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Devorah Kletenik - One of the best experts on this subject based on the ideXlab platform.

  • approximation algorithms for stochastic submodular set cover with applications to Boolean Function evaluation and min knapsack
    ACM Transactions on Algorithms, 2016
    Co-Authors: Amol Deshpande, Lisa Hellerstein, Devorah Kletenik
    Abstract:

    We present a new approximation algorithm for the stochastic submodular set cover (SSSC) problem called adaptive dual greedy. We use this algorithm to obtain a 3-approximation algorithm solving the stochastic Boolean Function evaluation (SBFE) problem for linear threshold formulas (LTFs). We also obtain a 3-approximation algorithm for the closely related stochastic min-knapsack problem and a 2-approximation for a variant of that problem. We prove a new approximation bound for a previous algorithm for the SSSC problem, the adaptive greedy algorithm of Golovin and Krause. We also consider an approach to approximating SBFE problems using the adaptive greedy algorithm, which we call the Q-value approach. This approach easily yields a new result for evaluation of CDNF (conjunctive / disjunctive normal form) formulas, and we apply variants of it to simultaneous evaluation problems and a ranking problem. However, we show that the Q-value approach provably cannot be used to obtain a sublinear approximation factor for the SBFE problem for LTFs or read-once disjunctive normal form formulas.

  • approximation algorithms for stochastic Boolean Function evaluation and stochastic submodular set cover
    Symposium on Discrete Algorithms, 2014
    Co-Authors: Amol Deshpande, Lisa Hellerstein, Devorah Kletenik
    Abstract:

    We present approximation algorithms for two problems: Stochastic Boolean Function Evaluation (SBFE) and Stochastic Submodular Set Cover (SSSC). Our results for SBFE problems are obtained by reducing them to SSSC problems through the construction of appropriate utility Functions. We give a new algorithm for the SSSC problem that we call Adaptive Dual Greedy. We use this algorithm to obtain a 3-approximation algorithm solving the SBFE problem for linear threshold formulas. We also get a 3-approximation algorithm for the closely related Stochastic Min-Knapsack problem, and a 2-approximation for a natural special case of that problem. In addition, we prove a new approximation bound for a previous algorithm for the SSSC problem, Adaptive Greedy. We consider an approach to approximating SBFE problems using existing techniques, which we call the Q-value approach. This approach easily yields a new result for evaluation of CDNF formulas, and we apply variants of it to simultaneous evaluation problems and a ranking problem. However, we show that the Q-value approach provably cannot be used to obtain a sublinear approximation factor for the SBFE problem for linear threshold formulas or read-once DNF.

  • approximation algorithms for stochastic Boolean Function evaluation and stochastic submodular set cover
    arXiv: Data Structures and Algorithms, 2013
    Co-Authors: Amol Deshpande, Lisa Hellerstein, Devorah Kletenik
    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.

Amol Deshpande - One of the best experts on this subject based on the ideXlab platform.

  • approximation algorithms for stochastic submodular set cover with applications to Boolean Function evaluation and min knapsack
    ACM Transactions on Algorithms, 2016
    Co-Authors: Amol Deshpande, Lisa Hellerstein, Devorah Kletenik
    Abstract:

    We present a new approximation algorithm for the stochastic submodular set cover (SSSC) problem called adaptive dual greedy. We use this algorithm to obtain a 3-approximation algorithm solving the stochastic Boolean Function evaluation (SBFE) problem for linear threshold formulas (LTFs). We also obtain a 3-approximation algorithm for the closely related stochastic min-knapsack problem and a 2-approximation for a variant of that problem. We prove a new approximation bound for a previous algorithm for the SSSC problem, the adaptive greedy algorithm of Golovin and Krause. We also consider an approach to approximating SBFE problems using the adaptive greedy algorithm, which we call the Q-value approach. This approach easily yields a new result for evaluation of CDNF (conjunctive / disjunctive normal form) formulas, and we apply variants of it to simultaneous evaluation problems and a ranking problem. However, we show that the Q-value approach provably cannot be used to obtain a sublinear approximation factor for the SBFE problem for LTFs or read-once disjunctive normal form formulas.

  • approximation algorithms for stochastic Boolean Function evaluation and stochastic submodular set cover
    Symposium on Discrete Algorithms, 2014
    Co-Authors: Amol Deshpande, Lisa Hellerstein, Devorah Kletenik
    Abstract:

    We present approximation algorithms for two problems: Stochastic Boolean Function Evaluation (SBFE) and Stochastic Submodular Set Cover (SSSC). Our results for SBFE problems are obtained by reducing them to SSSC problems through the construction of appropriate utility Functions. We give a new algorithm for the SSSC problem that we call Adaptive Dual Greedy. We use this algorithm to obtain a 3-approximation algorithm solving the SBFE problem for linear threshold formulas. We also get a 3-approximation algorithm for the closely related Stochastic Min-Knapsack problem, and a 2-approximation for a natural special case of that problem. In addition, we prove a new approximation bound for a previous algorithm for the SSSC problem, Adaptive Greedy. We consider an approach to approximating SBFE problems using existing techniques, which we call the Q-value approach. This approach easily yields a new result for evaluation of CDNF formulas, and we apply variants of it to simultaneous evaluation problems and a ranking problem. However, we show that the Q-value approach provably cannot be used to obtain a sublinear approximation factor for the SBFE problem for linear threshold formulas or read-once DNF.

  • approximation algorithms for stochastic Boolean Function evaluation and stochastic submodular set cover
    arXiv: Data Structures and Algorithms, 2013
    Co-Authors: Amol Deshpande, Lisa Hellerstein, Devorah Kletenik
    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.

Scott Aaronson - One of the best experts on this subject based on the ideXlab platform.

