University of Colorado Denver University of Colorado Denver College of Liberal Arts and Sciences
Alexander Engau

Http: Faculty & Staff Directory

Email: Alexander [dot] Engau
[at] UCDenver [dot] edu

Phone: [+1] (303) 315-1719
Fax: [+1] (303) 315-1704

Office: SCB 4223
1201 Larimer Street
Denver, Colorado 80204

Mail: UCD Math & Stats
C Box 170, PO Box 173364
Denver, CO 80217-3364

Alexander Engau

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Alexander Engau, Assistant Professor

Math 5490 Network Flows

Below, please find the most recent description of this course as taught during the Spring of 2010. An updated syllabus, class materials and lectures notes will be posted before the course is offered the next time, but early enough for students to decide if they want to enroll. Thank you for your patience.

Mathematical Sciences Course Catalog Description

Infrequent. Begins with the classical min-cost flow problem, defined on an ordinary network. Other problems, such as shortest path, are also shown in this class. Both theory and algorithms are presented. Extensions include generalized networks, nonlinear costs, fixed charges, multi-commodity flows, and additional applications, such as in communications networks. (3 credit hours)

Instructor Description

Over the last sixty years, the study of network flows has led to some of the most appealing and useful results in optimization and applied mathematics, in general. Initially motivated by problems from industrial operations research and developed in close relationship to linear programming, for which network structures can often be exploited very efficiently yielding solution algorithms with significantly reduced computational complexity, network flows have since then become a fascinating topic by themselves that attracts researchers and involves concepts from a wide variety of different areas including but not limited to operations research and graph theory, combinatorics and optimization, mathematical programming and computer science, and many other sciences and engineering disciplines. The lasting impact and truly interdisciplinary nature of this field is also reflected in its many successful applications by both researchers and practitioners to some of today's most challenging problems ranging from water distribution and transportation over telecommunication and integrated circuits to bioinformatics and cancer radiation therapy.

In this introductory graduate course, we will explore the foundations, models, and methods of network flows with a strong emphasis on the stimulating interplay between theory and practice as well as inherently hard combinatorial and computational optimization problems and the efficient design and implementation of algorithms. Keeping the course prerequisites at a minimum level, however, students are expected to show a great deal of flexibility and willingness to read and learn supporting concepts quickly and independently if necessary, including LaTeX, basic data structures, and programming competence in a compiled or interpreted object-oriented programming language (recommended and supported by the instructor are C, C++, Fortran, Java, or Python). [From the textbook's preface: ``Although students require some mathematical maturity - for example, a basic understanding of proof techniques - and some familiarity with computer programming, they need not be specialists in mathematics, computer science, or optimization.''] In addition to these new or refreshed computer skills, the successful student's rewards will include a solid understanding of how to find shorter paths to greater flows at smaller costs, combined with practical knowledge of some fundamental network modeling techniques and culminating in the opportunity to extend her or his networking, communication, and writing skills in a final team project.