Paradigms for Parameterized Enumeration

TL;DR

This paper explores the parameterized complexity of enumeration problems, defining notions of efficiency and demonstrating how paradigms like kernelization enable fixed-parameter tractable enumeration algorithms.

Contribution

It introduces formal notions of efficient enumeration in parameterized complexity and connects kernelization to fixed-parameter tractability for enumeration problems.

Findings

Kernelization characterizes fixed-parameter tractable enumeration problems

Algorithmic paradigms like self-reducibility are effective for parameterized enumeration

The paper formalizes notions of efficiency in parameterized enumeration

Abstract

The aim of the paper is to examine the computational complexity and algorithmics of enumeration, the task to output all solutions of a given problem, from the point of view of parameterized complexity. First we define formally different notions of efficient enumeration in the context of parameterized complexity. Second we show how different algorithmic paradigms can be used in order to get parameter-efficient enumeration algorithms in a number of examples. These paradigms use well-known principles from the design of parameterized decision as well as enumeration techniques, like for instance kernelization and self-reducibility. The concept of kernelization, in particular, leads to a characterization of fixed-parameter tractable enumeration problems.