Social Network Analysis Hansen and Smith

Total Page:16

File Type:pdf, Size:1020Kb

Social Network Analysis Hansen and Smith Social Network Analysis Hansen and Smith Heather Huynh What is Social Network Analysis? • Social network analysis (SNA) is the systematic study of collections of social relationships, which consist of social actors implicitly or explicitly connected to one another What is Social Network Analysis? • Entities joined together by relationships • Relationships used to measure changes in patterns of relationships and workflow that are not visible in more common metrics (count of users, rates of resource usage) • This perspective distinguishes between simple population growth and the development of important social structures within that population • Social networks existed long before internet, but social networking services like Facebook and LinkedIn, support the creation of large, distributed, real-time social networks History of Social Network Analysis Foundational phase (18th century – 1970s) • Focus on defining terms and establishing the necessary mathematical graph theory foundation • Erdos and Renyi: formal mechanisms for generating random graphs that made statistical tests of network properties viable • Mereno, Warner, and Mayo: applied formal mathematical methods to describe, analyze, and visualize networks (“psychological geography”, “sociometrics”, and “sociograms” • Milgram: Six degrees of separation • Granovetter: showed ”weak ties” much better source of new jobs than “strong ties” => value of social network approach History of Social Network Analysis Computational phase (1970s – mid-1990s) • Creation and systematic use of computational tools and methods • SNA as a methodological approach which leveraged the new capabilities of computers to analyze and visualize networks in novel ways • By mid 1990’s, SNA well-respected approach in numerous fields (organizational behavior, social psychology, communication networks, epidemiology, etc.) • “SNA Bible”: Social Network Analysis: Methods and Applications by Stanley Wasserman and Katherine Faust • Summarizes decades of research into a coherent mathematical framework, identifying core metrics and techniques used by SNA tools and researchers today History of Social Network Analysis Network Deluge Phase (current) • People outside academics now use SNA techniques like corporations, governments, and nonprofits • Lots of tools created: Pajek, SNAP, NodeXL, and Gephi • Mining of data from Facebook, IM services, other social media channels • Techniques pioneered for inferring friendship networks from data captured via mobile devices Goals of Social Network Analysis for HCI Researchers Goal 1: Inform the design and implementation of new CSCW systems • SNA can characterize the social structure of a population of intended users of a new CSCW system before the system is put in place • Research has shown mapping the social network of members of a large organization can help design social and technical strategies to facilitate more effective information flow • Use SNA to identify, educate, and leverage those who will influence the maximal spread of adoption through the network to assure its rapid, effective use or help others to know to to use a new technology • Data for these analyses may come from network surveys or from existing data sources such as communication exchanges • Individuals with unique and important network positions can be identified and interviewed or observed as part of a comprehensive contextual inquiry process Goal 2: Understand and improve current CSCW systems • SNA of data from existing CSCW systems can illustrate the ways current features are utilized by users in different locations in the network • SNA may help community managers understand what is happening in large scale communities where reading through even a meaningful sample of the content is not feasible • Example: knowing about “Theorist” subgroup on Lostpedia allowed designers to develop tools to meet needs of subgroup like page templates Goal 2: Understand and improve current CSCW systems • Several studies have developed recommendations for improving virtual reality games based on network analysis of guild networks and social interaction patterns • Network methods that identify subpopulations can offer customized interfaces and services to different groups of users, using the history of other users in the same group as a guide • Education researchers have shown how students use different social features to interact within small groups and class-wide, with implications for system design and instructional strategies Goal 3: Evaluate the impact of CSCW system on social relationships • Evaluate the impact of a CSCW system on the existing social structure of a population • Measuring the changes in aggregate and person-specific network metrics can help systematically evaluate the effectiveness of such systems • Evaluation can also be performed to assess the impact of a specific feature or social intervention (e.g. effect of an online “icebreaker”) • Education researchers are also using network data to identify students using online course management systems that may be in need of extra support • Data for evaluation assessments may come from offline network surveys, existing communications captured over time, or system usage data • For large-scale evaluations, SNA can be used as a part of a mixed method approach (like identifying who to interview in a network) Goal 4: Design novel CSCW systems and features using SNA methods • SNA can be used as input to new CSCW systems and features • A growing number of research prototypes and innovative products leverage SNA metrics and methods to provide enhanced functionality • Work done for identifying