A randomized algorithm for long directed cycle

Meirav Zehavi

doi:10.1016/j.ipl.2016.02.005

A randomized algorithm for long directed cycle

Meirav Zehavi

Research output: Contribution to journal › Article › peer-review

21 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 language	English
Pages (from-to)	419-422
Number of pages	4
Journal	Information Processing Letters
Volume	116
Issue number	6
DOIs	https://doi.org/10.1016/j.ipl.2016.02.005
State	Published - 1 Jun 2016
Externally published	Yes

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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10.1016/j.ipl.2016.02.005

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title = "A randomized algorithm for long directed cycle",

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).",

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AB - 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).

KW - Algorithms

KW - Long directed cycle

KW - Parameterized complexity

KW - k-Path

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SP - 419

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JO - Information Processing Letters

JF - Information Processing Letters

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ER -

A randomized algorithm for long directed cycle

Abstract

Keywords

ASJC Scopus subject areas

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