We address the design of parallel algorithms that are oblivious to machine parameters for two dominant machine configurations: the chip multiprocessor (or multicore) and the network of processors.

First, and of independent interest, we propose HM, a hierarchical multi-level caching model for multicores, and we propose a multicore-oblivious approach to algorithms and schedulers for HM. We instantiate this approach with provably efficient multicore-oblivious algorithms for matrix and prefix sum computations, FFT, the Gaussian Elimination paradigm (which represents an important class of computations including Floyd-Warshall's all-pairs shortest paths, Gaussian Elimination and LU decomposition without pivoting), sorting, list ranking, Euler tours and connected components.

We then use the network oblivious framework proposed earlier as an oblivious framework for a network of processors, and we present provably efficient network-oblivious algorithms for sorting, the Gaussian Elimination paradigm, list ranking, Euler tours and connected components. Many of these network-oblivious algorithms perform efficiently also when executed on the Decomposable-BSP.