political tendencies of followers of different news agencies on Twitter which could be used for tools that personalize news, etc • Recent work has explored the theoretical and practical design implications for promoting “social translucence” within directed social network systems, like Twitter, where users can only see a portion of the social space (unlike chatrooms and discussion forums) Goal 5: Answer fundamental social science questions • “Computational social science”: a set of techniques that use computational techniques to address core social science questions in novel ways • So much data automatically captured via social media -> provide new opportunities to test hypotheses and theories at a much larger scale than previously possible • Predicting strength of ties from social media interactions or mobile phone usage patterns can support further large-scale studies of social networks by reducing the need for raw data collection from users • Work done by professors and students here at UIUC! Performing Social Network Analysis Identify Goals and Research Questions • Essential that analysts hone in on a few critical goals and turn them into specific research questions • Within HCI, SNA is often exploratory in nature and analysts may only recognize what they are looking for once they see it • Often questions are refined after preliminary analysis of initial data Types of Questions SNA answers • Questions about Individual Social actors • Find prominent individuals; use “centrality metrics” or “equivalence metrics” • Questions about overall network structure • Focus on overall distribution instead of position of individuals; use “community detection algorithms” (network clustering) and variety of “aggregate network metrics” • Questions about Network Dynamics and Flows • How networks change over time and how information, etc flows through networks (information diffusion) Collect Data • Sources of data: • Raw data from system usage (i.e. database or XML files) [Medium-high] • Network survey [High] • Application Programming Interfaces (APIs) [Medium-high] • Screen scraping [Medium-high] • Network analysis importer tools (can import from 3rd party sites) [Easy] • Existing datasets, like Enron email network and Amazon related items (more at http://snap.stanford.edu/data/) [Easy] • Type of social network will determine how to appropriately analyze, visualize, and interpret data • Type determined by underlying phenomena it represents (i.e. Facebook vs. Twitter relationships) Networks can be… • Directed vs. Undirected: directed = not necessarily reciprocated; undirected = always mutual • Weighted vs. Unweighted: weighted = edges have values associated with them; unweighted = edges either exist or do not • Multiplex networks: includes multiple types of edges (could be analyzed as a multiplex network or multiple distinct networks) • Unimodal vs. multimodal: unimodal networks = include only one type of node (i.e. all nodes represent people); multimodal networks = include more than one type of node, can have subset called bimodal or bipartite networks (which can be transformed into unimodal networks) Networks can be… • Partial networks: “egocentric network” = includes a single node called an “ego” and all nodes that ego is directly connected to (called ”alters”); adding connections adds on degrees; can also sample a large network to find some network boundary to create partial networks • A single socio-technical system has many types of networks; the choice of which to focus on depends on the goals of your study Representing Network Data • Network data can be represented in three primary ways: • Edge lists – adjacency lists • Matrices – adjacency matrix • Graphs – visually show nodes as vertices and edges as lines connecting them • Usually include additional attribute data to describe nodes and/or edges • In practice, several common network file formats: .graphml, .net, .gml, .dot,
Recommended publications
  • Creating & Connecting: Research and Guidelines on Online Social
    CREATING & CONNECTING//Research and Guidelines on Online Social — and Educational — Networking NATIONAL SCHOOL BOARDS ASSOCIATION CONTENTS Creating & Connecting//The Positives . Page 1 Online social networking Creating & Connecting//The Gaps . Page 4 is now so deeply embedded in the lifestyles of tweens and teens that Creating & Connecting//Expectations it rivals television for their atten- and Interests . Page 7 tion, according to a new study Striking a Balance//Guidance and Recommendations from Grunwald Associates LLC for School Board Members . Page 8 conducted in cooperation with the National School Boards Association. Nine- to 17-year-olds report spending almost as much time About the Study using social networking services This study was made possible with generous support and Web sites as they spend from Microsoft, News Corporation and Verizon. watching television. Among teens, The study was comprised of three surveys: an that amounts to about 9 hours a online survey of 1,277 nine- to 17-year-old students, an online survey of 1,039 parents and telephone inter- week on social networking activi- views with 250 school district leaders who make deci- ties, compared to about 10 hours sions on Internet policy. Grunwald Associates LLC, an a week watching TV. independent research and consulting firm that has conducted highly respected surveys on educator and Students are hardly passive family technology use since 1995, formulated and couch potatoes online. Beyond directed the study. Hypothesis Group managed the basic communications, many stu- field research. Tom de Boor and Li Kramer Halpern of dents engage in highly creative Grunwald Associates LLC provided guidance through- out the study and led the analysis.
