Improved lower bounds on the randomized complexity of graph properties

Amit Chakrabarti, Subhash Khot

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings
Pages285-296
Number of pages12
Volume2076 LNCS
StatePublished - 2001
Event28th International Colloquium on Automata, Languages and Programming, ICALP 2001 - Crete, Greece
Duration: Jul 8 2001Jul 12 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2076 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other28th International Colloquium on Automata, Languages and Programming, ICALP 2001
CountryGreece
CityCrete
Period7/8/017/12/01

Fingerprint

Graph Packing
Lemma
Monotone
Lower bound
Graph in graph theory
Vertex of a graph
Decision tree
Bipartite Graph
Packing
Decision trees

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

Chakrabarti, A., & Khot, S. (2001). Improved lower bounds on the randomized complexity of graph properties. In 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.

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Chakrabarti, A & Khot, S 2001, Improved lower bounds on the randomized complexity of graph properties. in 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.
Chakrabarti A, Khot S. Improved lower bounds on the randomized complexity of graph properties. In Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings. Vol. 2076 LNCS. 2001. p. 285-296. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Chakrabarti, Amit ; Khot, Subhash. / Improved lower bounds on the randomized complexity of graph properties. Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings. Vol. 2076 LNCS 2001. pp. 285-296 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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