Algebraic fingerprints for faster algorithms

Ioannis Koutis, Ryan Williams

Research output: Contribution to journalReview articlepeer-review

20 Scopus citations

Abstract

It was a major surprise when, in 2010, Andreas Björklund discovered what many previously thought impossible: A significantly improved algorithm for the famous Hamiltonian path problem, also known as Hamiltonicity.4 Hamiltonicity asks if a given graph contains a path that goes through each vertex exactly once, as illustrated in Figure 1. Hamiltonicity was one of the first problems shown to be NP-complete by Karp.20 The only known algorithms for NP-complete problems require time scaling exponentially with the size of the input. It is believed they cannot be solved much faster in general, although the possibility has not been ruled out.17 Given an undirected graph on n vertices, Björklund's algorithm can find a Hamiltonian path or report that no such path exists in O∗(1.657n) time.a The algorithm still runs in exponential time but it is much faster than the O∗(2n) running time of the previously fastest algorithm, known since the 1960s.

Original languageEnglish (US)
Pages (from-to)98-105
Number of pages8
JournalCommunications of the ACM
Volume59
Issue number1
DOIs
StatePublished - Jan 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computer Science(all)

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