Path algebra algorithm for finding longest increasing subsequence

TL;DR

This paper introduces a novel algorithm for the longest increasing subsequence problem utilizing max-plus algebra and matrix reformulation, offering a linear algebra-based approach rooted in idempotent mathematics.

Contribution

It presents a new algorithm based on max-plus algebra and matrix reformulation, advancing the application of idempotent mathematics to sequence analysis.

Findings

Algorithm effectively finds longest increasing subsequences

Utilizes max-plus algebra for problem reformulation

Demonstrates linear algebra approach in sequence analysis

Abstract

New algorithm for finding longest increasing subsequence is discussed. This algorithm is based on the ideas of idempotent mathematics and uses Max-Plus idempotent semiring. Problem of finding longest increasing sub- sequence is reformulated in a matrix form and solved with linear algebra.