Space Efficient Algorithms for Parameterised Problems

TL;DR

This paper introduces space-efficient fixed-parameter tractable algorithms for graph problems, enabling large-scale data processing with limited memory by reducing space complexity while maintaining fixed-parameter tractable time.

Contribution

It presents novel algorithms for k-Path, MaxLeaf SubTree, and Multicut in Trees that operate in polylogarithmic space, addressing memory constraints in big-data scenarios.

Findings

Algorithms run in f(k)*poly(n) time with g(k)*polylog(n) space.

Applicable to large graph instances with limited memory.

Provides new methods for space-efficient fixed-parameter algorithms.

Abstract

We study "space efficient" FPT algorithms for graph problems with limited memory. Let n be the size of the input graph and k be the parameter. We present algorithms that run in time f(k)*poly(n) and use g(k)*polylog(n) working space, where f and g are functions of k alone, for k-Path, MaxLeaf SubTree and Multicut in Trees. These algorithms are motivated by big-data settings where very large problem instances must be solved, and using poly(n) memory is prohibitively expensive. They are also theoretically interesting, since most of the standard methods tools, such as deleting a large set of vertices or edges, are unavailable, and we must a develop different way to tackle them.