    [Show full text]
  • Networkx: Network Analysis with Python
    NetworkX: Network Analysis with Python Salvatore Scellato Full tutorial presented at the XXX SunBelt Conference “NetworkX introduction: Hacking social networks using the Python programming language” by Aric Hagberg & Drew Conway Outline 1. Introduction to NetworkX 2. Getting started with Python and NetworkX 3. Basic network analysis 4. Writing your own code 5. You are ready for your project! 1. Introduction to NetworkX. Introduction to NetworkX - network analysis Vast amounts of network data are being generated and collected • Sociology: web pages, mobile phones, social networks • Technology: Internet routers, vehicular flows, power grids How can we analyze this networks? Introduction to NetworkX - Python awesomeness Introduction to NetworkX “Python package for the creation, manipulation and study of the structure, dynamics and functions of complex networks.” • Data structures for representing many types of networks, or graphs • Nodes can be any (hashable) Python object, edges can contain arbitrary data • Flexibility ideal for representing networks found in many different fields • Easy to install on multiple platforms • Online up-to-date documentation • First public release in April 2005 Introduction to NetworkX - design requirements • Tool to study the structure and dynamics of social, biological, and infrastructure networks • Ease-of-use and rapid development in a collaborative, multidisciplinary environment • Easy to learn, easy to teach • Open-source tool base that can easily grow in a multidisciplinary environment with non-expert users
    [Show full text]
  • Dynamic Social Network Analysis: Present Roots and Future Fruits
    Dynamic Social Network Analysis: Present Roots and Future Fruits Ms. Nancy K Hayden Project Leader Defense Threat Reduction Agency Advanced Systems and Concepts Office Stephen P. Borgatti, Ronald L. Breiger, Peter Brooks, George B. Davis, David S. Dornisch, Jeffrey Johnson, Mark Mizruchi, Elizabeth Warner July 2009 DEFENSE THREAT REDUCTION AGENCY •ADVANCED SYSTEMS AND CONCEPTS OFFICE REPORT NUMBER ASCO 2009 009 The mission of the Defense Threat Reduction Agency (DTRA) is to safeguard America and its allies from weapons of mass destruction (chemical, biological, radiological, nuclear, and high explosives) by providing capabilities to reduce, eliminate, and counter the threat, and mitigate its effects. The Advanced Systems and Concepts Office (ASCO) supports this mission by providing long-term rolling horizon perspectives to help DTRA leadership identify, plan, and persuasively communicate what is needed in the near term to achieve the longer-term goals inherent in the agency’s mission. ASCO also emphasizes the identification, integration, and further development of leading strategic thinking and analysis on the most intractable problems related to combating weapons of mass destruction. For further information on this project, or on ASCO’s broader research program, please contact: Defense Threat Reduction Agency Advanced Systems and Concepts Office 8725 John J. Kingman Road Ft. Belvoir, VA 22060-6201 [email protected] Or, visit our website: http://www.dtra.mil/asco/ascoweb/index.htm Dynamic Social Network Analysis: Present Roots and Future Fruits Ms. Nancy K. Hayden Project Leader Defense Threat Reduction Agency Advanced Systems and Concepts Office and Stephen P. Borgatti, Ronald L. Breiger, Peter Brooks, George B. Davis, David S.
