skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Editors contains: "Byrka, J"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; ; (, Springer)
    Vygen, J; Byrka, J (Ed.)
    One of the most famous conjectures in combinatorial optimization is the four-thirds conjecture, which states that the integrality gap of the subtour LP relaxation of the TSP is equal to $$\frac43$$. For 40 years, the best known upper bound was $1.5$$. Recently, Karlin, Klein, and Oveis Gharan \cite{KKO21b} showed that the max entropy algorithm for the TSP gives an improved bound of $$1.5 - 10^{-36}$. In this paper, we show that the approximation ratio of the max entropy algorithm is at least 1.375, even for graphic TSP. Thus the max entropy algorithm does not appear to be the algorithm that will ultimately resolve the four-thirds conjecture in the affirmative, should that be possible. 
    more » « less
    Accepted Manuscript Full Text Available