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

Creators/Authors contains: "Donald G. Saari"

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. (, arXiv:2204.13230 [math.CO])
    Problems with majority voting over pairs as represented by Arrow’s Theorem and those of finding the lengths of closed paths as captured by the Traveling Salesperson Problem (TSP) appear to have nothing in common. In fact, they are connected. As shown, pairwise voting and a version of the TSP share the same domain where each system can be simplified by restricting it to complementary regions to eliminate extraneous terms. Central for doing so is the Borda Count, where it is shown that its outcome most accurately reflects the voter preferences. 
    more » « less
    Accepted Manuscript Full Text Available
  2. (, arXiv:2204.11987v1 [math.CO])
    Without imposing restrictions on a weighted graph’s arc lengths, symmetry structures cannot be expected. But, they exist. To find them, the graphs are decomposed into a component that dictates all closed path properties (e.g., shortest and longest paths), and a superfluous component that can be removed. The simpler remaining graph exposes inherent symmetry structures that form the basis for all closed path properties. For certain asymmetric problems, the symmetry is that of three-cycles; for the general undirected setting it is a type of four-cycles; for general directed problems with asymmetric costs, it is a product of three and four cycles. Everything extends immediately to incomplete graphs. 
    more » « less
    Accepted Manuscript Full Text Available