Worst-Case Optimal Tree Layout in External Memory

• Main Authors: Demaine, Erik D. (Contributor), Iacono, John (Author), Langerman, Stefan (Author)
• Other Authors: Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory (Contributor), Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor)
• Format: Article
• Language: English
• Published: Springer-Verlag, 2014-04-11T19:51:16Z.
• Subjects: Article
• Online Access: Get fulltext

Consider laying out a fixed-topology binary 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 Θ([D over lg(1+B))] when D = O(lgN), Θ([lgN over lg(1+[BlgN over D])]) when D=Ω(lgN) and D=O(BlgN), Θ([D over B]) ,when D=Ω(BlgN).
National Science Foundation (U.S.) (Grant CCF-0430849)
National Science Foundation (U.S.) (Grant OISE-0334653)