Showing papers by "Charles E. Leiserson published in 1988"
TL;DR: A model for parallel computation, called the distributed randomaccess machine (DRAM), in which the communication requirements of parallel algorithms can be evaluated and the notion of aconservative algorithm is introduced 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.
Abstract: This paper introduces a model for parallel computation, called thedistributed randomaccess 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 aconservative 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 giveO(lgn)-step, linear-processor, linear-space, conservative algorithms for a variety of problems onn-node trees, such as computing treewalk numberings, finding the separator of a tree, and evaluating all subexpressions in an expression tree. We giveO(lg2n)-step, linear-processor, linear-space, conservative algorithms for problems on graphs of sizen, 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 suchtreefix computation can be performed inO(lgn) steps using a conservative variant of Miller and Reif's tree-contraction technique.
74 citations
TL;DR: An efficient solution to the mixed-integer linear programming variant where some, but not necessarily all, of the unknowns are required to be integers is given.
42 citations
TL;DR: A simple demonstration that the n×n×n tree of meshes graph truncated to l levels can be embedded in a three-dimensional (3D) grid using volume O(n 3 l 3 2 ) .
20 citations
01 Oct 1988
TL;DR: In this paper, the problem of determining an equivalent retimed circuit with minimum state (total number of registers) is polynomial-time solvable, and a chacterization of optimal retiming based on an efficiently solvable mixed-integer linear programming problem is given.
Abstract: This paper describes a circuit transformation calledretiming in which registers are added at some points in a circuit and removed from others in such a way that the functional behavior of the circuit as a whole is preserved. We show that retiming can be used to transform a given synchronous circuit into a more efficient circuit under a variety of different cost criteria. We model a circuit as a graph in which the vertex setV is a collection of combinational logic elements and the edge setE is the set of interconnections, each of which may pass through zero or more registers. We give anO(?VźE?lg?V?) algorithm for determining an equivalent retimed circuit with the smallest possible clock period. We show that the problem of determining an equivalent retimed circuit with minimum state (total number of registers) is polynomial-time solvable. This result yields a polynomial-time optimal solution to the problem of pipelining combinational circuitry with minimum register cost. We also give a chacterization of optimal retiming based on an efficiently solvable mixed-integer linear-programming problem.
3 citations