License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2023.38
URN: urn:nbn:de:0030-drops-175411
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Chuzhoy, Julia ; Dalirrooyfard, Mina ; Grinberg, Vadim ; Tan, Zihan

A New Conjecture on Hardness of 2-CSP’s with Implications to Hardness of Densest k-Subgraph and Other Problems

LIPIcs-ITCS-2023-38.pdf (0.7 MB)


We propose a new conjecture on hardness of 2-CSP’s, and show that new hardness of approximation results for Densest k-Subgraph and several other problems, including a graph partitioning problem, and a variation of the Graph Crossing Number problem, follow from this conjecture. The conjecture can be viewed as occupying a middle ground between the d-to-1 conjecture, and hardness results for 2-CSP’s that can be obtained via standard techniques, such as Parallel Repetition combined with standard 2-prover protocols for the 3SAT problem. We hope that this work will motivate further exploration of hardness of 2-CSP’s in the regimes arising from the conjecture. We believe that a positive resolution of the conjecture will provide a good starting point for other hardness of approximation proofs.
Another contribution of our work is proving that the problems that we consider are roughly equivalent from the approximation perspective. Some of these problems arose in previous work, from which it appeared that they may be related to each other. We formalize this relationship in this work.

BibTeX - Entry

  author =	{Chuzhoy, Julia and Dalirrooyfard, Mina and Grinberg, Vadim and Tan, Zihan},
  title =	{{A New Conjecture on Hardness of 2-CSP’s with Implications to Hardness of Densest k-Subgraph and Other Problems}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{38:1--38:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-175411},
  doi =		{10.4230/LIPIcs.ITCS.2023.38},
  annote =	{Keywords: Hardness of Approximation, Densest k-Subgraph}

Keywords: Hardness of Approximation, Densest k-Subgraph
Collection: 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Issue Date: 2023
Date of publication: 01.02.2023

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