Arbitrary order operations on trees

Abstract

We consider techniques for the large scale parallel execution of algorithms on trees. We show that there is much parallelism in these algorithms, and introduce efficient means to exploit this parallelism. In particular, arbitrary order operations on trees are considered. An execution of a set arbitrary order operations must be equivalent to some sequential execution of a permutation of these operations.

A new algorithm is introduced for efficiently performing these operations under the condition that an operation consists of a sequence of reads starting at the root of a tree down a path towards some leaf, followed by a partial retrace of that path in reverse during which writes can occur — this is the standard form for performing inserts, searches, and deletes on most forms of balanced and unbalanced binary trees. We show that this new algorithm, tree interference is correct and produces execution schedules which are at least as parallel as other techniques including locking and graph coloring based interference. We also show some estimate of the performance on a sample computation, AVL trees.