Apply Sorting Algorithms to FAST Problem

TL;DR

This paper explores novel sorting-based algorithms for the FAST problem, specifically the minimum feedback arc set in tournaments, analyzing their effectiveness and probabilistic properties.

Contribution

It introduces new algorithms inspired by sorting methods for the FAST problem and provides analytical results on their behavior.

Findings

Pseudo_InsertionSort reduces backward edges with a specific average formula.

Pseudo_MergeSort's probability of backward edges is characterized.

Additional algorithms for FAST problem are proposed and analyzed.

Abstract

FAST problem is finding minimum feedback arc set problem in tournaments. In this paper we present some algorithms that are similar to sorting algorithms for FAST problem and we analyze them. We present Pseudo_InsertionSort algorithm for FAST problem and we show that average number of all backward edges in output of that is equal to ((n^2-5n+8)/4)-2^(1-n). We introduce Pseudo_MergeSort algorithm and we find the probability of being backward for an edge. Finally we introduce other algorithms for this problem.