Space-Efficient FPT Algorithms

TL;DR

This paper introduces new space-efficient fixed-parameter tractable algorithms for various problems, expanding the understanding of parameterized complexity classes with practical algorithmic results.

Contribution

It provides the first algorithmic results for problems in the classes Para-L and FPT+XL, including Hitting Set, graph deletion, and Feedback Vertex Set.

Findings

Algorithms for Hitting Set and graph deletion in restricted-space classes.

Problems parameterized by vertex cover number are solvable in space-efficient fixed-parameter time.

Enhanced understanding of the algorithmic capabilities within Para-L and FPT+XL classes.

Abstract

We prove algorithmic results showing that a number of natural parameterized problems are in the restricted-space parameterized classes Para-L and FPT+XL. The first class comprises problems solvable in f(k) n^{O(1)} time using g(k) + O(log n)) bits of space (k is the parameter and n is the input size; f and g are computable functions). The second class comprises problems solvable under the same time bound, but using g(k) log n bits of space instead. Earlier work on these classes has focused largely on their structural aspects and their relationships with various other classes. We complement this with Para-L and FPT+XL algorithms for a restriction of Hitting Set, some graph deletion problems where the target class has an infinite forbidden set characterization, a number of problems parameterized by vertex cover number, and Feedback Vertex Set.