The different concepts involved in "reversal complexity"--counting reversals (sweeps), visits to a square, or crossing sequences--are discussed for nondeterministic off-line Turing machines with one working tape and for preset Turing machines, a generalization of two-way checking automata. Restriction to finite reversals or visits or crosses yields the same family, NSPACE(log2 n), for off-line ...

We describe an asynchronous parallel variant of the randomized Kaczmarz (RK) algorithm for solving the linear system Ax = b. The analysis shows linear convergence and indicates that nearly linear speedup can be expected if the number of processors is bounded by a multiple of the number of rows in A.

It is demonstrated that supra-linear (greater than linear) speedup is possible in processing distributed divisible computational loads where computation time is a nonlinear function of load size. This result is radically different from the traditional distributed processing of computational loads with linear processing complexity appearing in over 50 journal papers.

There seems to be, at least in practice, a fundamental conflict within program transformations. One way: hand transformations can yield dramatic speedups, but seem to require human insight. They are thus are only suited to small programs and have not been successfully automated. On the other hand, there exist a number of well-known automatic program transformations; but these have been proven t...

We investigate improvements to the algorithm for the computation of ideal class groups described by Jacobson in the imaginary quadratic case. These improvements rely on the large prime strategy and a new method for performing the linear algebra phase. We achieve a significant speed-up and are able to compute ideal class groups with discriminants of 110 decimal digits in less than a week.

When N processors perform depth-first search on-disjoint parts of a state space tree to find a solution, the speedup can be superlinear (i.e., > N) or sublinear (i.e., < N) depending upon when a solution is first encountered in the space by one of the processors. It may appear that on the average, the speedup would be either linear or sublinear. Using an analytical model, we show that if the se...

Branch and bound algorithms for Mixed-Integer Linear Programming (MILP) almost universally branch on a single variable to create disjunctions. General linear expressions involving multiple variables are another option for branching disjunctions, but are not used for two main reasons: (i) descendent LPs tend to solve more slowly because of the added constraints, so the overall solution time is i...

The least-squares probabilistic classifier (LSPC) is a computationally efficient alternative to kernel logistic regression (KLR). A key idea for the speedup is that, unlike KLR that uses maximum likelihood estimation for a log-linear model, LSPC uses least-squares estimation for a linear model. This allows us to obtain a global solution analytically in a classwise manner. In exchange for the sp...

The finite difference discretization of the Poisson equation in three dimensions results in a large, sparse, and highly structured system of linear equations. This prototype problem is used to analyze the performance of the parallel linear solver on coarse-grained clusters of workstations. The conjugate gradient method with a matrix-free implementation of the matrix-vector product with the syst...