Algebraic fingerprints for faster algorithms

There has recently been impressive progress –after nearly fifty years of stagnation– in algorithms that find exact solutions for certain hard computational problems, including the famous Hamiltonian path problem. This progress has been due to a few core ideas that have found several applications. A unifying theme is algebra: we ‘transform’ the given problem into a more general algebraic format, then solve the corresponding algebraic problem that arises. This article walks the reader through some of these exciting developments and the underlying ideas. It also puts them in context with the discovery process that led to them, highlighting the role of parameterization as a way of dealing with intractability.

• Type: Journal
• Year: 2016
• Where: CACM
• Authors: Ioannis Koutis, Ryan Williams
• Keywords: CACM 2016