2025-05-09 17:20:03 +08:00

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BibTeX

@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},
file = {Submitted Version:/Users/congyu/Zotero/storage/GALRKD2A/Arora et al. - 2004 - Expander flows, geometric embeddings and graph partitioning.pdf:application/pdf},
}
@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},
file = {Full Text PDF:/Users/congyu/Zotero/storage/EVDSDZAH/Leighton and Rao - 1999 - Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms.pdf:application/pdf},
}