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- Andrew V. Goldberg, Serge A. Plotkin, Gregory E. Shannon
- SIAM J. Discrete Math.
- 1987

We describe efficient deterministic techniques for breaking symmetry in parallel. The techniques work well on rooted trees and graphs of constant degree or genus. Our primary technique allows us to 3-color a rooted tree in <italic>&Ogr;</italic>(lg<supscrpt>*</supscrpt><italic>n</italic>) time on an EREW PRAM using a linear number of processors. We apply… (More)

- Jonathan W. Berry, Nathaniel Dean, Mark K. Goldberg, Gregory E. Shannon, Steven Skiena
- Graph Drawing
- 1997

This paper introduces the LINK system as a flexible tool for the creation , manipulation, and drawing of graphs and hypergraphs. We describe the basic architecture of the system and illustrate its flexibility with several examples. LINK is distinguished from existing software for discrete mathematics by its layered interface, including a graphical user… (More)

The matrix chain ordering problem is to find the cheapest way to multiply a chain of n matrices, where the matrices are pairwise compatible but of varying dimensions. Here we give several new parallel algorithms including O(lg 3 n)-time and n/lg n-processor algorithms for solving the matrix chain ordering problem and for solving an optimal triangulation… (More)

- Ming-Yang Kao, Gregory E. Shannon
- STOC
- 1989

Almost every problem on digraphs requires computing <italic>strongly</italic> connected components and <italic>directed</italic> spanning trees in one form or another. It has long been an open problem whether polylog time and <italic>linear</italic> processors are enough to find the strongly connected components of a digraph and compute directed spanning… (More)

- Ming-Yang Kao, Gregory E. Shannon
- SIAM J. Comput.
- 1993

- Kurt S. Silverman, Michael R. Brenner, Gregory E. Shannon
- Bell Labs Technical Journal
- 2000

- Gregory E. Shannon
- Inf. Process. Lett.
- 1988

- Jonathan W. Berry, Nathaniel Dean, Mark K. Goldberg, Gregory E. Shannon, Steven Skiena
- Softw., Pract. Exper.
- 2000

- Gregory E. Shannon
- SPAA
- 1989

A b s t r a c t We present a general technique for simulating a broad class of T(n)-time and P(n)-processor algorithms on P(n)/T(n) processors using only O(T(n)) time for problems of size n. Surprisingly, this technique is not work conserving; many processors might be idle for long periods of time during the simulation. This generafizes and extends recent… (More)

- Francine Berman, Gregory E. Shannon
- Inf. Sci.
- 1993

An edge grammar is a formal mechanism for representing families of related graphs (binary trees, hypercubes, meshes, etc.). Given an edge grammar, larger graphs in the family are derived from simple basis graphs using edge rewriting rules. A drawback to many graph grammars is that they cannot represent some important, highly regular graph families such as… (More)