sparsest-cut/ref.bib

@article{chalermsook_approximating_2024,
	title = {Approximating {Sparsest} {Cut} in {Low}-{Treewidth} {Graphs} via {Combinatorial} {Diameter}},
	volume = {20},
	issn = {1549-6325, 1549-6333},
	url = {http://arxiv.org/abs/2111.06299},
	doi = {10.1145/3632623},
	number = {1},
	urldate = {2025-05-07},
	journal = {ACM Transactions on Algorithms},
	author = {Chalermsook, Parinya and Kaul, Matthias and Mnich, Matthias and Spoerhase, Joachim and Uniyal, Sumedha and Vaz, Daniel},
	month = jan,
	year = {2024},
	note = {arXiv:2111.06299 [cs]},
	keywords = {Computer Science - Data Structures and Algorithms},
	pages = {1--20},
	annote = {Comment: 15 pages, 3 figures},
}
@misc{sparsest_cut_notes,
  author       = {Chekuri, Chandra},
  title        = {Introduction to Sparsest Cut},
  howpublished = {Lecture notes, UIUC CS 598CSC: Topics in Graph Algorithms},
  year         = {2024},
  note         = {Accessed on May 9, 2025},
  url          = {https://courses.grainger.illinois.edu/cs598csc/fa2024/Notes/lec-sparsest-cut.pdf}
}

@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}({\textbackslash}sqrt\{{\textbackslash}logn\})\$ {Approximation} to {SPARSEST} {CUT} in \${\textbackslash}tilde\{{O}\}(n{\textasciicircum}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{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},
}