Toward a Universal Mapping Algorithm for Accessing Trees in Parallel Memory Systems

We study the problem of mapping the N nodes of a complete t-ary tree on M memory modules so that they can be accessed in parallel 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 to as 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 of 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  SpM logM + c and the memory load is 1 + o1 where load is de ned as the ratio between the maximum and minimum number of data items mapped onto each memory module.

• Type: Conference
• Year: 1998
• Where: IPPS
• Authors: Vincenzo Auletta, Sajal K. Das, Amelia De Vivo, Maria Cristina Pinotti, Vittorio Scarano
• Keywords: Complete T-ary Tree, Distributed And Parallel Computing, Elementary Templates, IPPS 1998, Memory Module