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## Mixed Integer Programming and Graph Algorithms for Engineering Problems

Vortragende/r (Mitwirkende/r) Helmut Gräb 0000004343 4 SWS Wintersemester 2022/23 Englisch Siehe TUMonline

### Lernziele

After accomplishing this module, students are able to construct abstract models (e.g. graphs) for commonly-seen engineering problems, and apply algorithms or mathematical modeling methods to solve the problems systematically. In particular, students are able to analyze the problem space and solution space for a given engineering problem and understand that a small variance of the problem formulation can cause a significant change to the methodology. In addition, with a given method, students are able to evaluate its time complexity and measure its solution quality.

### Beschreibung

Content covered in this course: - Physical modeling, mixed integer linear programming (MILP), time complexity - Graph: vertex, edge, directed, degree, cyclic, planarity - Tree: binary search tree, MILP sort, quick sort, heaps - Distance-oriented graph: MILP shortest path, Dijkstra, A*, MILP spanning tree, Kruskal, MILP steiner tree, MILP planar routing - Conflict-oriented graph: vertex coloring, edge coloring, maximum independent set - Graph partition: max-flow min-cut, clustering - Set: set covering, exact covering - Scheduling and binding: time slot modeling, non-uniform time slot

### Inhaltliche Voraussetzungen

Fundamental programming knowledge

### Lehr- und Lernmethoden

Students learn the content of this course by attending the lectures and the tutorials. While the lectures focus on teaching the theories, the tutorials focus on consolidating students’ knowledge by applying learnt models and methods to solve varying problems. Both the lectures and tutorials are held in a teacher-centered style, but the students are always encouraged to interact with the lecturer and the tutor, especially when the students have different ideas regarding the models or algorithms.

### Studien-, Prüfungsleistung

The examination will be in written form, the duration is 75 minutes. The students will demonstrate their capability to construct abstract models for commonly-seen engineering problems at given examples. They will show that they can select and apply appropriate solution algorithms and derive the corresponding mathematical constraints and objectives. They will also show that they can analyze the algorithm efficiency as well as the result quality.

### Empfohlene Literatur

The following literatures are recommended: - Applied Mathematical Programming; Bradley, Hax, and Magnanti; Addison-Wesley 1977. - Introduction to Algorithms; Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein; The MIT Press 2009. - Introduction to Graph Theory; Douglas B. West; Pearson 2000.

## Vollständiges Lehrangebot

Bachelorbereich: BSc-EI, MSE, BSEDE

 WS SS Diskrete Mathematik für Ingenieure (BSEI, EI00460) Discrete Mathematics for Engineers (BSEDE ) (Schlichtmann) (Januar) WS SS Entwurf digitaler Systeme mit VHDL u. System C (BSEI, EI0690) (Ecker) SS Entwurfsverfahren für integrierte Schaltungen (MSE, EI43811) (Schlichtmann) WS Methoden der Unternehmensführung (BSEI, EI0481) (Weigel) WS Praktikum System- und Schaltungstechnik (BSEI, EI0664) (Schlichtmann et al.) SS Schaltungssimulation (BSEI, EI06691) (Gräb/Schlichtmann)

Masterbereich: MSc-EI, MSCE, ICD

 SS Advanced Topics in Communication Electronics (MSCE, MSEI, EI79002) WS Electronic Design Automation (MSCE, MSEI, EI70610) (B. Li, Tseng) WS Design Methodology and Automation (ICD) (Schlichtmann) (Nov) WS SS Machine Learning: Methods and Tools (MSCE, MSEI, EI71040) (Ecker) WS SS SS Mathematical Methods of Circuit Design (MSCE, MSEI, EI74042) (Gräb) Simulation and Optimization of Analog Circuits (ICD) (Gräb) (Mai) WS Mixed Integer Programming and Graph Algorithms in Engineering Problems (MSCE, MSEI, EI71059) (Tseng) WS SS Numerische Methoden der Elektrotechnik (MSEI, EI70440) (Schlichtmann oder Gräb) WS WS SS Seminar VLSI-Entwurfsverfahren (MSEI, EI7750) (Schlichtmann/Müller-Gritschneder) Seminar on Topics in Electronic Design Automation (MSCE, EI77502) (Schlichtmann/Müller-Gritschneder) WS SS Synthesis of Digital Systems (MSCE, MSEI, EI70640) (Müller-Gritschneder) WS Testing Digital Circuits (MSCE, MSEI, EI50141) (Otterstedt) WS Timing of Digital Circuits (MSCE, MSEI, EI70550) (B. Li, Zhang) WS SS VHDL System Design Laboratory (MSCE, MSEI, EI7403) (Schlichtmann)

`MSE: Munich School of Engineering (TUM)`

BSEDE`: Bachelor of Science in Electronics and Data Engineering`` (TUM-Asia)`

`ICD: Master of Science in Integrated Circuit Design (TUM-Asia)`

`MSCE: Master of Science in Communications Engineering (TUM)`

`MSEI: Master of Science in Elektrotechnik und Informationstechnik`

`BSEI: Bachelor of Science in Elektrotechnik und Informationstechnik`

Aktuelle Infos zur Lehre/Current information on teaching: https://www.tum.de/die-tum/aktuelles/coronavirus/studium/, www.ei.tum.de