    [Show full text]
  • Examples of Online Social Network Analysis Social Networks
    Examples of online social network analysis Social networks • Huge field of research • Data: mostly small samples, surveys • Multiplexity Issue of data mining • Longitudinal data McPherson et al, Annu. Rev. Sociol. (2001) New technologies • Email networks • Cellphone call networks • Real-world interactions • Online networks/ social web NEW (large-scale) DATASETS, longitudinal data New laboratories • Social network properties – homophily – selection vs influence • Triadic closure, preferential attachment • Social balance • Dunbar number • Experiments at large scale... 4 Another social science lab: crowdsourcing, e.g. Amazon Mechanical Turk Text http://experimentalturk.wordpress.com/ New laboratories Caveats: • online links can differ from real social links • population sampling biases? • “big” data does not automatically mean “good” data 7 The social web • social networking sites • blogs + comments + aggregators • community-edited news sites, participatory journalism • content-sharing sites • discussion forums, newsgroups • wikis, Wikipedia • services that allow sharing of bookmarks/favorites • ...and mashups of the above services An example: Dunbar number on twitter Fraction of reciprocated connections as a function of in- degree Gonçalves et al, PLoS One 6, e22656 (2011) Sharing and annotating Examples: • Flickr: sharing of photos • Last.fm: music • aNobii: books • Del.icio.us: social bookmarking • Bibsonomy: publications and bookmarks • … •“Social” networks •“specialized” content-sharing sites •Users expose profiles (content) and links
    [Show full text]
  • Evolving Networks and Social Network Analysis Methods And
    DOI: 10.5772/intechopen.79041 ProvisionalChapter chapter 7 Evolving Networks andand SocialSocial NetworkNetwork AnalysisAnalysis Methods and Techniques Mário Cordeiro, Rui P. Sarmento,Sarmento, PavelPavel BrazdilBrazdil andand João Gama Additional information isis available atat thethe endend ofof thethe chapterchapter http://dx.doi.org/10.5772/intechopen.79041 Abstract Evolving networks by definition are networks that change as a function of time. They are a natural extension of network science since almost all real-world networks evolve over time, either by adding or by removing nodes or links over time: elementary actor-level network measures like network centrality change as a function of time, popularity and influence of individuals grow or fade depending on processes, and events occur in net- works during time intervals. Other problems such as network-level statistics computation, link prediction, community detection, and visualization gain additional research impor- tance when applied to dynamic online social networks (OSNs). Due to their temporal dimension, rapid growth of users, velocity of changes in networks, and amount of data that these OSNs generate, effective and efficient methods and techniques for small static networks are now required to scale and deal with the temporal dimension in case of streaming settings. This chapter reviews the state of the art in selected aspects of evolving social networks presenting open research challenges related to OSNs. The challenges suggest that significant further research is required in evolving social networks, i.e., existent methods, techniques, and algorithms must be rethought and designed toward incremental and dynamic versions that allow the efficient analysis of evolving networks. Keywords: evolving networks, social network analysis 1.
    [Show full text]
  • Opportunities and Challenges for Standardization in Mobile Social Networks
    Opportunities and Challenges for Standardization in Mobile Social Networks Laurent-Walter Goix, Telecom Italia [email protected] Bryan Sullivan, AT&T [email protected] Abstract This paper describes the opportunities and challenges related to the standardization of interoperable “Mobile Social Networks”. Challenges addressed include the effect of social networks on resource usage, the need for social network federation, and the needs for a standards context. The concept of Mobile Federated Social Networks as defined in the OMA SNEW specification is introduced as an approach to some of these challenges. Further specific needs and opportunities in standards and developer support for mobile social apps are described, including potentially further work in support of regulatory requirements. Finally, we conclude that a common standard is needed for making mobile social networks interoperable, while addressing privacy concerns from users & institutions as well as the differentiations of service providers. 1 INTRODUCTION Online Social Networks (OSN) are dominated by Walled Gardens that have attracted users by offering new paradigms of communication / content exchange that better fit their modern lifestyle. Issues are emerging related to data ownership, privacy and identity management and some institutions such as the European Commission have started to provide measures for controlling this. The impressive access to OSN from ever smarter mobile devices, as well as the growth of mobile- specific SN services (e.g. WhatsApp) have further stimulated the mobile industry that is already starving for new attractive services (RCS 1). In this context OMA 2 as mobile industry forum has recently promoted the SNEW specifications that can leverage network services such as user identity and native interoperability of mobile networks (the approach promoted by “federated social networks”).
    [Show full text]
  • Basics of Social Network Analysis Distribute Or
    1 Basics of Social Network Analysis distribute or post, copy, not Do Copyright ©2017 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. Chapter 1 Basics of Social Network Analysis 3 Learning Objectives zz Describe basic concepts in social network analysis (SNA) such as nodes, actors, and ties or relations zz Identify different types of social networks, such as directed or undirected, binary or valued, and bipartite or one-mode zz Assess research designs in social network research, and distinguish sampling units, relational forms and contents, and levels of analysis zz Identify network actors at different levels of analysis (e.g., individuals or aggregate units) when reading social network literature zz Describe bipartite networks, know when to use them, and what their advan- tages are zz Explain the three theoretical assumptions that undergird social networkdistribute studies zz Discuss problems of causality in social network analysis, and suggest methods to establish causality in network studies or 1.1 Introduction The term “social network” entered everyday language with the advent of the Internet. As a result, most people will connect the term with the Internet and social media platforms, but it has in fact a much broaderpost, application, as we will see shortly. Still, pictures like Figure 1.1 are what most people will think of when they hear the word “social network”: thousands of points connected to each other. In this particular case, the points represent political blogs in the United States (grey ones are Republican, and dark grey ones are Democrat), the ties indicating hyperlinks between them.
