A Survey on Graph Partitioning Techniques
Santosh Nage2015
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Abstract
In real life, there are many problems like shortest path, graph coloring, travelling Salesmen problem (TSP) etc, thus providing solution to each problem is nearly or highly impossible with the help of traditional methods in reasonable amount of time. But it may be possible with the help of heuristic approach. It provides solution but don’t guarantee optimal solution. Graph partitioning problems are NP-Complete problems, partitioning graph into p-partitions using multilevel method, spectral method etc. for various purposes .Here we are studying several techniques to partition graph.
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Journal of Parallel and Distributed Computing, 2009
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Mathematical Programming, 1998
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1991
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International journal of engineering research and technology, 2013
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Benchmarking of Graph Partitioning Tools and Techniques
International Journal of Recent Technology and Engineering (IJRTE), 2019
In this paper the authors have used a systematic literature review to provide benchmarking on influencing parameters for graph partitioning tools, which is the principal contribution of the present paper. Tools are compared on the basis of parameters which will impact the performance of tool. The paper elucidates about the tools and techniques along with their features, merits and demerits and also highlighted on influencing parameters which is missing in other reviews. These techniques are analysed by identifying merits and demerits of each technique. This research paper can help the researchers to choose the appropriate tool or technique for their own partitioning problems. Also authors have suggested future research directions and anomalies for improvement in tools and techniques for Graph Partitioning.
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Graph partitioning requires the division of a graph's vertex set into k equally sized subsets s. t. some objective function is optimized. High-quality partitions are important for many applications, whose objective functions are often N P-hard to optimize. Most state-of-the-art graph partitioning libraries use a variant of the Kernighan-Lin (KL) heuristic within a multilevel framework. While these libraries are very fast, their solutions do not always meet all user requirements. Moreover, due to its sequential nature, KL is not easy to parallelize. Its use as a load balancer in parallel numerical applications therefore requires complicated adaptations. That is why we developed previously an inherently parallel algorithm, called Bubble-FOS/C (Meyerhenke et al., IPDPS'06), which optimizes partition shapes by a diusive mechanism. However, it is too slow for practical use, despite its high solution quality.
An efficient matlab algorithm for graph partitioning
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Linear and quadratic programming approaches for the general graph partitioning problem
Journal of Global Optimization, 2010
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AN APPROACH TO SOLVE GRAPH PARTITIONING PROBLEM USING GENETIC ALGORITHM
IAEME PUBLICATION, 2013
This paper addresses the problem of partitioning a graph and particular the use of the genetic algorithms for graph partitioning. It is a NP hard problem. The solution of a graph (circuit) partitioning problem is global optimum. In this practical paper solution is easy and we can easily apply genetic operator in this type of problem. One of the application of Graph partitioning in chip designing. The target of our approach is to design modular chip which can be realized with self standard IC chip if VLSI circuit can be converted into a graph and obviously we have taken into account minimum power consumption. Our approach to partition the Graph into sub Graphs and minimization of the number of cuts is our main objective. Our approach with Genetic algorithm calculates the fitness (number of cuts) and discard the solution with low fitness value. Multi way partitioning can be easily implemented if we increase number of crossover point. Fitness value achievement depends on crossover and mutation probability. We can change crossover boundary when fitness value is low in previous generation and continue until optimum result is found.
588 Graph Partitioning and Graph Clustering
2013
We present an overview over our graph partitioners KaFFPa (Karlsruhe Fast Flow Partitioner) and KaFFPaE (KaFFPa Evolutionary). KaFFPa is a multilevel graph partitioning algorithm which on the one hand uses novel local improvement algorithms based on max-flow and min-cut computations and more localized FM searches and on the other hand uses more sophisticated global search strategies transferred from multi-grid linear solvers. KaFFPaE is a distributed evolutionary algorithm to solve the Graph Partitioning Problem. KaFFPaE uses KaFFPa and provides new effective crossover and mutation operators. By combining these with a scalable communication protocol we obtain a system that is able to improve the best known partitioning results for many inputs.
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