The Longest You Can Sail Without Hitting Land? An Algorithm Found It

Two geometry puzzles that circulated online—what’s the longest straight-line sea route that never touches land, and the longest overland route that never crosses major water—turn out to be genuine optimization problems. Rohan Chabukswar and Kushal Mukherjee formalized them and computed exact answers rather than eyeballing a globe. The difficulty comes from the terrain itself: islands, lakes, and the fractal, jagged nature of real coastlines make brute-force search over every possible great-circle path intractable.

Their solution applies the branch-and-bound algorithm, which recursively partitions the search space and discards whole regions once they provably can’t beat the best path found so far. That pruning is what makes an otherwise chaotic search feasible, letting them pin down the optimal sea and land paths without evaluating every candidate. The work is a clean example of a classic combinatorial-optimization technique applied to messy real-world geographic data.

The result is more a piece of recreational and computational mathematics than a practical tool, but it illustrates how a well-chosen search strategy tames a problem that looks hopeless at first glance. It’s the kind of rigorous answer to a viral ‘what if’ question that shows up periodically on Hacker News.