Many small sample problems are solved to illustrate the method and the practical situations in which these optimization problems arise.SETS is used for symbolic manipulation of Boolean equations, particularly the reduction of equations by the application of Boolean identities. The second moment method is used to exhibit the sharp concentration of the minimal size of H for a variety of values of p.AB - Consider the random set system (Formula presented. The feasible solutions are obtained by Boolean formula manipulations, and the optimum solutions are obtained by comparing the weight sums of the feasible solutions. Abstract. ), where (Formula presented.) The second moment method is used to exhibit the sharp concentration of the minimal size of H for a variety of values of p.T1 - Sharp Concentration of Hitting Size for Random Set SystemsN2 - Consider the random set system (Formula presented. The method generates feasible solutions algebraically as terms of a disjunctive normal form of a Boolean function. ), where (Formula presented.) The equation manipulation capabilities of SETS can also be used to analyze noncoherent fault trees and determine prime implicants of Boolean functions, to verify circuit design implementation, to determine minimum cost fire protection requirements for nuclear reactor plants, to obtain solutions to combinatorial optimization problems with Boolean constraints, and to determine the susceptibility of a facility to unauthorized access throughSETS is used for symbolic manipulation of Boolean equations, particularly the reduction of equations by the application of Boolean identities. Very frequently, in wireless sensor networks , one wishes to identify a subset of sensors, called “master” sensors, that will have a particular role in messages transmission, namely, to centralize and process messages sent by the rest of the sensors, called “slave” sensors, in the network. Sample problems illustrate how to make optimum choices in the contexts of physical protection, packing knapsacks, designing manufacturing processes and making assignments.This report shows how Boolean algebraic formula manipulation can be used to solve certain kinds of optimization problems.

One application is to physical protection problems. D. Jamieson, Jessie ; Godbole, Anant ; Jamieson, William title = "Sharp Concentration of Hitting Size for Random Set Systems", abstract = "Consider the random set system (Formula presented. A set H⊆[n] is said to be a hitting set for (Formula presented.). The second moment method is used to exhibit the sharp concentration of the minimal size of H for a variety of values of p. operator whose output set is called an -hitting set. priate polynomial size is a hitting set with high probability. Abstract.

Problems of minimizing or maximizing a linear objective function in zero-one variables subject to linear constraints can be solved by Boolean algebraic methods. It is a flexible and efficient tool for performing probabilistic risk analysis (PRA), vital area analysis, and common cause analysis. The equation manipulation capabilities of SETS can also be used to analyze noncoherent fault trees and determine prime implicants of Boolean functions, to verify circuit design implementation, to determine minimum cost fire protection requirements for nuclear reactor plants, to obtain solutions to combinatorial optimization problems with Boolean constraints, and to determine the susceptibility of a facility to unauthorized access through99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE nullification of sensors in its protection system.

The program uses the Boolean algebraic formula manipulation techniques of the SETS language. A set H⊆[n] is said to be a hitting set for (Formula presented.).

By continuing you agree to the View full fingerprint In other words, the linear program LP is a relaxation of the given set-cover problem.. 377–391) 71 Basic Probability Definition: An experiment is any process whose outcome is uncertain. The feasible solutions are obtained by Boolean formula manipulations, and the optimum solutions are obtained by comparing the weight sums of the feasible solutions. Definition 1.2 ( -Hitting Set). This report presents the results of computational experience in solving weighted hitting set problems by Boolean algebraic methods. Since ∗ has minimum cost among feasible solutions to the LP, the cost of ∗ is a lower bound on the cost of the optimal set cover. A set H⊆[n] is said to be a hitting set for (Formula presented.). ), where (Formula presented.) The second moment method is used to exhibit the sharp concentration of the minimal size of H for a variety of values of p.UR - http://www.scopus.com/inward/record.url?scp=84896059236&partnerID=8YFLogxKUR - http://www.scopus.com/inward/citedby.url?scp=84896059236&partnerID=8YFLogxK"We use cookies to help provide and enhance our service and tailor content. Sharp Concentration of Hitting Size for Random Set SystemsSharp Concentration of Hitting Size for Random Set SystemsSharp Concentration of Hitting Size for Random Set Systems ), where (Formula presented.) Dive into the research topics of 'Sharp Concentration of Hitting Size for Random Set Systems'. It is a flexible and efficient tool for performing probabilistic risk analysis (PRA), vital area analysis, and common cause analysis. nullification of sensors in its protection system.

and Ajselected with probabilityp=pn}. and Ajselected with probabilityp=pn}.