Longest Straight Line Paths on Water or Land on the Earth

TL;DR

This paper introduces a branch-and-bound algorithm to determine the longest possible sailing and driving paths on Earth without hitting land or water, addressing complex coastal geometries and islands.

Contribution

It presents a novel computational methodology for solving the optimization problem of longest land and water routes on Earth using branch-and-bound techniques.

Findings

Successfully computed longest sailing and driving paths

Addresses complexity of coastlines and islands

Provides a systematic approach for similar geographic optimization problems

Abstract

There has been some interest recently in determining the longest distance one can sail for on the earth without hitting land, as well as in the converse problem of determining the longest distance one could drive for on the earth without encountering a major body of water. In its basic form, this is an optimisation problem, rendered chaotic by the presence of islands and lakes, and indeed the fractal nature of the coasts. In this paper we present a methodology for calculating the two paths using the branch-and-bound algorithm.