A randomized algorithm for long directed cycle

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18 Scopus citations

Abstract

Given a directed graph G and a parameter k, the Long Directed Cycle (LDC) problem asks whether G contains a simple cycle on at least k vertices, while the k-Path problem asks whether G contains a simple path on exactly k vertices. Given a deterministic (randomized) algorithm for k-Path as a black box, which runs in time t(G,k), we prove that LDC can be solved in deterministic time O∗(max{t(G,2k),4k+o(k)}) or in randomized time O(maxi{t(G,2k),4k}). In particular, we get that LDC can be solved in randomized time O(4k).

Original languageEnglish
Pages (from-to)419-422
Number of pages4
JournalInformation Processing Letters
Volume116
Issue number6
DOIs
StatePublished - 1 Jun 2016
Externally publishedYes

Keywords

  • Algorithms
  • Long directed cycle
  • Parameterized complexity
  • k-Path

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

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