14279 - Network Optimization Modulübersicht

Module Number: 14279
Module Title:Network Optimization
  Netzwerkoptimierung
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. habil. Köhler, Ekkehard
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: On special announcement
Credits: 8
Learning Outcome:The students
  • know important terms, relationships and algorithms from the field of network optimization
  • are able to analyse and prove the correctness and runtime of the algorithms
  • are able to apply concepts from the field of network optimization to solve practical problems
  • have gained experience in independent scientific work using network optimization topics as examples.
Contents:
  • basic concepts of network optimization
  • shortest paths
  • network flow algorithms, network flows with minimum cost, k-splittable flows
  • time-dependent/dynamic network flows (flows over time)
  • maximum matching and weighted matching, matching algorithms
  • social responsibility of researchers in the context of network optimization
Recommended Prerequisites:Knowledge of the contents of modules
  • 11101: Lineare Algebra und analytische Geometrie I
  • 12868: Algorithmische Diskrete Mathematik
or of modules
  • 11112: Mathematik IT-1 (Diskrete Mathematik)
  • 11113: Mathematik IT-2 (Lineare Algebra)
Mandatory Prerequisites:None
Forms of Teaching and Proportion:
  • Lecture / 4 Hours per Week per Semester
  • Exercise / 2 Hours per Week per Semester
  • Self organised studies / 150 Hours
Teaching Materials and Literature:
  • Korte, Vygen: Combinatorial Optimization – Theory and Algorithms, Springer
  • Cook, Cunningham, Pulleyblank, Schrijver: Combinatorial Optimization. Wiley.
  • Ahuja, Magnanti, Orlin: Network Flows: Theory and Applications, Prentice Hall
Module Examination:Prerequisite + Final Module Examination (MAP)
Assessment Mode for Module Examination:

Prerequisite:

  • Successful completion of homework (fortnightly) and successful completion of tests (approx. 4 tests of 15-30 minutes each, written during the lecture period)

Final module examination:

  • Written examination, 90 min. OR
  • Oral examination, 30 min.

During the first class meeting, notice will be given on how the prerequisite will be structured and whether the examination will be in written or oral form.

Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:None
Part of the Study Programme:
  • Master (research-oriented) / Angewandte Mathematik / PO 2019 - 1. SÄ 2021
  • Master (research-oriented) / Artificial Intelligence / PO 2022 - 1. SÄ 2024
  • Master (research-oriented) / Informatik / PO 2008 - 3. SÄ 2024
  • Bachelor (research-oriented) / Künstliche Intelligenz / PO 2022
  • Master (research-oriented) / Mathematical Data Science / PO 2025
  • Master (research-oriented) / Mathematics / PO 2025
  • Bachelor (research-oriented) / Mathematik / PO 2023
  • Bachelor (research-oriented) - Co-Op Programme with Practical Placement / Mathematik - dual / PO 2023
  • Bachelor (research-oriented) / Wirtschaftsmathematik / PO 2023
  • Bachelor (research-oriented) - Co-Op Programme with Practical Placement / Wirtschaftsmathematik - dual / PO 2023
Remarks:
  • study programme Mathematics M.Sc.: Compulsory elective module in the complex „Optimization”
  • study programme Mathematical Data Science M.Sc.: Compulsory elective module in the complex „Advanced Mathematical Methods in Data Science”
  • study programme Artificial Intelligence M.Sc.: Compulsory elective module in the complex „Knowledge Acquisition, Representation, and Processing”
  • study programme Angewandte Mathematik M.Sc.: Compulsory elective module in the complex „Optimierung”
  • study programme Mathematik B.Sc.: Compulsory elective module in the complex „Vertiefung”, in limited extend
  • study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in the complex „Vertiefung”, in limited extend
  • study programme Künstliche Intelligenz B.Sc.: Compulsory elective module in the complex „Wissensakquise, -repräsentation und -verarbeitung”
  • study programme Informatik M.Sc.: Compulsory elective module in the complex „Mathematik” or in field of application „Mathematik”
Module Components:
  • Lecture: Network Optimization
  • Accompanying exercise
  • Related examination
Components to be offered in the Current Semester: