Search Results for author: Christian Schulz

Found 27 papers, 11 papers with code

Recent Advances in Fully Dynamic Graph Algorithms

no code implementations22 Feb 2021 Kathrin Hanauer, Monika Henzinger, Christian Schulz

In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms.

Data Structures and Algorithms

Buffered Streaming Graph Partitioning

no code implementations18 Feb 2021 Marcelo Fonseca Faraj, Christian Schulz

In this work, we make a first step to close this gap by presenting an algorithm that computes high-quality partitions of huge graphs using a single machine with little memory.

graph partitioning Data Structures and Algorithms

Decidability for Sturmian words

no code implementations16 Feb 2021 Philipp Hieronymi, Dun Ma, Reed Oei, Luke Schaeffer, Christian Schulz, Jeffrey Shallit

We show that the first-order theory of Sturmian words over Presburger arithmetic is decidable.

Logic in Computer Science Combinatorics Logic

Practical Fully Dynamic Minimum Cut Algorithms

1 code implementation13 Jan 2021 Monika Henzinger, Alexander Noe, Christian Schulz

We present a practically efficient algorithm for maintaining a global minimum cut in large dynamic graphs under both edge insertions and deletions.

Data Structures and Algorithms

Efficient Process-to-Node Mapping Algorithms for Stencil Computations

1 code implementation19 May 2020 Sascha Hunold, Konrad von Kirchbach, Markus Lehr, Christian Schulz, Jesper Larsson Träff

An extensive experimental evaluation on several HPC machines shows that our algorithms are up to two orders of magnitude faster in running time than a (sequential) high-quality general graph mapping tool, while obtaining similar results in communication performance.

Distributed, Parallel, and Cluster Computing

Faster Parallel Multiterminal Cuts

1 code implementation24 Apr 2020 Monika Henzinger, Alexander Noe, Christian Schulz

We give an improved branch-and-bound solver for the multiterminal cut problem, based on the recent work of Henzinger et al.. We contribute new, highly effective data reduction rules to transform the graph into a smaller equivalent instance.

Data Structures and Algorithms Combinatorics

Engineering Data Reduction for Nested Dissection

3 code implementations23 Apr 2020 Wolfgang Ost, Christian Schulz, Darren Strash

Many applications rely on time-intensive matrix operations, such as factorization, which can be sped up significantly for large sparse matrices by interpreting the matrix as a sparse graph and computing a node ordering that minimizes the so-called fill-in.

Data Structures and Algorithms Combinatorics

Finding All Global Minimum Cuts In Practice

2 code implementations17 Feb 2020 Monika Henzinger, Alexander Noe, Christian Schulz, Darren Strash

We present a practically efficient algorithm that finds all global minimum cuts in huge undirected graphs.

Data Structures and Algorithms

Multilevel Acyclic Hypergraph Partitioning

no code implementations6 Feb 2020 Merten Popp, Sebastian Schlag, Christian Schulz, Daniel Seemaier

The acyclic hypergraph partitioning problem is to partition the hypernodes of a directed acyclic hypergraph into a given number of blocks of roughly equal size such that the corresponding quotient graph is acyclic while minimizing an objective function on the partition.

hypergraph partitioning

Scalable Graph Algorithms

no code implementations30 Nov 2019 Christian Schulz

Designing and evaluating scalable graph algorithms to handle these data sets is a crucial task on the road to understanding the underlying systems.

Shared-Memory Branch-and-Reduce for Multiterminal Cuts

no code implementations12 Aug 2019 Monika Henzinger, Alexander Noe, Christian Schulz

We introduce the fastest known exact algorithm~for~the multiterminal cut problem with k terminals.

Data Structures and Algorithms Distributed, Parallel, and Cluster Computing

Faster Support Vector Machines

no code implementations20 Aug 2018 Sebastian Schlag, Matthias Schmitt, Christian Schulz

The time complexity of support vector machines (SVMs) prohibits training on huge data sets with millions of data points.

General Classification

Shared-memory Exact Minimum Cuts

2 code implementations16 Aug 2018 Monika Henzinger, Alexander Noe, Christian Schulz

State-of-the-art algorithms like the algorithm of Padberg and Rinaldi or the algorithm of Nagamochi, Ono and Ibaraki identify edges that can be contracted to reduce the graph size such that at least one minimum cut is maintained in the contracted graph.

