Garbage-First is a server-style garbage collector, targeted for multi-processors with large memories, that meets a soft real-time goal with high probability, while achieving high throughput. Whole-heap operations, such as global marking, are performed concurrently with mutation, to prevent interruptions proportional to heap or live-data size. Concurrent marking both provides collection ”completeness ” and identifies regions ripe for reclamation via compacting evacuation. This evacuation is performed in parallel on multiprocessors, to increase throughput.

We present a linear algebraic formulation for a class of index transformations such as Gray code encoding and decoding, matrix transpose, bit reversal, vector reversal, shuffles, and other index or dimension permutations. This formulation unifies, simplifies, and can be used to derive algorithms for hypercube multiprocessors. We show how all the widely known properties of Gray codes, and some not so well-known properties as well, can be derived using this framework. Using this framework, we relate hypercube communications algorithms to Gauss-Jordan elimination on a matrix of 0's and 1's.>