    [Show full text]
  • Social Network Analysis and Information Propagation: a Case Study Using Flickr and Youtube Networks
    International Journal of Future Computer and Communication, Vol. 2, No. 3, June 2013 Social Network Analysis and Information Propagation: A Case Study Using Flickr and YouTube Networks Samir Akrouf, Laifa Meriem, Belayadi Yahia, and Mouhoub Nasser Eddine, Member, IACSIT 1 makes decisions based on what other people do because their Abstract—Social media and Social Network Analysis (SNA) decisions may reflect information that they have and he or acquired a huge popularity and represent one of the most she does not. This concept is called ″herding″ or ″information important social and computer science phenomena of recent cascades″. Therefore, analyzing the flow of information on years. One of the most studied problems in this research area is influence and information propagation. The aim of this paper is social media and predicting users’ influence in a network to analyze the information diffusion process and predict the became so important to make various kinds of advantages influence (represented by the rate of infected nodes at the end of and decisions. In [2]-[3], the marketing strategies were the diffusion process) of an initial set of nodes in two networks: enhanced with a word-of-mouth approach using probabilistic Flickr user’s contacts and YouTube videos users commenting models of interactions to choose the best viral marketing plan. these videos. These networks are dissimilar in their structure Some other researchers focused on information diffusion in (size, type, diameter, density, components), and the type of the relationships (explicit relationship represented by the contacts certain special cases. Given an example, the study of Sadikov links, and implicit relationship created by commenting on et.al [6], where they addressed the problem of missing data in videos), they are extracted using NodeXL tool.
    [Show full text]
  • Chazen Society Fellow Interest Paper Orkut V. Facebook: the Battle for Brazil
    Chazen Society Fellow Interest Paper Orkut v. Facebook: The Battle for Brazil LAUREN FRASCA MBA ’10 When it comes to stereotypes about Brazilians – that they are a fun-loving people who love to dance samba, wear tiny bathing suits, and raise their pro soccer players to the levels of demi-gods – only one, the idea that they hold human connection in high esteem, seems to be born out by concrete data. Brazilians are among the savviest social networkers in the world, by almost all engagement measures. Nearly 80 percent of Internet users in Brazil (a group itself expected to grow by almost 50 percent over the next three years1) are engaged in social networking – a global high. And these users are highly active, logging an average of 6.3 hours on social networks and 1,220 page views per month per Internet user – a rate second only to Russia, and almost double the worldwide average of 3.7 hours.2 It is precisely this broad, highly engaged audience that makes Brazil the hotly contested ground it is today, with the dominant social networking Web site, Google’s Orkut, facing stiff competition from Facebook, the leading aggregate Web site worldwide. Social Network Services Though social networking Web sites would appear to be tools born of the 21st century, they have existed since even the earliest days of Internet-enabled home computing. Starting with bulletin board services in the early 1980s (accessed over a phone line with a modem), users and creators of these Web sites grew increasingly sophisticated, launching communities such as The WELL (1985), Geocities (1994), and Tripod (1995).
