of {Negative} {Type} {Metrics}},
	volume = {38},
	issn = {1432-0444},
	url = {https://doi.org/10.1007/s00454-007-9007-0},
	doi = {10.1007/s00454-007-9007-0},
	language = {en},
	number = {4},
	urldate = {2025-05-19},
	journal = {Discrete \& Computational Geometry},
	author = {Arora, Sanjeev and Lee, James R. and Naor, Assaf},
	month = dec,
	year = {2007},
	keywords = {Convex and Discrete Geometry, Differential Geometry, Distortion, Euclidean, Functional Analysis, Geometry, Global Analysis and Analysis on Manifolds, Hyperbolic Geometry, L 1, Metric embeddings, Sparsest cut problem},
	pages = {726--739},
}

@inproceedings{arora_euclidean_2005,
	address = {New York, NY, USA},
	series = {{STOC} '05},
	title = {Euclidean distortion and the sparsest cut},
	isbn = {978-1-58113-960-0},
	url = {https://doi.org/10.1145/1060590.1060673},
	doi = {10.1145/1060590.1060673},
	urldate = {2025-05-19},
	booktitle = {Proceedings of the thirty-seventh annual {ACM} symposium on {Theory} of computing},
	publisher = {Association for Computing Machinery},
	author = {Arora, Sanjeev and Lee, James R. and Naor, Assaf},
	month = may,
	year = {2005},
	pages = {553--562},
}

@inproceedings{guruswami_approximating_2013,
	address = {USA},
	series = {{SODA} '13},
	title = {Approximating non-uniform sparsest cut via generalized spectra},
	isbn = {978-1-61197-251-1},
	urldate = {2025-05-18},
	booktitle = {Proceedings of the twenty-fourth annual {ACM}-{SIAM} symposium on {Discrete} algorithms},
	publisher = {Society for Industrial and Applied Mathematics},
	author = {Guruswami, Venkatesan and Sinop, Ali Kemal},
	month = jan,
	year = {2013},
	pages = {295--305},
}
@book{Williamson_Shmoys_2011, place={Cambridge}, title={The Design of Approximation Algorithms}, publisher={Cambridge University Press}, author={Williamson, David P. and Shmoys, David B.}, year={2011}}

@inproceedings{arora_towards_2013,
	address = {Berkeley, CA, USA},
	title = {Towards a {Better} {Approximation} for {Sparsest} {Cut}?},
	isbn = {978-0-7695-5135-7},
	url = {http://ieeexplore.ieee.org/document/6686163/},
	doi = {10.1109/FOCS.2013.37},
	language = {en},
	urldate = {2025-05-09},
	booktitle = {2013 {IEEE} 54th {Annual} {Symposium} on {Foundations} of {Computer} {Science}},
	publisher = {IEEE},
	author = {Arora, Sanjeev and Ge, Rong and Sinop, Ali Kemal},
	month = oct,
	year = {2013},
	pages = {270--279},
}