#### Title

Some optimally adaptive parallel graph algorithms on erew pram model

#### Abstract

The study of graph algorithms is an important area of research in computer science, since graphs offer useful tools to model many real-world situations. The commercial availability of parallel computers have led to the development of efficience parallel graph algorithms. Using an exclusive-read and exclusive-write (EREW) parallel random access marchine (PRAM) as the computation model with a fixed number of processors, we design and analyze parallel algorithms for seven undirected graph problems, such as, connected components, spanning forest, fundamental cycle set, bridges, bipartieness, assignment problems, and apporximate vertex coloring. For all but the last two problems, the input data structure is an unordered list of edges, and divide-and-conquer is the paradigm for designing algorithms. One of the algorithms to solve the assignment problem makes use of an appropriate variant of dynamic programming strategy. An elegant data structure, called the adjacency list matrix, used in a vertex-coloring algorithm avoids the sequential nature of linked adjacency lists. Each of the proposed algorithms achieves optimal speedup, choosing an optimal granularity (thus exploiting maximum parallelism) which depends on the density or the number of vertices of the given graph. The processor-(time)2 product has been identified as a useful parameter to measure the cost-effectiveness of a parallel algorithm. We derive a lower bound on this measure for each of our algorithms.

#### Notes

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#### Graduation Date

1988

#### Semester

Summer

#### Advisor

Deo, Narsingh

#### Degree

Doctor of Philosophy (Ph.D.)

#### College

College of Arts and Sciences

#### Department

Computer Science

#### Format

#### Language

English

#### Length of Campus-only Access

None

#### Access Status

Doctoral Dissertation (Open Access)

#### Subjects

Arts and Sciences--Dissertations, Academic; Dissertations, Academic--Arts and Sciences

#### STARS Citation

Das, Sajal K., "Some optimally adaptive parallel graph algorithms on erew pram model" (1988). *Retrospective Theses and Dissertations*. 4270.

http://stars.library.ucf.edu/rtd/4270