    [Show full text]
  • 2010 Nonprofit Social Network Benchmark Report
    April 2010 Nonprofit Social Network Benchmark Report www.nonprofitsocialnetworksurvey.com www.nten.org www.commonknow.com www.theport.com Introduction NTEN, Common Knowledge, and ThePort Network offer this second annual installment of the Nonprofit Social Networking Benchmark Report. This report’s objective is to provide nonprofits with insights and trends surrounding social networking technology as part of nonprofit organizations’ marketing, communications, fundraising, and program house social network services. Social networking community built on Between February 3 and March 15, 2010, a nonprofit’s own 1,173 nonprofit professionals responded to website. Term derived a survey about their organization’s use of from direct mail online social networks. house lists. Two groups of questions were posed to survey participants: commercial 1. Tells us about your use of commercial social network social networks such as Facebook, Twitter, An online community LinkedIn, and others. owned and operated by a corporation. 2. Tell us about your work building and Popular examples using social networks on your own include Facebook and websites, called house social networks . MySpace. Survey respondents represented small, medium and large nonprofits and all nonprofit segments: Arts & Culture, Association, Education, Environment & Animals, Health & Healthcare, Human Services, International, Public & Societal Benefit, Religious and others (See Appendix A for more details). www.nonprofitsocialnetworksurvey.com 1 Executive Summary Commercial Social Networks Nonprofits continued to increase their use of commercial social networks over 2009 and early 2010 with Facebook and Twitter proving to be the preferred networks. LinkedIn and YouTube held steady, but MySpace lost significant ground. The following are the key excerpts from this section: • Facebook is still used by more nonprofits than any other commercial social network with 86% of nonprofits indicating that they have a presence on this network.
    [Show full text]
  • Applying Social Network Analysis to Identify Project Critical Success Factors
    sustainability Article Applying Social Network Analysis to Identify Project Critical Success Factors Marco Nunes 1,* and António Abreu 2,* 1 Industrial Engineering Department, University of Beira Interior, 6201-001 Covilhã, Portugal 2 Mechanical Engineering Department, Polytechnic Institute of Lisbon and CTS Uninova, 1959-007 Lisbon, Portugal * Correspondence: [email protected] or [email protected] (M.N.); [email protected] (A.A.) Received: 13 January 2020; Accepted: 14 February 2020; Published: 18 February 2020 Abstract: A key challenge in project management is to understand to which extent the dynamic interactions between the different project people—through formal and informal networks of collaboration that temporarily emerge across a project´s lifecycle—throughout all the phases of a project lifecycle, influence a project’s outcome. This challenge has been a growing concern to organizations that deliver projects, due their huge impact in economic, environmental, and social sustainability. In this work, a heuristic two-part model, supported with three scientific fields—project management, risk management, and social network analysis—is proposed, to uncover and measure the extent to which the dynamic interactions of project people—as they work through networks of collaboration—across all the phases of a project lifecycle, influence a project‘s outcome, by first identifying critical success factors regarding five general project collaboration types ((1) communication and insight, (2) internal and cross collaboration, (3) know-how and power sharing, (4) clustering, and (5) teamwork efficiency) by analyzing delivered projects, and second, using those identified critical success factors to provide guidance in upcoming projects regarding the five project collaboration types.
    [Show full text]
  • Social Networks Influence Analysis
    University of North Florida UNF Digital Commons UNF Graduate Theses and Dissertations Student Scholarship 2017 Social Networks Influence Analysis Doaa Gamal University of North Florida, [email protected] Follow this and additional works at: https://digitalcommons.unf.edu/etd Part of the Computer Sciences Commons Suggested Citation Gamal, Doaa, "Social Networks Influence Analysis" (2017). UNF Graduate Theses and Dissertations. 723. https://digitalcommons.unf.edu/etd/723 This Master's Thesis is brought to you for free and open access by the Student Scholarship at UNF Digital Commons. It has been accepted for inclusion in UNF Graduate Theses and Dissertations by an authorized administrator of UNF Digital Commons. For more information, please contact Digital Projects. © 2017 All Rights Reserved SOCIAL NETWORKS INFLUENCE ANALYSIS by Doaa H. Gamal A thesis submitted to the School of Computing in partial fulfillment of the requirements for the degree of Master of Science in Computing and Information Sciences UNIVERSITY OF NORTH FLORIDA SCHOOL OF COMPUTING Spring, 2017 Copyright (©) 2017 by Doaa H. Gamal All rights reserved. Reproduction in whole or in part in any form requires the prior written permission of Doaa H. Gamal or designated representative. ii This thesis titled “Social Networks Influence Analysis” submitted by Doaa H. Gamal in partial fulfillment of the requirements for the degree of Master of Science in Computing and Information Sciences has been Approved by the thesis committee: Date Dr. Karthikeyan Umapathy Thesis Advisor and Committee Chairperson Dr. Lakshmi Goel Dr. Sandeep Reddivari Accepted for the School of Computing: Dr. Sherif A. Elfayoumy Director of the School Accepted for the College of Computing, Engineering, and Construction: Dr.
    [Show full text]