Memory-optimal evaluation of expression trees involving large objects

Authors:
Chi-Chung Lam;Thomas Rauber;Gerald Baumgartner;Daniel Cociorva;P. Sadayappan
Affiliations:
Department of Computer Science and Engineering, The Ohio State University, Columbus, OH 43210, USA;University of Bayreuth, Lehrstuhl für Angewandte Informatik II, D-95447 Bayreuth, Germany;Department of Computer Science, Louisiana State University, Baton Rouge, LA 70803, USA;Department of Computer Science and Engineering, The Ohio State University, Columbus, OH 43210, USA;Department of Computer Science and Engineering, The Ohio State University, Columbus, OH 43210, USA
Venue:
Computer Languages, Systems and Structures
Year:
2011

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Abstract

The need to evaluate expression trees involving large objects arises in scientific computing applications such as electronic structure calculations. Often, the tree node objects are so large that only a subset of them can fit into memory at a time. This paper addresses the problem of finding an evaluation order of the nodes in a given expression tree that uses the least amount of memory. We present an algorithm that finds an optimal evaluation order in @Q(nlog^2n) time for an n-node expression tree and prove its correctness. We demonstrate the utility of our algorithm using representative equations from quantum chemistry.