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Im Werk suchen
Classification and approximation of geometric location problems / Sascha Brauer, M. Sc. ; [Prof. Dr. Johannes Blömer, Paderborn University, Prof. Dr. Heiko Röglin, University of Bonn]. Paderborn, 2019
Inhalt
Introduction
Outline
Publication Notes
Fundamentals
Remarks on Notation
Problem Statements
Facility Location
Clustering
Hard Clustering
Soft Clustering
Discussion
Further Analysis
Related Work
Classification and Impossibility
Classical Hardness
Basics of Computational Complexity
Discrete Clustering Problems
Related Work
Towards a Classification of DFKM
Construction
Correctness
Parameterized Hardness of DFRKM
DKM is Hard in Fixed Dimensions
Complexity of Single-Swap Local Search
Polynomial Local Search
Related Work
Completeness of MUFL/SingleSwap
Construction
Correctness
Tightness
Completeness of DKM/SingleSwap
Construction
Correctness and Tightness
Embedding
Completeness of DFKM/SingleSwap
Construction
Correctness, Tightness, and Embedding
Non-Representability of Solutions
Algebraic Basics
Related Work
Unsolvability of Optimal FKM Solutions
Implementation of the Finite Taylor Grid
Approaching Hard Problems
Approximation Algorithms
Related Work
A PTAS for FKM With Fixed Number of Clusters
From Soft to Hard Clusters
A Sampling Based Approach
Solving Small FRKM Instances
Coresets
Related Work
Small Coresets for FKM
From Weak to Strong via Non-Negligibility
Weak Coresets for Non-Negligible Solutions
Applying FKM Coresets
Correctness of our Weak Coreset Algorithm
Future Research
Bibliography
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