Data Structures and Algorithms

Memetic Graph Clustering

no code implementations20 Feb 2018 Sonja Biedermann, Monika Henzinger, Christian Schulz, Bernhard Schuster

It is common knowledge that there is no single best strategy for graph clustering, which justifies a plethora of existing approaches.

Graph Clustering

Communication-free Massively Distributed Graph Generation

1 code implementation20 Oct 2017 Daniel Funke, Sebastian Lamm, Peter Sanders, Christian Schulz, Darren Strash, Moritz von Looz

Analyzing massive complex networks yields promising insights about our everyday lives.

Distributed, Parallel, and Cluster Computing Data Structures and Algorithms Social and Information Networks

Memetic Multilevel Hypergraph Partitioning

2 code implementations GECCO 2018 2018 Robin Andre, Sebastian Schlag, Christian Schulz

Hypergraph partitioning has a wide range of important applications such as VLSI design or scientific computing.

Data Structures and Algorithms

Evolutionary Acyclic Graph Partitioning

no code implementations25 Sep 2017 Orlando Moreira, Merten Popp, Christian Schulz

Directed graphs are widely used to model data flow and execution dependencies in streaming applications.

graph partitioning

Practical Minimum Cut Algorithms

2 code implementations21 Aug 2017 Monika Henzinger, Alexander Noe, Christian Schulz, Darren Strash

The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges.

Data Structures and Algorithms Distributed, Parallel, and Cluster Computing

Graph Partitioning with Acyclicity Constraints

no code implementations3 Apr 2017 Orlando Moreira, Merten Popp, Christian Schulz

In this work, we show that this more constrained version of the graph partitioning problem is NP-complete and present heuristics that achieve a close approximation of the optimal solution found by an exhaustive search for small problem instances and much better scalability for larger instances.

graph partitioning

Distributed Evolutionary k-way Node Separators

no code implementations6 Feb 2017 Peter Sanders, Christian Schulz, Darren Strash, Robert Williger

Computing high quality node separators in large graphs is necessary for a variety of applications, ranging from divide-and-conquer algorithms to VLSI design.

k-way Hypergraph Partitioning via n-Level Recursive Bisection

1 code implementation ALENEX 2016 2017 Sebastian Schlag, Vitali Henne, Tobias Heuer, Henning Meyerhenke, Peter Sanders, Christian Schulz

We develop a multilevel algorithm for hypergraph partitioning that contracts the vertices one at a time.

Data Structures and Algorithms

Finding Near-Optimal Independent Sets at Scale

no code implementations2 Sep 2015 Sebastian Lamm, Peter Sanders, Christian Schulz, Darren Strash, Renato F. Werneck

To avoid this problem, we recursively choose vertices that are likely to be in a large independent set (using an evolutionary approach), then further kernelize the graph.

n-Level Hypergraph Partitioning

1 code implementation4 May 2015 Vitali Henne, Henning Meyerhenke, Peter Sanders, Sebastian Schlag, Christian Schulz

Using label propagation local search is several times faster than hMetis and gives better quality than PaToH for a VLSI benchmark set.

Data Structures and Algorithms G.2.2; D.1.4

Incorporating Road Networks into Territory Design

no code implementations29 Apr 2015 Nitin Ahuja, Matthias Bender, Peter Sanders, Christian Schulz, Andreas Wagner

Given a set of basic areas, the territory design problem asks to create a predefined number of territories, each containing at least one basic area, such that an objective function is optimized.

graph partitioning

Graph Partitioning for Independent Sets

no code implementations5 Feb 2015 Sebastian Lamm, Peter Sanders, Christian Schulz

The core innovations of the algorithm are very natural combine operations based on graph partitioning and local search algorithms.

graph partitioning

Parallel Graph Partitioning for Complex Networks

no code implementations18 Apr 2014 Henning Meyerhenke, Peter Sanders, Christian Schulz

This paper addresses this problem by parallelizing and adapting the label propagation technique originally developed for graph clustering.

Graph Clustering graph partitioning

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