Deciding football sequences

TL;DR

This paper addresses the computational challenge of determining whether a sequence of nonnegative integers can represent the final scores of a football tournament, providing new algorithms with varying computational complexities.

Contribution

It introduces polynomial-time approximate and exponential-time exact algorithms for deciding if a score sequence is feasible in a football tournament.

Findings

Polynomial-time approximate algorithm developed

Exponential-time exact algorithm proposed

Problem complexity characterized

Abstract

An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential time exact algorithms which solve the problem.