A Computational Proof of the Highest-Scoring Boggle Board

TL;DR

This paper uses advanced algorithms to exhaustively identify the highest-scoring Boggle boards, confirming that previous local optimization methods had already found the global optimum.

Contribution

It introduces a novel application of Branch and Bound and decision diagrams to perform the first exhaustive search for the optimal Boggle board.

Findings

The highest-scoring boards are globally optimal.

Hillclimbing finds the optimal boards.

First exhaustive search for Boggle board optimization.

Abstract

Finding all the words on a Boggle board is a classic computer programming problem. With a fast Boggle solver, local optimization techniques such as hillclimbing and simulated annealing can be used to find particularly high-scoring boards. The sheer number of possible Boggle boards has historically prevented an exhaustive search for the global optimum board. We apply Branch and Bound and a decision diagram-like data structure to perform the first such search. We find that the highest-scoring boards found via hillclimbing are, in fact, the global optima.