# Moment-based approximations of algorithms on semirings

## Document Type

Presentation Abstract

## Presentation Date

9-18-2017

## Abstract

Many problems can be computed more efficiently through divide-and-conquer approaches by exploiting inverse operations on a ring (e.g., fast matrix multiplication and fast convolution via Karatsuba or FFT); however, these same well-studied problems often have poor solutions on semirings, because the lack of an inverse operation renders many divide-and-conquer techniques impossible. For this reason, the fastest known algorithms for max-matrix multiplication (which can be used with an adjacency matrix to find the shortest/longest paths in a graph) and max-convolution (used to compute max-product marginals / MAP of random variables with sum relationships Y=X_1+X_2+\cdots) are substantially slower than the ring-based algorithms. A generic method is presented, which uses the moments of distributions containing the correct solution. This method allows ring-based, divide-and-conquer algorithms to approximate the solutions on the semiring (\times, max).

## Recommended Citation

Serang, Oliver, "Moment-based approximations of algorithms on semirings" (2017). *Colloquia of the Department of Mathematical Sciences*. 534.

https://scholarworks.umt.edu/mathcolloquia/534

## Additional Details

Monday, September 18, 2017 at 4:00 p.m. in Math 103

Refreshments at 3:30 p.m. in Math Lounge 109