Output-sensitive Complexity of Multiobjective Combinatorial Optimization

TL;DR

This paper investigates the computational complexity of multiobjective combinatorial optimization problems, focusing on output-sensitive algorithms that run efficiently relative to input and output sizes, and identifies problems with or without such algorithms.

Contribution

It introduces a framework for analyzing output-sensitive complexity in MOCO problems and provides examples of problems with or without efficient algorithms under certain assumptions.

Findings

Some MOCO problems admit output-sensitive algorithms.

Certain MOCO problems lack such algorithms under mild assumptions.

The framework helps classify MOCO problems based on their computational complexity.

Abstract

We study output-sensitive algorithms and complexity for multiobjective combinatorial optimization problems. In this computational complexity framework, an algorithm for a general enumeration problem is regarded efficient if it is output-sensitive, i.e., its running time is bounded by a polynomial in the input and the output size. We provide both practical examples of MOCO problems for which such an efficient algorithm exists as well as problems for which no efficient algorithm exists under mild complexity theoretic assumptions.