In this paper, we present a survey of results about the problem of mapping the N items of a data structure on M memory modules so that items can be accessed in parallel by templates i.e. distinct sets of nodes. In particular, we present some results that allow to access several different templates at once, i.e. we focus on versatile mapping algorithms (for a comprehensive survey of other related results see [14] in this volume). In particular, we present some of the algorithms in literature for accessing arrays (by rows, columns, diagonals and subarrays) and trees (accessed by subtrees, root-to-leaf paths, levels and compositions thereof). 1 Introduction In this paper we present a survey of results related to the problem of mapping a data structure to M memory modules when it is known how the access is required i.e. templates of memory access are known. The problem is to minimize the conflicts on the memory modules, i.e. simultaneous access to the same module to retrieve different dat...

Since the divergence between the processor speed and the memory access rate is progressively increasing, an efficient partition of the main memory into multibanks is useful to improve the overall system performance. The effectiveness of the multibank partition can be degraded by memory conflicts, that occur when there are many references to the same memory bank while accessing the same memory pattern. Therefore, mapping schemes are needed to distribute data in such a way that data can be retrieved via regular patterns without conflicts. In this paper, the problem of conflict-free access of arbitrary paths in bidimensional arrays, circular lists and complete trees is considered for the first time and reduced to variants of graph-coloring problems. Balanced and fast mappings are proposed which require an optimal number of colors (i.e., memory banks). The solution for bidimensional arrays is based on a combinatorial object similar to a Latin Square. The functions that map an array node or a circular list node to a memory bank can be calculated in constant time. As for complete trees, the mapping of a tree node to a memory bank takes time that grows logarithmically with the number of nodes of the tree.

The main memory access latency can significantly slowdown the overall performance of a computer system due to the fact that average cycle time of the main memory is typically a factor of 5-10 higher than that of a processor. To cope up with this problem, in addition to the use of caches, the main memory of a multiprocessor architecture is usually organized in multiple modules or banks. Although such organization enhances memory bandwidth, the amount of data that the multiprocessor can retrieve in the same memory cycle, conflicts due to simultaneous attempt to access the same memory module, may reduce the effective bandwidth. Therefore, efficient mapping schemes are required to distribute data in such a way that regular patterns, called templates, of various structures can be retrieved in parallel without memory conflicts. Prior work on data mappings mostly deal with conflict-free access to templates like rows, columns, or diagonals of (multi-dimensional) arrays, and only limited attention has been paid to access templates of non-numeric structures such as trees.