Finding All Minimum Size Separating Vertex Sets in a Graph

Coordinated Science Laboratory was formerly known as Control Systems LaboratorySemiconductor Research Corporation / 87-DP-10

Compact Representation of the Separating k-Sets of a Graph

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNational Science Foundation / ECS 8404866Joint Services Electronics Program / N00014-84-C-0149Semiconductor Research Corporation / 87-DP-10

Standardization of a Communication Middleware for High-Performance Real-Time Systems

The last several years saw an emergence of standardization activities for real-time systems including standardization of operating systems (series of POSIX standards [1]), of communication for distributed (POSIX.21 [10]) and parallel systems (MPI/RT [5]) and real-time object management (realtime CORBA [9]). This article describes the ongoing standardization work and implementation of communication middleware for high performance real-time computing. The real-time message passing interface (MPI/RT) advances the non-real-time high-performance communication standard Message Passing Interface Standard (MPI), emphasizing changes that enable and support real-time communication, and is targeted for embedded, fault-tolerant and other real-time systems. MPI/RT is the only communication middleware layer that provides guaranteed quality of service and timeliness for data transfers, is also targeted for real-time CORBA to replace RPC layer and for real-time and embedded JAVAs

On the Number of Minimum Size Separating Vertex Sets in a Graph

National Science Foundation / ECS 84-10902 and 8404866Semiconductor Research Corporation / 86-12-109Joint Services Electronics Program / JSEP N00014-84-C-0149Ope

On the Number of Minimum Size Separating Vertex Sets in a Graph

National Science Foundation / ECS 84-10902 and 8404866Semiconductor Research Corporation / 86-12-109Joint Services Electronics Program / JSEP N00014-84-C-0149Ope

Vertex Connectivity of Graphs: Algorithms and Bounds

131 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1988.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 k-sets in a k-connected 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 k-sets is not linear but quadratic in n, we have obtained a linear representation for the separating k-sets of a k-connected 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 four-connected or not. Consequently, we find all separating triplets of the graph if it is not four-connected. 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 k-sets of a k-connected 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.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

Vertex Connectivity of Graphs: Algorithms and Bounds

Coordinated Science Laboratory changed its name from Control Systems LaboratoryNational Science Foundation / ECS 8404866JSEP / N00014-84-C-0149Semiconductor Research Corporation / ECS 87-DP-109Ope

On the Embedding of Cycles in Pancake Graphs

In recent times the use of star and pancake networks as a viable interconnection scheme for parallel computers has been examined by a number of researchers. An attractive feature of these two classes of graphs is that they have sublogarithmic diameter and have a great deal of symmetry akin to the binary hypercube. In this paper we describe new algorithms for embedding: (a) Hamiltonian cycles along with ranking and unranking algorithms with respect to them, and (b) The set of cycles. The analogous problems for star graphs has been solved recently [5]

Improved algorithms for graph four-connectivity

We present a new algorithm based on open ear decomposition for testing vertex four-connectivity and for finding all separating triplets in a triconnected graph. A sequential implementation of our algorithm runs in O(n 2) time and a parallel implementation runs in O(log 2 n) time using O(n 2) processors on an ARBITRARY CRCW PRAM, where n is the number of vertices in the graph. This improves previous bounds for the problem for both the sequential and parallel cases. The sequential time bound is the best possible, to within a constant factor, if the input is specified in adjacency matrix form, or if the input graph is dense. 1