Files in this item
Files  Description  Format 

application/pdf 8908726.pdf (5MB)  (no description provided) 
Description
Title:  Vertex Connectivity of Graphs: Algorithms and Bounds 
Author(s):  Kanevsky, Arkady 
Doctoral Committee Chair(s):  Ramachandran, V. 
Department / Program:  Computer Science 
Discipline:  Computer Science 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Computer Science 
Abstract:  This thesis concerns several problems concerning vertex connectivity of undirected graphs and presents new bounds and algorithms for these problems. We have proved that the upper bound of the number of separating triplets of a triconnected graph is ${(n  1)(n  4)\over 2}$, and it exactly matches the lower bound, which is achieved by the wheel graph. This result has been generalized to an $O(2\sp{k}{n\sp2 \over k})$ upper bound on the number of separating ksets in a kconnected graph. We have also obtained a new $\Omega(2\sp{k}{n\sp2 \over k\sp2})$ lower bound. Even though the upper bound for the number of separating ksets is not linear but quadratic in n, we have obtained a linear representation for the separating ksets of a kconnected graph. For $k = 3$ this representation is a collection of wheels, where every nonadjacent pair on the cycle of a wheel gives a separating triplet of a triconnected graph. For general k, we have obtained an $O(k\sp2 n)$ representation. We have designed a new sequential $O(n\sp2)$ algorithm for the problem of determining if the graph is fourconnected or not. Consequently, we find all separating triplets of the graph if it is not fourconnected. The algorithm has a parallel version which runs in O(log$\sp2 n$) time using $O(n\sp2)$ processors, which is also an improvement over $O(nm)$ processor count of the best previously known parallel algorithm. We have designed algorithms for generating all separating ksets of a kconnected graph. The sequential algorithm runs in $O(2\sp{k}n\sp3)$ time and parallel one runs in $O(k{\rm log}n)$ deterministic parallel time or in $O({\rm log}\sp2 n)$ randomized time using $O(4\sp{k}{n\sp6 \over k\sp2})$ processors on a CRCW PRAM. 
Issue Date:  1988 
Type:  Text 
Description:  131 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 1988. 
URI:  http://hdl.handle.net/2142/69601 
Other Identifier(s):  (UMI)AAI8908726 
Date Available in IDEALS:  20141215 
Date Deposited:  1988 
This item appears in the following Collection(s)

Dissertations and Theses  Computer Science
Dissertations and Theses from the Dept. of Computer Science 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois