#### Date of Award

1991

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Computer Science

#### First Advisor

Sitharama S. Iyengar

#### Abstract

There exist at least two models of parallel computing, namely, shared-memory and message-passing. This research addresses problems in both these types of systems, and proposes efficient parallel (Shared-Memory Model) and distributed (message-passing) algorithms for a variety of graph related computational problems. In part I, we design algorithms for three generic problems in distributed systems: set manipulation, network structure recognition and facility placement. We present optimal distributed algorithms for recognizing rectangular-mesh networks. The time and message complexity of our algorithm is linear in the number of nodes in the network. We also lay the foundation for the recognition of 2-reducible, outer-planar and cactus graphs. These algorithms have a message complexity of O(kn), where, k is the number of isolated two degree nodes in the network. We introduce the problem of reliable r-domination and design unified optimal distributed algorithms for the total, reliable and independent r-domination on trees. The time and message complexity of our algorithm is O(n), where n is the number of nodes in the tree. In the domain of set manipulation we design optimal algorithms for determining the intersection of sets in a distributed environment, where each processor is assumed to have its own set. The time and message complexity of our set intersection algorithm is O(mn), where m is the cardinality of the smallest set. In part II of our research we design optimal algorithms for r-domination and efficient parallel algorithms for the p-center problems on trees. We also present an optimal algorithm for computing the maximum independent set on intervals i the EREW-PRAM model. The r-domination problem on trees can now be solved in O(logn)time with O(n/logn) processors using the EREW-PRAM model. A parallel algorithm for range searching is developed using the concept of distributed data structures. We show that O(logn) search time can be effected for a range search on n 3-dimensional points using (2.log$\sp2n-14.logn + 8$) processors. Our algorithm can easily be generalized for the case of d-dimensional range search. (Abstract shortened with permission of author.).

#### Recommended Citation

Subbiah, Rajanarayanan, "Parallel and Distributed Algorithms for a Class of Graph-Related Computational Problems." (1991). *LSU Historical Dissertations and Theses*. 5277.

https://digitalcommons.lsu.edu/gradschool_disstheses/5277

#### Pages

167