# Analyzing Branch-and-Bound Algorithms for the Multiprocessor Scheduling Problem

## TL;DR

This paper surveys various algorithms for the NP-Complete Multiprocessor Scheduling Problem and evaluates a specific Branch-and-Bound method, finding no improvement over existing bounds in their tests.

## Contribution

It provides a comprehensive survey of MSP algorithms and experimentally compares Fujita's Branch-and-Bound method with Fernandez bound.

## Key findings

- Fujita's method does not outperform Fernandez bound on tested data
- Survey covers polynomial, heuristic, and meta-heuristic algorithms for MSP
- Implementation and evaluation of Fujita's Branch-and-Bound algorithm

## Abstract

The Multiprocessor Scheduling Problem (MSP) is an NP-Complete problem with significant applications in computer and operations systems. We provide a survey of the wide array of polynomial-time approximation, heuristic, and meta-heuristic based algorithms that exist for solving MSP. We also implement Fujita's state-of-the-art Branch-and-Bound algorithm and evaluate the benefit of using Fujita's binary search bounding method instead of the Fernandez bound. We find that in fact Fujita's method does not offer any improvement over the Fernandez bound on our data set.