The Divide & Conquer fast direct method for solving the Poisson equation in rectangular domains is formulated in the classical block cyclic reduction manner, demonstrating the close relationship between the two approaches. Diierent ways of solving the arising reduced systems are considered. The partial solution approach leads to the standard Divide & Conquer method, while the new variants are o...

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be...

We show how to implement divide-and-conquer algorithms without undue overhead on a wide class of networks. We give an optimal generic divide-and-conquer implementation on hypercubes for the class of divide-and-conquer algorithms for which the total size of the subproblems on any level of the recursion does not exceed the parent problem size. For this implementation, appropriately sized subcubes...

In this paper we present a simple language for expressing divide and conquer computations. The language allows for many variations in the standard divide and conquer paradigm. It is implemented using the Chare Kernel parallel programming system. The Chare Kernel supports dynamic creation of work with dynamic load balancing strategies, and machine independent execution. As a result, implementati...

A bordered almost block diagonal system (BABD) results from discretizing and linearizing ordinary diierential equation (ODE) boundary value problems (BVPs) with non-separated boundary conditions (BCs) by either spline collocation, nite diierences, or multiple shooting. After internal condensation, if necessary, this BABD system reduces to a standard-nite diierence BABD structure. This system ca...

We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks that are amenable to the principle of divide and conquer, and study what are its implications in terms of learning. This principle creates a powerful induct...

This contribution will be freewheeling in the domain of signal, image and surface processing and touch briefly upon some topics that have been close to the heart of people in our research group. A lot of the research of the last 20 years in this domain that has been carried out world wide is dealing with multiresolution. Multiresolution allows to represent a function (in the broadest sense) at ...