Parametric shortest-path algorithms via tropical geometry

TL;DR

This paper explores parameterized shortest-path algorithms using tropical geometry, with applications to traffic networks where link travel times vary, offering new insights into dynamic routing problems.

Contribution

Introduces a tropical geometry framework for parameterized shortest-path algorithms, extending classical methods to handle variable network conditions.

Findings

Develops a tropical geometric approach to parameterized shortest paths

Demonstrates applicability to traffic networks with variable travel times

Provides theoretical foundations for dynamic routing algorithms

Abstract

We study parameterized versions of classical algorithms for computing shortest-path trees. This is most easily expressed in terms of tropical geometry. Applications include shortest paths in traffic networks with variable link travel times.