# The complexity of approximating averages on bounded-degree graphs

@article{Galanis2020TheCO, title={The complexity of approximating averages on bounded-degree graphs}, author={Andreas Galanis and Daniel Stefankovic and Eric Vigoda}, journal={ArXiv}, year={2020}, volume={abs/2004.09238} }

We prove that, unless P=NP, there is no polynomial-time algorithm to approximate within some multiplicative constant the average size of an independent set in graphs of maximum degree 6. This is a special case of a more general result for the hard-core model defined on independent sets weighted by a parameter $\lambda>0$. In the general setting, we prove that, unless P=NP, for all $\Delta\geq 3$, all $\lambda>\lambda_c(\Delta)$, there is no FPTAS which applies to all graphs of maximum degree… CONTINUE READING

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 20 REFERENCES

On a conjecture of Sokal concerning roots of the independence polynomial

- Mathematics, Computer Science
- 2017

38

Inapproximability of the Partition Function for the Antiferromagnetic Ising and Hard-Core Models

- Computer Science, Physics
- 2016

73

Spectral Independence in High-Dimensional Expanders and Applications to the Hardcore Model

- Mathematics, Computer Science
- 2020

9

Approximation Algorithms for Two-State Anti-Ferromagnetic Spin Systems on Bounded Degree Graphs

- Computer Science, Mathematics
- 2012

106

Inapproximability of the independent set polynomial in the complex plane

- Mathematics, Computer Science
- 2018

13