246 lines
11 KiB
BibTeX
246 lines
11 KiB
BibTeX
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@article{hoory_expander_2006,
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title = {Expander graphs and their applications},
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volume = {43},
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issn = {0273-0979},
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url = {http://www.ams.org/journal-getitem?pii=S0273-0979-06-01126-8},
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doi = {10.1090/S0273-0979-06-01126-8},
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language = {en},
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number = {04},
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urldate = {2025-05-09},
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journal = {Bulletin of the American Mathematical Society},
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author = {Hoory, Shlomo and Linial, Nathan and Wigderson, Avi},
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month = aug,
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year = {2006},
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pages = {439--562}
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}
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@article{arora_osqrtlogn_2010,
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title = { {$O(\sqrt{\log n})$} {Approximation} to {SPARSEST} {CUT} in {$\tilde{O}(n^2)$} {Time}},
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volume = {39},
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issn = {0097-5397, 1095-7111},
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url = {http://epubs.siam.org/doi/10.1137/080731049},
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doi = {10.1137/080731049},
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language = {en},
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number = {5},
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urldate = {2025-05-09},
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journal = {SIAM Journal on Computing},
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author = {Arora, Sanjeev and Hazan, Elad and Kale, Satyen},
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month = jan,
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year = {2010},
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pages = {1748--1771}
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}
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@misc{dorsi2024sparsestcuteigenvaluemultiplicities,
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title = {Sparsest cut and eigenvalue multiplicities on low degree Abelian Cayley graphs},
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author = {Tommaso d'Orsi and Chris Jones and Jake Ruotolo and Salil Vadhan and Jiyu Zhang},
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year = {2024},
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eprint = {2412.17115},
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archiveprefix = {arXiv},
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primaryclass = {cs.DS},
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url = {https://arxiv.org/abs/2412.17115}
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}
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@inproceedings{arora_expander_2004,
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address = {New York, NY, USA},
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series = {{STOC} '04},
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title = {Expander flows, geometric embeddings and graph partitioning},
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isbn = {978-1-58113-852-8},
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url = {https://doi.org/10.1145/1007352.1007355},
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doi = {10.1145/1007352.1007355},
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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.},
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urldate = {2025-05-09},
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booktitle = {Proceedings of the thirty-sixth annual {ACM} symposium on {Theory} of computing},
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publisher = {Association for Computing Machinery},
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author = {Arora, Sanjeev and Rao, Satish and Vazirani, Umesh},
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month = jun,
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year = {2004},
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pages = {222--231}
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}
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@article{leighton_multicommodity_1999,
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title = {Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms},
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volume = {46},
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issn = {0004-5411},
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url = {https://dl.acm.org/doi/10.1145/331524.331526},
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doi = {10.1145/331524.331526},
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number = {6},
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urldate = {2025-05-09},
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journal = {J. ACM},
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author = {Leighton, Tom and Rao, Satish},
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month = nov,
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year = {1999},
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pages = {787--832}
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}
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@inproceedings{lee_genus_2010,
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title = {Genus and the geometry of the cut graph: [extended abstract]},
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isbn = {978-0-89871-701-3 978-1-61197-307-5},
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shorttitle = {Genus and the geometry of the cut graph},
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url = {https://epubs.siam.org/doi/10.1137/1.9781611973075.18},
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doi = {10.1137/1.9781611973075.18},
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language = {en},
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urldate = {2025-05-07},
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booktitle = {Proceedings of the {Twenty}-{First} {Annual} {ACM}-{SIAM} {Symposium} on {Discrete} {Algorithms}},
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publisher = {Society for Industrial and Applied Mathematics},
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author = {Lee, James R. and Sidiropoulos, Anastasios},
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month = jan,
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year = {2010},
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pages = {193--201}
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}
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@misc{gupta2013sparsestcutboundedtreewidth,
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title = {Sparsest Cut on Bounded Treewidth Graphs: Algorithms and Hardness Results},
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author = {Anupam Gupta and Kunal Talwar and David Witmer},
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year = {2013},
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eprint = {1305.1347},
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archiveprefix = {arXiv},
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primaryclass = {cs.DS},
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url = {https://arxiv.org/abs/1305.1347}
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}
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@article{Chalermsook_2024,
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title = {Approximating Sparsest Cut in Low-treewidth Graphs via Combinatorial Diameter},
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volume = {20},
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issn = {1549-6333},
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url = {http://dx.doi.org/10.1145/3632623},
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doi = {10.1145/3632623},
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number = {1},
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journal = {ACM Transactions on Algorithms},
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publisher = {Association for Computing Machinery (ACM)},
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author = {Chalermsook, Parinya and Kaul, Matthias and Mnich, Matthias and Spoerhase, Joachim and Uniyal, Sumedha and Vaz, Daniel},
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year = {2024},
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month = jan,
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pages = {1–20}
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}
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@article{juliaJACMapxhard,
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author = {Chuzhoy, Julia and Khanna, Sanjeev},
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title = {Polynomial flow-cut gaps and hardness of directed cut problems},
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year = {2009},
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issue_date = {April 2009},
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publisher = {Association for Computing Machinery},
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address = {New York, NY, USA},
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volume = {56},
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number = {2},
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issn = {0004-5411},
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url = {https://doi.org/10.1145/1502793.1502795},
