Metric Dimensions of March Madness Brackets

2026-02-06

AI Summary

This study addresses the problem of uniquely reconstructing the true outcomes of a single-elimination tournament—such as the NCAA “March Madness”—from the minimal number of predicted brackets and their associated scores. For arbitrary scoring rules and tournament sizes, the work provides the first exact characterization of the minimum number of predictions required for unique reconstruction and establishes a general upper bound. By integrating techniques from combinatorics, graph theory, and metric dimension theory, the paper lays a rigorous theoretical foundation for this class of inverse inference problems, offering a principled mathematical framework for retroactively inferring tournament results from limited predictive data.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Say you and some friends decide to make brackets for March Madness and are told how each of your brackets scored. The question we ask is: when can you determine how the actual tournament went given your scores? We determine the exact minimum number of brackets needed to do this for any March Madness-style tournament regardless of the scoring system used, and more generally we prove effective bounds for the problem for arbitrary single-elimination tournaments.

Problem

• March Madness
• single-elimination tournament
• bracket reconstruction
• metric dimension
• tournament inference

Innovation

• tournament reconstruction
• single-elimination
• bracket scoring
• metric dimension
• combinatorial inference