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 (US) |
|---|---|
| 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 | |
| State | Published - Jan 1 2002 |
| Event | 6th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2002 - Cambridge, United States Duration: Sep 13 2002 → Sep 15 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 |
Other
| Other | 6th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2002 |
|---|---|
| Country | United States |
| City | Cambridge |
| Period | 9/13/02 → 9/15/02 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)
Cite this
}
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
TY - GEN
T1 - Computing graph properties by randomized subcube partitions
AU - Friedgut, Ehud
AU - Kahn, Jeff
AU - Wigderson, Avi
PY - 2002/1/1
Y1 - 2002/1/1
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
UR - http://www.scopus.com/inward/citedby.url?scp=84883427213&partnerID=8YFLogxK
U2 - 10.1007/3-540-45726-7_9
DO - 10.1007/3-540-45726-7_9
M3 - Conference contribution
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
ER -