A classical problem in logic synthesis is to find a sum-of-product (SOP) Boolean expression with the minimum number of product terms that implements a Boolean function. In this paper, we focus on a related yet different synthesis problem targeted toward probabilistic computation. In our scenario, we want to synthesize a Boolean function that covers an exact number of minterms, say m minterms. T...

An upper bound for sorting permutations with an operation estimates the diameter of the corresponding Cayley graph and an exact upper bound equals the diameter. Computing tight upper bounds for various operations is of theoretical and practical (e.g. interconnection networks, genetics) interest. Akers and Krishnamurthy gave a Ω(n! n) time method that examines n! permutations to compute an upper...

Reliable estimates for the condition number of a large, sparse, real matrix A are important in many applications. To get an approximation for the condition number κ(A), an approximation for the smallest singular value is needed. Standard Krylov subspaces are usually unsuitable for finding a good approximation to the smallest singular value. Therefore, we study extended Krylov subspaces which tu...

This paper presents a scheduling problem with unrelated parallel machines and sequencedependent setup times that minimizes the total weighted tardiness. A new branch-and-bound (B and B) algorithm is designed incorporating the lower and upper bounding schemes and several dominance properties. The lower and upper bounds are derived through an assignment problem and the composite dispatching rule ...

This paper introduces a robust task-space control scheme for a robotic system with an adaptive observer. The proposed approach does not require the availability of the system states and an adaptive observer is developed to estimate the state variables. These estimated states are then used in the control scheme. First, the dynamic model of a robot is derived. Next, an observer-based robust contr...

We present a Chebyshev-Davidson method to compute a few smallest positive eigenvalues and corresponding eigenvectors of the linear response eigenvalue problem. The method is actually applicable to the slightly more general linear response eigenvalue problem where purely imaginary eigenvalues may occur. For the Chebyshev filter, a tight upper bound is obtained by a computable bound estimator con...

in this paper, a single machine sequencing problem is considered in order to find the sequence of jobs minimizing the sum of the maximum earliness and tardiness with idle times (n/1/i/etmax). due to the time complexity function, this sequencing problem belongs to a class of np-hard ones. thus, a special design of a simulated annealing (sa) method is applied to solve such a hard problem. to comp...

It is well known that in operations research‎, ‎degeneracy can cause a cycle in a network‎ ‎simplex algorithm which can be prevented by maintaining strong‎ ‎feasible bases in each pivot‎. ‎Also‎, ‎in a network consists of n arcs‎ ‎and m nodes‎, ‎not considering any new conditions on the entering‎ ‎variable‎, ‎the upper bound of consecutive degenerate pivots is equal‎ $left( ‎begin{array}{c}‎ ‎n...