Let  be a path with n vertices, where each vertex v_i has a non-negative initial weight w(v_i) and is a fixed vertex. We investigate the maximization of w(x) through iterative averaging on subpaths. This paper proposes a novel approach that provides a simple proof of the strategy’s optimality.

graph algorithms.

Received: April 4, 2025; Revised: April 28, 2025; Accepted: May 15, 2025; Published: June 10, 2025

How to cite this article: Tianyi Tao, Water transport on a path: finding the strategy through its existence, Advances and Applications in Discrete Mathematics 42(5) (2025), 471-480. https://doi.org/10.17654/0974165825031