### Abstract

We study several P-complete graph problems and show that they are in NC if the input graphs are restricted to be tree-structured. These graphs are also known as partial k-trees, decomposable graphs or graphs of bounded tree width, and include outerplanar graphs, series-parallel graphs and Halin graphs. The particular problems investigated herein include the lexicographically first (l.f.) depth-first search tree and the l.f. maximal independent set. It is also shown that if a tree of faces of an outerplanar graph is given, then its dfs tree can be found in O(log_{2}n) time using O(n/log_{2}n) processors.

Original language | English (US) |
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Title of host publication | Mathematical Foundations of Computer Science 1989, Proceedings |

Editors | Antoni Kreczmar, Grazyna Mirkowska |

Publisher | Springer Verlag |

Pages | 185-195 |

Number of pages | 11 |

ISBN (Print) | 9783540514862 |

DOIs | |

State | Published - Jan 1 1989 |

Externally published | Yes |

Event | 14th Symposium on Mathematical Foundations of Computer Science, MFCS 1989 - Porabka-Kozubnik, Poland Duration: Aug 28 1989 → Sep 1 1989 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 379 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 14th Symposium on Mathematical Foundations of Computer Science, MFCS 1989 |
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Country | Poland |

City | Porabka-Kozubnik |

Period | 8/28/89 → 9/1/89 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Mathematical Foundations of Computer Science 1989, Proceedings*(pp. 185-195). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 379 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-51486-4_66

**Parallel complexity of lexicographically first problems for tree-structured graphs.** / Chlebus, Bogdan; Diks, Krzysztof; Rytter, Wojciech; Szymacha, Tomasz.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Mathematical Foundations of Computer Science 1989, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 379 LNCS, Springer Verlag, pp. 185-195, 14th Symposium on Mathematical Foundations of Computer Science, MFCS 1989, Porabka-Kozubnik, Poland, 8/28/89. https://doi.org/10.1007/3-540-51486-4_66

}

TY - GEN

T1 - Parallel complexity of lexicographically first problems for tree-structured graphs

AU - Chlebus, Bogdan

AU - Diks, Krzysztof

AU - Rytter, Wojciech

AU - Szymacha, Tomasz

PY - 1989/1/1

Y1 - 1989/1/1

N2 - We study several P-complete graph problems and show that they are in NC if the input graphs are restricted to be tree-structured. These graphs are also known as partial k-trees, decomposable graphs or graphs of bounded tree width, and include outerplanar graphs, series-parallel graphs and Halin graphs. The particular problems investigated herein include the lexicographically first (l.f.) depth-first search tree and the l.f. maximal independent set. It is also shown that if a tree of faces of an outerplanar graph is given, then its dfs tree can be found in O(log2n) time using O(n/log2n) processors.

AB - We study several P-complete graph problems and show that they are in NC if the input graphs are restricted to be tree-structured. These graphs are also known as partial k-trees, decomposable graphs or graphs of bounded tree width, and include outerplanar graphs, series-parallel graphs and Halin graphs. The particular problems investigated herein include the lexicographically first (l.f.) depth-first search tree and the l.f. maximal independent set. It is also shown that if a tree of faces of an outerplanar graph is given, then its dfs tree can be found in O(log2n) time using O(n/log2n) processors.

UR - http://www.scopus.com/inward/record.url?scp=0041480792&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041480792&partnerID=8YFLogxK

U2 - 10.1007/3-540-51486-4_66

DO - 10.1007/3-540-51486-4_66

M3 - Conference contribution

AN - SCOPUS:0041480792

SN - 9783540514862

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 185

EP - 195

BT - Mathematical Foundations of Computer Science 1989, Proceedings

A2 - Kreczmar, Antoni

A2 - Mirkowska, Grazyna

PB - Springer Verlag

ER -