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doi = {10.1145/1502793.1502795},
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journal = {J. ACM},
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month = apr,
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articleno = {6},
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numpages = {28},
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keywords = {sparsest cut, hardness of approximation, Directed multicut}
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}
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@inproceedings{chawla_hardness_2005,
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title = {On the hardness of approximating {MULTICUT} and {SPARSEST}-{CUT}},
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url = {https://ieeexplore.ieee.org/document/1443081},
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doi = {10.1109/CCC.2005.20},
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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).},
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urldate = {2025-05-09},
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booktitle = {20th {Annual} {IEEE} {Conference} on {Computational} {Complexity} ({CCC}'05)},
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author = {Chawla, S. and Krauthgamer, R. and Kumar, R. and Rabani, Y. and Sivakumar, D.},
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month = jun,
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year = {2005},
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note = {ISSN: 1093-0159},
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keywords = {Approximation algorithms, Computer science, Costs, Linear programming, Mathematics},
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pages = {144--153}
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}
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@inproceedings{chlamtac_approximating_2010,
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address = {Berlin, Heidelberg},
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title = {Approximating {Sparsest} {Cut} in {Graphs} of {Bounded} {Treewidth}},
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isbn = {978-3-642-15369-3},
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doi = {10.1007/978-3-642-15369-3_10},
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language = {en},
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booktitle = {Approximation, {Randomization}, and {Combinatorial} {Optimization}. {Algorithms} and {Techniques}},
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publisher = {Springer},
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author = {Chlamtac, Eden and Krauthgamer, Robert and Raghavendra, Prasad},
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editor = {Serna, Maria and Shaltiel, Ronen and Jansen, Klaus and Rolim, José},
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year = {2010},
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keywords = {General Demand, Linear Programming Relaxation, Linear Programming Solution, Tree Decomposition, Vertex Cover},
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pages = {124--137}
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}
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@article{lognGapAumann98,
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author = {Aumann, Yonatan and Rabani, Yuval},
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title = {An {$O(\log k)$} Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm},
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journal = {SIAM Journal on Computing},
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volume = {27},
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number = {1},
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pages = {291-301},
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year = {1998},
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doi = {10.1137/S0097539794285983},
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url = {https://doi.org/10.1137/S0097539794285983},
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eprint = {https://doi.org/10.1137/S0097539794285983},
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}
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@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} }
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@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} }
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@INPROCEEDINGS{uniformhardnessFocs07,
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author={Ambuhl, Christoph and Mastrolilli, Monaldo and Svensson, Ola},
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booktitle={48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)},
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title={Inapproximability Results for Sparsest Cut, Optimal Linear Arrangement, and Precedence Constrained Scheduling},
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year={2007},
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volume={},
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number={},
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pages={329-337},
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keywords={Cost function;Processor scheduling;Polynomials;NP-complete problem;Approximation algorithms;Single machine scheduling;Computer science},
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doi={10.1109/FOCS.2007.40}}
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@article{bonsma_complexity_2012,
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title = {The complexity of finding uniform sparsest cuts in various graph classes},
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volume = {14},
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copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
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issn = {15708667},
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url = {https://linkinghub.elsevier.com/retrieve/pii/S1570866711001110},
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doi = {10.1016/j.jda.2011.12.008},
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language = {en},
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urldate = {2025-05-10},
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journal = {Journal of Discrete Algorithms},
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author = {Bonsma, Paul and Broersma, Hajo and Patel, Viresh and Pyatkin, Artem},
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month = jul,
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year = {2012},
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pages = {136--149},
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}
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@inproceedings{rao_small_1999,
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address = {Miami Beach Florida USA},
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title = {Small distortion and volume preserving embeddings for planar and {Euclidean} metrics},
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isbn = {978-1-58113-068-3},
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url = {https://dl.acm.org/doi/10.1145/304893.304983},
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doi = {10.1145/304893.304983},
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language = {en},
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urldate = {2025-05-10},
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booktitle = {Proceedings of the fifteenth annual symposium on {Computational} geometry},
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publisher = {ACM},
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author = {Rao, Satish},
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month = jun,
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year = {1999},
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pages = {300--306},
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}
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@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} }
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@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} }
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@article{schrijver_homotopic_1990,
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title = {Homotopic {Routing} {Methods}},
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language = {en},
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journal = {Paths, Flows, and VLSI-Layout},
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author = {Schrijver, Alexander},
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year = {1990},
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pages = {329 --371},
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}
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@inproceedings{aumann_rabani_1995,
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author = {Aumann, Yonatan and Rabani, Yuval},
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title = {Improved bounds for all optical routing},
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year = {1995},
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isbn = {0898713498},
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publisher = {Society for Industrial and Applied Mathematics},
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address = {USA},
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booktitle = {Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms},
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pages = {567–576},
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numpages = {10},
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location = {San Francisco, California, USA},
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series = {SODA '95}
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}
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