Computing graph properties by randomized subcube partitions

Ehud Friedgut; Jeff Kahn; Avi Wigderson

doi:10.1007/3-540-45726-7_9

Computing graph properties by randomized subcube partitions

Ehud Friedgut, Jeff Kahn, Avi Wigderson

The Rachel and Selim Benin School of Engineering and Computer Science

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

12 Scopus citations

Abstract

We prove a new lower bound on the randomized decision tree complexity of monotone graph properties. For a monotone property A of graphs on n vertices, let p = p(A) denote the threshold probability of A, namely the value of p for which a randomgraph from G(n, p) has property A with probability 1/2. Then the expected number of queries made by any decision tree for A on such a randomgraph is at least Ω(n²/ max{pn, log n}). Our lower bound holds in the subcube partition model, which generalizes the decision tree model. The proof combines a simple combinatorial lemma on subcube partitions (which may be of independent interest) with simple graph packing arguments. Our approach motivates the study of packing of "typical" graphs, which may yield better lower bounds.

Original language	English
Title of host publication	Randomization and Approximation Techniques in Computer Science - 6th International Workshop, RANDOM 2002, Proceedings
Editors	Salil Vadhan, Jose D. P. Rolim
Publisher	Springer Verlag
Pages	105-113
Number of pages	9
ISBN (Print)	3540441476, 9783540457268
DOIs	https://doi.org/10.1007/3-540-45726-7_9
State	Published - 2002
Event	6th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2002 - Cambridge, United States Duration: 13 Sep 2002 → 15 Sep 2002

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2483
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	6th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2002
Country/Territory	United States
City	Cambridge
Period	13/09/02 → 15/09/02

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

Access to Document

10.1007/3-540-45726-7_9

Cite this

Friedgut, E., Kahn, J., & Wigderson, A. (2002). Computing graph properties by randomized subcube partitions. In S. Vadhan, & J. D. P. Rolim (Eds.), Randomization and Approximation Techniques in Computer Science - 6th International Workshop, RANDOM 2002, Proceedings (pp. 105-113). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2483). Springer Verlag. https://doi.org/10.1007/3-540-45726-7_9

Friedgut, Ehud ; Kahn, Jeff ; Wigderson, Avi. / Computing graph properties by randomized subcube partitions. Randomization and Approximation Techniques in Computer Science - 6th International Workshop, RANDOM 2002, Proceedings. editor / Salil Vadhan ; Jose D. P. Rolim. Springer Verlag, 2002. pp. 105-113 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{d7a3cafb033047d98448bf4ea792344c,

title = "Computing graph properties by randomized subcube partitions",

abstract = "We prove a new lower bound on the randomized decision tree complexity of monotone graph properties. For a monotone property A of graphs on n vertices, let p = p(A) denote the threshold probability of A, namely the value of p for which a randomgraph from G(n, p) has property A with probability 1/2. Then the expected number of queries made by any decision tree for A on such a randomgraph is at least Ω(n2/ max{pn, log n}). Our lower bound holds in the subcube partition model, which generalizes the decision tree model. The proof combines a simple combinatorial lemma on subcube partitions (which may be of independent interest) with simple graph packing arguments. Our approach motivates the study of packing of {"}typical{"} graphs, which may yield better lower bounds.",

author = "Ehud Friedgut and Jeff Kahn and Avi Wigderson",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2002.; 6th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2002 ; Conference date: 13-09-2002 Through 15-09-2002",

year = "2002",

doi = "10.1007/3-540-45726-7_9",

language = "אנגלית",

isbn = "3540441476",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "105--113",

editor = "Salil Vadhan and Rolim, {Jose D. P.}",

booktitle = "Randomization and Approximation Techniques in Computer Science - 6th International Workshop, RANDOM 2002, Proceedings",

address = "גרמניה",

}

Friedgut, E, Kahn, J & Wigderson, A 2002, Computing graph properties by randomized subcube partitions. in S Vadhan & JDP Rolim (eds), Randomization and Approximation Techniques in Computer Science - 6th International Workshop, RANDOM 2002, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2483, Springer Verlag, pp. 105-113, 6th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2002, Cambridge, United States, 13/09/02. https://doi.org/10.1007/3-540-45726-7_9

Computing graph properties by randomized subcube partitions. / Friedgut, Ehud; Kahn, Jeff; Wigderson, Avi.
Randomization and Approximation Techniques in Computer Science - 6th International Workshop, RANDOM 2002, Proceedings. ed. / Salil Vadhan; Jose D. P. Rolim. Springer Verlag, 2002. p. 105-113 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2483).

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

TY - GEN

T1 - Computing graph properties by randomized subcube partitions

AU - Friedgut, Ehud

AU - Kahn, Jeff

AU - Wigderson, Avi

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2002.

PY - 2002

Y1 - 2002

N2 - We prove a new lower bound on the randomized decision tree complexity of monotone graph properties. For a monotone property A of graphs on n vertices, let p = p(A) denote the threshold probability of A, namely the value of p for which a randomgraph from G(n, p) has property A with probability 1/2. Then the expected number of queries made by any decision tree for A on such a randomgraph is at least Ω(n2/ max{pn, log n}). Our lower bound holds in the subcube partition model, which generalizes the decision tree model. The proof combines a simple combinatorial lemma on subcube partitions (which may be of independent interest) with simple graph packing arguments. Our approach motivates the study of packing of "typical" graphs, which may yield better lower bounds.

AB - We prove a new lower bound on the randomized decision tree complexity of monotone graph properties. For a monotone property A of graphs on n vertices, let p = p(A) denote the threshold probability of A, namely the value of p for which a randomgraph from G(n, p) has property A with probability 1/2. Then the expected number of queries made by any decision tree for A on such a randomgraph is at least Ω(n2/ max{pn, log n}). Our lower bound holds in the subcube partition model, which generalizes the decision tree model. The proof combines a simple combinatorial lemma on subcube partitions (which may be of independent interest) with simple graph packing arguments. Our approach motivates the study of packing of "typical" graphs, which may yield better lower bounds.

UR - http://www.scopus.com/inward/record.url?scp=84883427213&partnerID=8YFLogxK

U2 - 10.1007/3-540-45726-7_9

DO - 10.1007/3-540-45726-7_9

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84883427213

SN - 3540441476

SN - 9783540457268

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

SP - 105

EP - 113

BT - Randomization and Approximation Techniques in Computer Science - 6th International Workshop, RANDOM 2002, Proceedings

A2 - Vadhan, Salil

A2 - Rolim, Jose D. P.

PB - Springer Verlag

T2 - 6th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2002

Y2 - 13 September 2002 through 15 September 2002

ER -

Friedgut E, Kahn J, Wigderson A. Computing graph properties by randomized subcube partitions. In Vadhan S, Rolim JDP, editors, Randomization and Approximation Techniques in Computer Science - 6th International Workshop, RANDOM 2002, Proceedings. Springer Verlag. 2002. p. 105-113. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45726-7_9

Computing graph properties by randomized subcube partitions

Abstract

Publication series

Conference

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this