The hardness of the Expected Decision Depth problem

Dana Ron; Amir Rosenfeld; Salil Vadhan

doi:10.1016/j.ipl.2006.08.012

The hardness of the Expected Decision Depth problem

Dana Ron^*, Amir Rosenfeld, Salil Vadhan

^*Corresponding author for this work

School of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

Given a function f over n binary variables, and an ordering of the n variables, we consider the Expected Decision Depth problem. Namely, what is the expected number of bits that need to be observed until the value of the function is determined, when bits of the input are observed according to the given order. Our main finding is that this problem is (essentially) #P-complete. Moreover, the hardness holds even when the function f is represented as a decision tree.

Original language	English
Pages (from-to)	112-118
Number of pages	7
Journal	Information Processing Letters
Volume	101
Issue number	3
DOIs	https://doi.org/10.1016/j.ipl.2006.08.012
State	Published - 14 Feb 2007

Keywords

Computational complexity
Decision trees

Access to Document

10.1016/j.ipl.2006.08.012

Cite this

@article{e4f57b8119c1435684705a3f37e5808c,

title = "The hardness of the Expected Decision Depth problem",

abstract = "Given a function f over n binary variables, and an ordering of the n variables, we consider the Expected Decision Depth problem. Namely, what is the expected number of bits that need to be observed until the value of the function is determined, when bits of the input are observed according to the given order. Our main finding is that this problem is (essentially) #P-complete. Moreover, the hardness holds even when the function f is represented as a decision tree.",

keywords = "Computational complexity, Decision trees",

author = "Dana Ron and Amir Rosenfeld and Salil Vadhan",

note = "Funding Information: * Corresponding author. E-mail addresses: danar@eng.tau.ac.il (D. Ron), amirrosenfeld@yahoo.com (A. Rosenfeld), salil@eecs.harvard.edu (S. Vadhan). 1 Work partially done while a fellow at the Radcliffe Institute for Advanced Study, Harvard University. Also supported by the Israel Science Foundation. 2 This work was part of the author{\textquoteright}s MSc thesis at the Department of EE-Systems, Tel Aviv University. 3 Work done while a fellow at the Radcliffe Institute for Advanced Study, Harvard University. Also supported by a Sloan Research Fellowship and NSF grant CCF-0133096.",

year = "2007",

month = feb,

day = "14",

doi = "10.1016/j.ipl.2006.08.012",

language = "אנגלית",

volume = "101",

pages = "112--118",

journal = "Information Processing Letters",

issn = "0020-0190",

publisher = "Elsevier",

number = "3",

}

TY - JOUR

T1 - The hardness of the Expected Decision Depth problem

AU - Ron, Dana

AU - Rosenfeld, Amir

AU - Vadhan, Salil

N1 - Funding Information: * Corresponding author. E-mail addresses: danar@eng.tau.ac.il (D. Ron), amirrosenfeld@yahoo.com (A. Rosenfeld), salil@eecs.harvard.edu (S. Vadhan). 1 Work partially done while a fellow at the Radcliffe Institute for Advanced Study, Harvard University. Also supported by the Israel Science Foundation. 2 This work was part of the author’s MSc thesis at the Department of EE-Systems, Tel Aviv University. 3 Work done while a fellow at the Radcliffe Institute for Advanced Study, Harvard University. Also supported by a Sloan Research Fellowship and NSF grant CCF-0133096.

PY - 2007/2/14

Y1 - 2007/2/14

N2 - Given a function f over n binary variables, and an ordering of the n variables, we consider the Expected Decision Depth problem. Namely, what is the expected number of bits that need to be observed until the value of the function is determined, when bits of the input are observed according to the given order. Our main finding is that this problem is (essentially) #P-complete. Moreover, the hardness holds even when the function f is represented as a decision tree.

AB - Given a function f over n binary variables, and an ordering of the n variables, we consider the Expected Decision Depth problem. Namely, what is the expected number of bits that need to be observed until the value of the function is determined, when bits of the input are observed according to the given order. Our main finding is that this problem is (essentially) #P-complete. Moreover, the hardness holds even when the function f is represented as a decision tree.

KW - Computational complexity

KW - Decision trees

UR - http://www.scopus.com/inward/record.url?scp=33845220785&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2006.08.012

DO - 10.1016/j.ipl.2006.08.012

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:33845220785

SN - 0020-0190

VL - 101

SP - 112

EP - 118

JO - Information Processing Letters

JF - Information Processing Letters

IS - 3

ER -

The hardness of the Expected Decision Depth problem

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this