Skip to main navigation
Skip to Content
Computer Science
University of Toronto
Quercus
Student Support
Contact
About
History of U of T Computer Science
Computer Science at U of T Mississauga
Computer Science at U of T Scarborough
Employment Opportunities for Faculty/Lecturers
How to Find Us
Contact
Undergraduate
Prospective Undergraduates
Current Undergraduates
Graduate
Prospective Graduate Students
Current Graduate Students
Research
Research Areas
Partner with us
People
Faculty
Staff
In Memoriam
Alumni and Friends
Honours & Awards
Women in Computer Science
Graduate Student Society
Undergraduate Student Union
Undergraduate Artificial Intelligence Group
Undergraduate Theory Group
News & Events
News
Events
@DCS Update
Alumni
Donate
You are viewing: >
Home
>
News & Events
>
Events
> Theory Seminar - June 18
About
Undergraduate
Graduate
Research
People
News & Events
Theory Seminar - June 18
Event date: Tuesday, June 18, 2013, at 11:10 AM
Location: PT 266
Speaker: Lisa Hellerstein, Polytechnic Institute of NYU
Title: Approximation Algorithms for Stochastic Boolean Function Evaluation and Stochastic Submodular Set Cover
Abstract:
Stochastic Boolean Function Evaluation is the problem of determining the value of a given Boolean function f on an unknown input x, when each bit of x_i of x can only be determined by paying an associated cost c_i. The assumption is that x is drawn from a given product distribution, and the goal is to minimize the expected cost. This problem has been studied in Operations Research, where it is known as "sequential testing" of Boolean functions. It has also been studied in learning theory in the context of learning with attribute costs. We consider the general problem of developing approximation algorithms for Stochastic Boolean Function Evaluation. We give a 3-approximation algorithm for evaluating Boolean linear threshold formulas. We also present an approximation algorithm for evaluating CDNF formulas (and decision trees) achieving a factor of O(log kd), where k is the number of terms in the DNF formula, and d is the number of clauses in the CNF formula.
In addition, we present approximation algorithms for simultaneous evaluation of linear threshold functions, and for ranking of linear functions. Our function evaluation algorithms are based on reductions to the Stochastic Submodular Set Cover (SSSC) problem. This problem was introduced by Golovin and Krause. They presented an approximation algorithm for the problem, called Adaptive Greedy. Our main technical contribution is a new approximation algorithm for the SSSC problem, which we call Adaptive Dual Greedy. It is an extension of the Dual Greedy algorithm for Submodular Set Cover due to Fujito, which is a generalization of Hochbaum's algorithm for the classical Set Cover Problem. We also give a new bound on the approximation achieved by the Adaptive Greedy algorithm of Golovin and Krause.