Worst-Case Optimal Tree Layout in a Memory Hierarchy

Consider laying out a fixed-topology tree of N nodes into external memory with block size B so as to minimize the worst-case number of block memory transfers required to traverse a path from the root to a node of depth D. We prove that the optimal number of memory transfers is D lg(1+B) when D = O(lg N) lg N lg 1+B lg N D when D = (lg N) and D = O(B lg N) D B when D = (B lg N) . This bound can be achieved even when B is unknown to the (cache-oblivious) layout algorithm.

• Type: Journal
• Year: 2004
• Where: CORR
• Authors: Erik D. Demaine, John Iacono, Stefan Langerman
• Keywords: Block Size, CORR 2004, Education, External Memory, Fixed-topology Tree