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Communication-Efficient Parallel Algorithms for Distributed Random-Access Machines

Charles E. Leiserson
Bruce M. Maggs
M.I.T. Laboratory for Computer Science
545 Technology Square
Cambridge, MA 02139


This paper introduces a model for parallel computation, called the distributed random-access machine (DRAM), in which the communication requirements of parallel algorithms can be evaluated. A DRAM is an abstraction of a parallel computer in which memory accesses are implemented by routing messages through a communication network. A DRAM explicitly models the congestion of messages across cuts of the network.

We introduce the notion of a conservative algorithm as one whose communication requirements at each step can be bounded by the congestion of pointers of the input data structure across cuts of a DRAM. We give a simple lemma that shows how to ``shortcut'' pointers in a data structure so that remote processors can communicate without causing undue congestion. We give tex2html_wrap_inline1011 -step, linear-processor, linear-space, conservative algorithms for a variety of problems on n-node trees, such as computing treewalk numberings, finding the separator of a tree, and evaluating all subexpressions in an expression tree. We give tex2html_wrap_inline1015 -step, linear-processor, linear-space, conservative algorithms for problems on graphs of size n, including finding a minimum-cost spanning forest, computing biconnected components, and constructing an Eulerian cycle. Most of these algorithms use as a subroutine a generalization of the prefix computation to trees. We show that any such treefix computation can be performed in tex2html_wrap_inline1019 steps using a conservative variant of Miller and Reif's tree-contraction technique.

Bruce Maggs
Thu Jul 25 19:12:36 EDT 1996
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