Improved lower bounds on the randomized complexity of graph properties

Amit Chakrabarti; Subhash Khot

doi:10.1007/3-540-48224-5_24

Improved lower bounds on the randomized complexity of graph properties

Amit Chakrabarti, Subhash Khot

Computer Science

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

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)
Title of host publication	Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings
Editors	Fernando Orejas, Paul G. Spirakis, Jan van Leeuwen
Publisher	Springer Verlag
Pages	285-296
Number of pages	12
ISBN (Print)	3540422870, 9783540422877
DOIs	https://doi.org/10.1007/3-540-48224-5_24
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)
Volume	2076 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	28th International Colloquium on Automata, Languages and Programming, ICALP 2001
Country/Territory	Greece
City	Crete
Period	7/8/01 → 7/12/01

Keywords

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

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-48224-5_24

Cite this

Chakrabarti, A., & Khot, S. (2001). Improved lower bounds on the randomized complexity of graph properties. In F. Orejas, P. G. Spirakis, & J. van Leeuwen (Eds.), Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings (pp. 285-296). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2076 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-48224-5_24

Improved lower bounds on the randomized complexity of graph properties. / Chakrabarti, Amit; Khot, Subhash.
Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings. ed. / Fernando Orejas; Paul G. Spirakis; Jan van Leeuwen. Springer Verlag, 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 proceeding › Conference contribution

Chakrabarti, A & Khot, S 2001, Improved lower bounds on the randomized complexity of graph properties. in F Orejas, PG Spirakis & J van Leeuwen (eds), Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2076 LNCS, Springer Verlag, pp. 285-296, 28th International Colloquium on Automata, Languages and Programming, ICALP 2001, Crete, Greece, 7/8/01. https://doi.org/10.1007/3-540-48224-5_24

Chakrabarti A, Khot S. Improved lower bounds on the randomized complexity of graph properties. In Orejas F, Spirakis PG, van Leeuwen J, editors, Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings. Springer Verlag. 2001. p. 285-296. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-48224-5_24

Chakrabarti, Amit ; Khot, Subhash. / Improved lower bounds on the randomized complexity of graph properties. Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings. editor / Fernando Orejas ; Paul G. Spirakis ; Jan van Leeuwen. Springer Verlag, 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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Improved lower bounds on the randomized complexity of graph properties

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Keywords

ASJC Scopus subject areas

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