Mappings for conflict-free access of paths in bidimensional array, circular lists, and complete trees

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 particular 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 problem solved here has further application in minimizing the number of frequencies assigned to the stations of a wireless network so as to avoid interference.