• Communication-efficient parallel algorithms for distributed random-access machines. C. E. Leiserson and B. M. Maggs, Algorithmica, Vol. 3, 1988, pp. 53-77.

  This paper introduces a model for parallel computation called the distributed random-access machine (DRAM). 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 O(log n)-step, linear-processor, linear-space, conservative algorithms for a variety of problems on n-node trees, such as computing treewalk numberings and evaluating all subexpressions in an expression tree, and O(log^2 n)-step conservative algorithms for problems on graphs of size n, including finding a minimum-cost spanning forest, computing biconnected components, and constructing an Eulerian cycle.

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