hardness

ref.bib

@@ -82,7 +82,6 @@
 	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,
@@ -98,5 +97,74 @@
 	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},
+}
+
+@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},
 }