  • algorithms for Boolean Function query properties
    SIAM Journal on Computing, 2003
    Co-Authors: Scott Aaronson
    Abstract:

    We investigate efficient algorithms for computing Boolean Function properties relevant to query complexity. Such properties include, for example, deterministic, randomized, and quantum query complexities; block sensitivity; certificate complexity; and degree as a real polynomial. The algorithms compute the properties, given an n-variable Function's truth table (of size N=2n) as input. Our main results are the following: O(N log2 3 log N) algorithms for many common properties, an O(N log2 5 log N) algorithm for block sensitivity, an O(N) algorithm for testing "quasi symmetry," a notion of a "tree decomposition" of a Boolean Function, proof that the decomposition is unique, and an O(Nlog2 3 log N) algorithm for finding it, a subexponential-time approximation algorithm for space-bounded quantum query complexity. To develop this algorithm, we give a new way to search systematically through unitary matrices using finite-precision arithmetic. The algorithms discussed have been implemented in a linkable library.

  • algorithms for Boolean Function query properties
    arXiv: Computational Complexity, 2001
    Co-Authors: Scott Aaronson
    Abstract:

    We present new algorithms to compute fundamental properties of a Boolean Function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,' and an O(N) algorithm for `quasisymmetry.' These algorithms are based on new insights into the structure of Boolean Functions that may be of independent interest. We also give a subexponential-time algorithm for the space-bounded quantum query complexity of a Boolean Function. To prove this algorithm correct, we develop a theory of limited-precision representation of unitary operators, building on work of Bernstein and Vazirani.

Pantelimon Stanica - One of the best experts on this subject based on the ideXlab platform.

  • Analysis on Boolean Function in a restricted (biased) domain
    IEEE Transactions on Information Theory, 2020
    Co-Authors: Subhamoy Maitra, Bimal Mandal, Thor Martinsen, Dibyendu Roy, Pantelimon Stanica
    Abstract:

    Boolean Functions are usually studied under the assumption that each input bit is considered independent and identically distributed. However, in the case of some stream ciphers, a keystream bit is generated by using a nonlinear Boolean Function with inputs from a restricted domain. At Eurocrypt 2016, one such stream cipher (FLIP) has been proposed, where a Boolean Function on n variables was exploited with inputs of weight n/2 only. Recently, Carlet et al. studied several properties of such Functions and obtained certain bounds on linear approximations of direct sum in the restricted domain. In this paper, we observe that for a direct sum like f = g+h, the inputs to each sub-Function g, h do not follow a uniform distribution in the restricted domain. In this regard, we study the properties of Boolean Functions by considering a general probability distribution on the inputs. We further obtain several bounds related to the biases of direct sums. Finally, we obtain a lower bound on the bias of the nonlinear filter Function of FLIP. Our results provide a general framework to study security parameters of ciphers over restricted domain.

Lisa Hellerstein - One of the best experts on this subject based on the ideXlab platform.

  • approximation algorithms for stochastic submodular set cover with applications to Boolean Function evaluation and min knapsack
    ACM Transactions on Algorithms, 2016
    Co-Authors: Amol Deshpande, Lisa Hellerstein, Devorah Kletenik
    Abstract:

    We present a new approximation algorithm for the stochastic submodular set cover (SSSC) problem called adaptive dual greedy. We use this algorithm to obtain a 3-approximation algorithm solving the stochastic Boolean Function evaluation (SBFE) problem for linear threshold formulas (LTFs). We also obtain a 3-approximation algorithm for the closely related stochastic min-knapsack problem and a 2-approximation for a variant of that problem. We prove a new approximation bound for a previous algorithm for the SSSC problem, the adaptive greedy algorithm of Golovin and Krause. We also consider an approach to approximating SBFE problems using the adaptive greedy algorithm, which we call the Q-value approach. This approach easily yields a new result for evaluation of CDNF (conjunctive / disjunctive normal form) formulas, and we apply variants of it to simultaneous evaluation problems and a ranking problem. However, we show that the Q-value approach provably cannot be used to obtain a sublinear approximation factor for the SBFE problem for LTFs or read-once disjunctive normal form formulas.

  • approximation algorithms for stochastic Boolean Function evaluation and stochastic submodular set cover
    Symposium on Discrete Algorithms, 2014
    Co-Authors: Amol Deshpande, Lisa Hellerstein, Devorah Kletenik
    Abstract:

    We present approximation algorithms for two problems: Stochastic Boolean Function Evaluation (SBFE) and Stochastic Submodular Set Cover (SSSC). Our results for SBFE problems are obtained by reducing them to SSSC problems through the construction of appropriate utility Functions. We give a new algorithm for the SSSC problem that we call Adaptive Dual Greedy. We use this algorithm to obtain a 3-approximation algorithm solving the SBFE problem for linear threshold formulas. We also get a 3-approximation algorithm for the closely related Stochastic Min-Knapsack problem, and a 2-approximation for a natural special case of that problem. In addition, we prove a new approximation bound for a previous algorithm for the SSSC problem, Adaptive Greedy. We consider an approach to approximating SBFE problems using existing techniques, which we call the Q-value approach. This approach easily yields a new result for evaluation of CDNF formulas, and we apply variants of it to simultaneous evaluation problems and a ranking problem. However, we show that the Q-value approach provably cannot be used to obtain a sublinear approximation factor for the SBFE problem for linear threshold formulas or read-once DNF.

  • approximation algorithms for stochastic Boolean Function evaluation and stochastic submodular set cover
    arXiv: Data Structures and Algorithms, 2013
    Co-Authors: Amol Deshpande, Lisa Hellerstein, Devorah Kletenik
    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.