Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2003. / Includes bibliographical references (p. 32).

Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2003. / Includes bibliographical references (p. 31).

Scientists often need to know how data was derived in addition to what it is. The detailed tracking of data transformation or provenance allows result reproducibility, knowledge reuse and data analysis. Scientific workflows are increasingly being used to represent provenance as they are capable of recording complicated processes at various levels of detail. In context of knowledge reuse and sharing; search technology is of paramount importance specially considering the huge and ever increasing amount of scientific data. It is computationally hard to produce a single exact answer to the user's query due to sheer volume and complicated structure of provenance.  One solution to this difficult problem is to produce a list of candidate matches and let user select the most relevant result. Here search result presentation becomes very important as the user is required to make the final decision by looking at the workflows in the result list. Presentation of these candidate matches needs to be brief, precise, clear and revealing. This is a challenging task in case of workflows as they contain textual content as well as graphical structure. Current workflow search engines such as Yahoo Pipes! or myExperiment ignore the actual workflow specification and use metadata to create summaries. Workflows which lack metadata do not make good summaries even if they are useful and relevant as search criteria. This work investigates the possibility of creating meaningful and usable summaries or snippets based on structure and specification of workflows. We shall  (1) present relevant published work done regarding snippet building techniques (2) explain how we mapped current techniques to our work (3) describe how we identified techniques from interface design theory in order to make usable graphical interface (4) present implementation of two new algorithms for workflow graph compression and their complexity analysis (5) identify future work in our implementation and outline open research problems in snippet building field.

The traveling salesman problem is although looking very simple problem but it is an important combinatorial problem. In this thesis I have tried to find the shortest distance tour in which each city is visited exactly one time and return to the starting city. I have tried to solve traveling salesman problem using multilevel graph partitioning approach.Although traveling salesman problem itself very difficult as this problem is belong to the NP-Complete problems but I have tried my best to solve this problem using multilevel graph partitioning it also belong to the NP-Complete problems. I have solved this thesis by using the k-mean partitioning algorithm which divides the problem into multiple partitions and solving each partition separately and its solution is used to improve the overall tour by applying Lin Kernighan algorithm on it. Through all this I got optimal solution which proofs that solving traveling salesman problem through graph partition scheme is good for this NP-Problem and through this we can solved this intractable problem within few minutes.Keywords: Graph Partitioning Scheme, Traveling Salesman Problem.

A graph is called star extremal if its fractional chromatic number is equal to its circular chromatic number. Given integers n,k,k' such that 1<=k<=k'<=n/2,the circulant graph G(n,S_k,k') has vertex set [n]={0,1,2,...,n-1} in which i~j if k<=|i-j|<=k' or n-k'<= |i-j|<=n-k. It was known that for n=q(k+k')+r,where 0<=r <k+k', if k'>=5/4k,then G(n,S_k,k') is star extremal. In the thesis, we prove that if k'>=7/6k and q>=4, then G(n,S_k,k') is star extremal.

In this thesis, we focus on the study of dependent arcs of acyclic orientations of graphs. Given an acyclic orientation D of G, Edelman cite{West} defined an arc to be {em dependent} if its reversal creates a cycle in D; otherwise, it is independent. Let d(D) and i(D) be the numbers of dependent arcs and independent arcs in D, respectively. And, let d_{max}(G)(d_{min}(G)) and i_{max}(G) (i_{min}(G)) be the maximum (minimum) numbers of dependent arcs and independent arcs over all acyclic orientations of G, respectively. Edelman cite{Fisher} showed that if G is connected, then d_{max}(G)=||G||-|G|+1. A graph G is said to satisfy the {em interpolation property} (or G is fully orientable) if $G$ has an acyclic orientation with exactly k dependent arcs for every k with d_{min}(G) leq k leq d_{max}(G). West established the interpolation property for complete bipartite graphs cite{West}. We obtain the minimum numbers of dependent arcs of the outerplane graphs and show that the outerplane graphs satisfy the interpolation property. Let N(G) be the set { i(D)| D is an acyclic orientation of G }. N(G) is called the independent-arc spectra of G. For complete k-partite graphs G, we obtain i_{max}(G) and discuss the independent-arc spectra for some classes. On the other hand, we consider the cover problem. A cover graph is the underlying graph of the Hasse diagram of a finite partially ordered set. The cover problem is that whether a given graph is a cover graph. It is easy to see that a graph G is a cover graph if and only if d_{min}(G)=0. We show that the generalized Mycielski graphs M_m(C_{2t+1}) of an odd cycle, Kneser graphs KG(n,k), and Schrijver graphs SG(n,k) are not cover graphs when m geq 1, t geq 1, k geq 3 and n geq 2k+2.

In state-of-the-art software library, such as Standard Template Library (STL) , they support a number of data models, for example, set, map, sequence, etc. Since graph data processing is widely used in combinatorial processing and optimization programs, in this research, we designed software implementation of a condition-based graph structure recognition method. This design consists of four kinds of condition functions specific to graph structures, control functions of structure recognition operation flow, and programming interface to facilitate programs writing various efficient graph structure recognition programs. We implemented a software library of this graph structure recognition method to support program design containing graph data and processing.

Design reuse and effective design integration is an important ways to increase design productivity. It is thus an important subject to develop, integrate and reuse design libraries provided by different designers. In this thesis, we developed software design of an instance graph expansion that can expand attribute composition graph instance from attribute composition graph schema. Designer can then effectively construct design organizations for application designs, and perform design reuse in real designs.

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 142-147).

Thesis (M.S.)--West Virginia University, 2002. / Title from document title page. Document formatted into pages; contains iii, 27 p. Includes abstract. Includes bibliographical references (p. 26-27).