Skip to main content
This website is in trial operation, support us!
We gratefully acknowledge support from all contributors.
Contribute Donate

Computer Science > Computational Complexity

arXiv:2311.00882v2 (cs)
[Submitted on 1 Nov 2023 (v1) , revised 17 Nov 2023 (this version, v2) , latest version 16 Sep 2024 (v3) ]

Title: Semidefinite programming and linear equations vs. homomorphism problems

Title: 半定规划和线性方程与同态问题

Authors:Lorenzo Ciardo, Stanislav Živný
Abstract: We introduce a relaxation for homomorphism problems that combines semidefinite programming with linear Diophantine equations, and propose a framework for the analysis of its power based on the spectral theory of association schemes. We use this framework to establish an unconditional lower bound against the semidefinite programming + linear equations model, by showing that the relaxation does not solve the approximate graph homomorphism problem and thus, in particular, the approximate graph colouring problem.
Subjects: Computational Complexity (cs.CC) ; Discrete Mathematics (cs.DM); Data Structures and Algorithms (cs.DS); Optimization and Control (math.OC)
Cite as: arXiv:2311.00882 [cs.CC]
  (or arXiv:2311.00882v2 [cs.CC] for this version)
  https://doi.org/10.48550/arXiv.2311.00882

Submission history

From: Stanislav Živný [view email]
[v1] Wed, 1 Nov 2023 22:15:19 UTC (70 KB)
[v2] Fri, 17 Nov 2023 05:02:40 UTC (70 KB)
[v3] Mon, 16 Sep 2024 19:55:38 UTC (68 KB)
Full-text links:

Access Paper:

license icon view license
Current browse context:
cs.CC
< prev   |   next >
new | recent | 2023-11
Change to browse by:
cs
cs.DM
cs.DS
math
math.OC

References & Citations

1 blog link

(what is this?)
export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
IArxiv Recommender (What is IArxiv?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)