Toward a universal mapping algorithm for accessing trees in parallel memory systems (original) (raw)

We study the problem of mapping the N nodes of a c omplete t-ary tree o n M memory modules so that they can be a c cessed i n p arallel by templates, i.e. distinct sets of nodes. Typical templates for accessing trees are subtrees, root-to-leaf paths, or levels which will be referred t o a s elementary templates. In this paper, we rst propose a new mapping algorithm for accessing both paths and subtrees of size M with an optimal number of con icts i.e., only one conict when the number of memory modules is limited to M. We also propose another mapping algorithm for a composite template, say V as versatile, such that its size is not xed and an instance o f V is composed of any combination of c instances of elementary templates. The number of con icts for accessing an S-node instance of template V is O S p M log M + c and the memory load is 1 + o1 where l o ad is de ned as the ratio between the maximum and minimum number of data items mapped onto each memory module.