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Motivated by the problem of estimating bottleneck capacities on the Internet, we formulate and study the problem of vantage point selection. We are given a graph G = (V, E) whose edges E have unknown capacity values that are to be discovered. Probes from a vantage point, i.e, a vertex v ∈ V, along shortest paths from v to all other vertices, reveal bottleneck edge capacities along each path. Our goal is to select k vantage points from V that reveal the maximum number of bottleneck edge capacities. We consider both a non-adaptive setting where all k vantage points are selected before any bottleneck capacity is revealed, and an adaptive setting where each vantage point selection instantly reveals bottleneck capacities along all shortest paths starting from that point. In the non-adaptive setting, by considering a relaxed model where edge capacities are drawn from a random permutation (which still leaves the problem of maximizing the expected number of revealed edges NP-hard), we are able to give a 1-1/e approximate algorithm. In the adaptive setting we work with the least permissive model where edge capacities are arbitrarily fixed but unknown. We compare with the best solution for the particular input instance (i.e. by enumerating all choices of k tuples), and provide both lower bounds on instance optimal approximation algorithms and upper bounds for trees and planar graphs. 

Stencil computations are widely used to simulate the change of state of physical systems across a multidimensional grid over multiple timesteps. The state-of-the-art techniques in this area fall into three groups: cache-aware tiled looping algorithms, cache-oblivious divide-and-conquer trapezoidal algorithms, and Krylov subspace methods. In this article, we present two efficient parallel algorithms for performing linear stencil computations. Current direct solvers in this domain are computationally inefficient, and Krylov methods require manual labor and mathematical training. We solve these problems for linear stencils by using discrete Fourier transforms preconditioning on a Krylov method to achieve a direct solver that is both fast and general. Indeed, while all currently available algorithms for solving general linear stencils perform Θ(NT) work, whereNis the size of the spatial grid andTis the number of timesteps, our algorithms performo(NT) work. To the best of our knowledge, we give the first algorithms that use fast Fourier transforms to compute final grid data by evolving the initial data for many timesteps at once. Our algorithms handle both periodic and aperiodic boundary conditions and achieve polynomially better performance bounds (i.e., computational complexity and parallel runtime) than all other existing solutions. Initial experimental results show that implementations of our algorithms that evolve grids of roughly 10⁷cells for around 10⁵timesteps run orders of magnitude faster than state-of-the-art implementations for periodic stencil problems, and 1.3× to 8.5× faster for aperiodic stencil problems. Code Repository:https://github.com/TEAlab/FFTStencils 

On shared-memory multicore machines, classic two-way recursive divide-and-conquer algorithms are implemented using common fork-join based parallel programming paradigms such as Intel Cilk+ or OpenMP. However, in such parallel paradigms, the use of joins for synchronization may lead to artificial dependencies among function calls which are not implied by the underlying DP recurrence. These artificial dependencies can increase the span asymptotically and thus reduce parallelism. From a practical perspective, they can lead to resource underutilization, i.e., threads becoming idle. To eliminate such artificial dependencies, task-based runtime systems and data-flow parallel paradigms, such as Concurrent Collections (CnC), PaRSEC, and Legion have been introduced. Such parallel paradigms and runtime systems overcome the limitations of fork-join parallelism by specifying data dependencies at a finer granularity and allowing tasks to execute as soon as dependencies are satisfied.In this paper, we investigate how the performance of data-flow implementations of recursive divide-and-conquer based DP algorithms compare with fork-join implementations. We have designed and implemented data-flow versions of DP algorithms in Intel CnC and compared the performance with fork-join based implementations in OpenMP. Considering different execution parameters (e.g., algorithmic properties such as recursive base size as well as machine configuration such as the number of physical cores, etc), our results confirm that a data-flow based implementation outperforms its fork-join based counter-part when due to artificial dependencies, the fork-join implementation fails to generate enough subtasks to keep all processors busy and does not have enough data locality to compensate for the lost performance. This phenomena happens when the input size of the DP algorithm is small or we have a huge number of compute cores in the system. As a result, with a fixed computation resource, moving from small input to larger input, fork-join implementation of DP algorithms outperforms the corresponding data-flow implementation. However, for a fixed size problem, moving the computation to a compute node with a larger number of cores, data-flow implementation outperforms the corresponding fork-join implementation.