### Abstract

We prove a lower bound of ω (n^{4/3} log^{1/3} n) on the randomized decision tree complexity of any nontrivial monotone n-vertex bipartite graph property, thereby improving the previous bound of ω(n ^{4/3}) due to Hajnal [H91]. Our proof works by improving a probabilistic argument in that paper, which also improves a graph packing lemma proved there. By a result of Gröger [G92] our complexity lower bound carries over from bipartite to general monotone n-vertex graph properties. Graph packing being a well-studied subject in its own right, our improved packing lemma and the probabilistic technique used to prove it, may be of independent interest.

Original language | English (US) |
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Title of host publication | Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings |

Pages | 285-296 |

Number of pages | 12 |

Volume | 2076 LNCS |

State | Published - 2001 |

Event | 28th International Colloquium on Automata, Languages and Programming, ICALP 2001 - Crete, Greece Duration: Jul 8 2001 → Jul 12 2001 |

### 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 | 2076 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 28th International Colloquium on Automata, Languages and Programming, ICALP 2001 |
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Country | Greece |

City | Crete |

Period | 7/8/01 → 7/12/01 |

### Fingerprint

### Keywords

- Decision tree complexity
- Gaph packing
- Mnotone graph properties
- Pobabilistic method
- Rn-domized complexity
- Rndomized algorithms

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings*(Vol. 2076 LNCS, pp. 285-296). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2076 LNCS).

**Improved lower bounds on the randomized complexity of graph properties.** / Chakrabarti, Amit; Khot, Subhash.

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

*Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings.*vol. 2076 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2076 LNCS, pp. 285-296, 28th International Colloquium on Automata, Languages and Programming, ICALP 2001, Crete, Greece, 7/8/01.

}

TY - GEN

T1 - Improved lower bounds on the randomized complexity of graph properties

AU - Chakrabarti, Amit

AU - Khot, Subhash

PY - 2001

Y1 - 2001

N2 - We prove a lower bound of ω (n4/3 log1/3 n) on the randomized decision tree complexity of any nontrivial monotone n-vertex bipartite graph property, thereby improving the previous bound of ω(n 4/3) due to Hajnal [H91]. Our proof works by improving a probabilistic argument in that paper, which also improves a graph packing lemma proved there. By a result of Gröger [G92] our complexity lower bound carries over from bipartite to general monotone n-vertex graph properties. Graph packing being a well-studied subject in its own right, our improved packing lemma and the probabilistic technique used to prove it, may be of independent interest.

AB - We prove a lower bound of ω (n4/3 log1/3 n) on the randomized decision tree complexity of any nontrivial monotone n-vertex bipartite graph property, thereby improving the previous bound of ω(n 4/3) due to Hajnal [H91]. Our proof works by improving a probabilistic argument in that paper, which also improves a graph packing lemma proved there. By a result of Gröger [G92] our complexity lower bound carries over from bipartite to general monotone n-vertex graph properties. Graph packing being a well-studied subject in its own right, our improved packing lemma and the probabilistic technique used to prove it, may be of independent interest.

KW - Decision tree complexity

KW - Gaph packing

KW - Mnotone graph properties

KW - Pobabilistic method

KW - Rn-domized complexity

KW - Rndomized algorithms

UR - http://www.scopus.com/inward/record.url?scp=42549083151&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42549083151&partnerID=8YFLogxK

M3 - Conference contribution

SN - 3540422870

SN - 9783540422877

VL - 2076 LNCS

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

SP - 285

EP - 296

BT - Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings

ER -