High quality graph partitioning

Sanders, Peter; Schulz, Christian

doi:10.1090/conm/588/11700

Cited by 34 publications

(22 citation statements)

References 114 publications

(303 reference statements)

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“…Sanders and Schulz [SS11,SS13a] introduce a max-flow min-cut based technique to improve the edge cut of a given bipartition (and generalize this to k-partitioning by successively looking at pairs of blocks that are adjacent in the quotient graph). The algorithm constructs an s-t flow problem by growing an area around the given boundary nodes/cut edges.…”

Section: Flow Based Improvementmentioning

confidence: 99%

“…The Global Path Algorithm (GPA) [MS07] is a synthesis of Greedy and Path Growing achieving somewhat higher quality in practice and is not a performance bottleneck in many cases. GPA is therefore used in KaHIP [SS11, SS,SS13b]. Linear time algorithms with better approximation guarantee are available [PS04, DH05, MS07, DPS11] and the simplest of them seem practical [MS07].…”

Section: Contracting a Matchingmentioning

confidence: 99%

“…The software packages DibaP and its MPI-parallel variant PDibaP by Meyerhenke [MMS09a,Mey12] implement the Bubble framework using diffusion; DibaP also uses AMG-based techniques for coarsening and solving linear systems arising in the diffusive approach. Recently, Sanders and Schulz [SS,SS13b] released the GP package KaHIP (Karlsruhe High Quality Partitioning) which implements for example flow-based methods, more-localized local searches and several parallel and sequential meta-heuristics. KaHIP scored most of the points in the GP subchallenge of the 10th DIMACS Implementation Challenge [BMSW13] and currently holds most of the entries in the Walshaw Benchmark.…”

Section: Software Toolsmentioning

confidence: 99%

See 2 more Smart Citations

Recent Advances in Graph Partitioning

Buluç

Meyerhenke

Safro

et al. 2016

Lecture Notes in Computer Science

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413

300

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Section: Flow Based Improvementmentioning

confidence: 99%

Section: Contracting a Matchingmentioning

confidence: 99%

Section: Software Toolsmentioning

confidence: 99%

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Recent Advances in Graph Partitioning

Buluç

Meyerhenke

Safro

et al. 2016

Lecture Notes in Computer Science

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413

300

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show abstract

“…We use this machine in Section 4.1 to solve the largest instances in our collection. We used the fastsocial configuration of the KaHIP v0.6 graph partitioning package [37] to obtain graph partitions and node separators necessary for the combine operations of the evolutionary algorithm. Ex- …”

Section: Experimental Evaluationmentioning

confidence: 99%

Finding Near-Optimal Independent Sets at Scale

Lamm¹,

Sanders²,

Schulz³

et al. 2015

2016 Proceedings of the Eighteenth Workshop on Algorithm Engineering and Experiments (ALENEX)

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The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs, which typically take exponential time to solve exactly using the best-known exact algorithms. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in huge sparse networks. A recent exact algorithm has shown that large networks can be solved exactly by employing a branch-and-reduce technique that recursively kernelizes the graph and performs branching. However, one major drawback of their algorithm is that, for huge graphs, branching still can take exponential time. 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. We show that identifying and removing vertices likely to be in large independent sets opens up the reduction space-which not only speeds up the computation of large independent sets drastically, but also enables us to compute high-quality independent sets on much larger instances than previously reported in the literature.

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“…Graph Contraction. We use the graphs considered by KaFFPa for partitioning graphs from the 10'th DIMACS Implementation Challenge [22].…”

Section: Implementations and Experimentsmentioning

confidence: 99%

Efficient Parallel and External Matching

Birn

Osipov

Sanders

et al. 2013

Euro-Par 2013 Parallel Processing

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Abstract. We show that a simple algorithm for computing a matching on a graph runs in a logarithmic number of phases incurring work linear in the input size. The algorithm can be adapted to provide efficient algorithms in several models of computation, such as PRAM, External Memory, MapReduce and distributed memory models. Our CREW PRAM algorithm is the first O log 2 n time, linear work algorithm. Our experimental results indicate the algorithm's high speed and efficiency combined with good solution quality.

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High quality graph partitioning

Cited by 34 publications

References 114 publications

Recent Advances in Graph Partitioning

Recent Advances in Graph Partitioning

Finding Near-Optimal Independent Sets at Scale

Efficient Parallel and External Matching

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