Fixed-Parameter Linear-Time Algorithms for NP-hard Graph and Hypergraph Problems Arising in Industrial Applications

Released on by Bevern, René van
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  • Fixed-Parameter Linear-Time Algorithms for NP-hard Graph and Hypergraph Problems Arising in Industrial Applications Book Detail

  • Author : Bevern, René van
  • Release Date : 2014-10-01
  • Publisher : Universitätsverlag der TU Berlin
  • Genre : Mathematics
  • Pages : 229
  • ISBN 13 : 379832705X
  • File Size : 1,1 MB
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Fixed-Parameter Linear-Time Algorithms for NP-hard Graph and Hypergraph Problems Arising in Industrial Applications by Bevern, René van PDF Summary

Book Description: This thesis aims for the development of efficient algorithms to exactly solve four selected NP-hard graph and hypergraph problems arising in the fields of scheduling, steel manufactoring, software engineering, radio frequency allocation, computer-aided circuit design, and social network analysis. NP-hard problems presumably cannot be solved exactly in a running time growing only polynomially with the input size. In order to still solve the considered problems efficiently, this thesis develops linear-time data reduction and fixed-parameter linear-time algorithms—algorithms that can be proven to run in linear time if certain parameters of the problem instances are constant. Besides proving linear worst-case running times, the efficiency of most of the developed algorithms is evaluated experimentally. Moreover, the limits of fixed-parameter linear-time algorithms and provably efficient and effective data reduction are shown. Diese Dissertation beschäftigt sich mit der Entwicklung effizienter Algorithmen zur exakten Lösung vier ausgewählter NP-schwerer Probleme aus der Ablaufplanung, Stahlverarbeitung, Softwaretechnik, Frequenzzuteilung, aus der computergestützten Hardwareentwicklung und der Analyse sozialer Netzwerke. NP-schwere Probleme können vermutlich nicht optimal in einer polynomiell mit der Eingabegröße wachsenden Zeit gelöst werden. Um sie dennoch effizient zu lösen, entwickelt diese Arbeit Linearzeitdatenreduktionsalgorithmen und Festparameter-Linearzeitalgorithmen – Algorithmen, die beweisbar in Linearzeit laufen, wenn bestimmte Parameter der Probleminstanzen konstant sind. Hierbei wird nicht nur bewiesen, dass die entwickelten Algorithmen in Linearzeit laufen, es findet zusätzlich eine experimentelle Evaluation der meisten der entwickelten Algorithmen statt. Ferner werden die Grenzen von Festparameter-Linearzeitalgorithmen und beweisbar effizienter und effektiver Datenreduktion aufgezeigt.

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Dualities in graphs and digraphs

Dualities in graphs and digraphs

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In this thesis we describe dualities in directed as well as undirected graphs based on tools such as width-parameters, obstructions and substructures. We mainly