Programming by Optimisation Meets Parameterised Algorithmics: A Case Study for Cluster Editing

Inspired by methods and theoretical results from parameterised algorithmics, we improve the state of the art in solving Cluster Editing, a prominent NP-hard clustering problem with applications in computational biology and beyond. In particular, we demonstrate that an extension of a certain preproce...

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Bibliographic Details
Published inLearning and Intelligent Optimization Vol. 8994; pp. 43 - 58
Main Authors Hartung, Sepp, Hoos, Holger H.
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2015
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Algorithms & data structures
Artificial intelligence
Cluster Graph
Computer programming / software development
Search Tree
Synthetic Dataset
Training Instance
Tree Cluster
Online AccessGet full text
ISBN9783319190839
3319190830
ISSN0302-9743
1611-3349
DOI10.1007/978-3-319-19084-6_5

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Summary:Inspired by methods and theoretical results from parameterised algorithmics, we improve the state of the art in solving Cluster Editing, a prominent NP-hard clustering problem with applications in computational biology and beyond. In particular, we demonstrate that an extension of a certain preprocessing algorithm, called the (k+1) $$(k+1)$$ -data reduction rule in parameterised algorithmics, embedded in a sophisticated branch-&-bound algorithm, improves over the performance of existing algorithms based on Integer Linear Programming (ILP) and branch-&-bound. Furthermore, our version of the (k+1) $$(k+1)$$ -rule outperforms the theoretically most effective preprocessing algorithm, which yields a 2k-vertex kernel. Notably, this 2k-vertex kernel is analysed empirically for the first time here. Our new algorithm was developed by integrating Programming by Optimisation into the classical algorithm engineering cycle – an approach which we expect to be successful in many other contexts.
Bibliography:Original Abstract: Inspired by methods and theoretical results from parameterised algorithmics, we improve the state of the art in solving Cluster Editing, a prominent NP-hard clustering problem with applications in computational biology and beyond. In particular, we demonstrate that an extension of a certain preprocessing algorithm, called the (k+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k+1)$$\end{document}-data reduction rule in parameterised algorithmics, embedded in a sophisticated branch-&-bound algorithm, improves over the performance of existing algorithms based on Integer Linear Programming (ILP) and branch-&-bound. Furthermore, our version of the (k+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k+1)$$\end{document}-rule outperforms the theoretically most effective preprocessing algorithm, which yields a 2k-vertex kernel. Notably, this 2k-vertex kernel is analysed empirically for the first time here. Our new algorithm was developed by integrating Programming by Optimisation into the classical algorithm engineering cycle – an approach which we expect to be successful in many other contexts.
Sepp Hartung—Major parts of this work were done during a research visit of SH at the University of British Columbia in Vancouver (Canada), supported by a “DFG Forschungsstipendium” (HA 7296/1-1).
ISBN:9783319190839
3319190830
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-319-19084-6_5