Browsing by Subject "Multilevel graph partitioning"

Now showing 1 - 3 of 3

Open Access
An effective model to decompose linear programs for parallel solution
(Springer, 1996-08) Pınar, Ali; Aykanat, Cevdet
Although inherent parallelism in the solution of block angulax Linear Programming (LP) problems has been exploited in many research works, the literature that addresses decomposing constraint matrices into block angular form for parallel solution is very rare and recent. We have previously proposed hypergraph models, which reduced the problem to the hypergraph partitioning problem. However, the quality of the results reported were limited due to the hypergraph partitioning tools we have used. Very recently, multilevel graph partitioning heuristics have been proposed leading to very successful graph partitioning tools; Chaco and Metis. In this paper, we propose an effective graph model to decompose matrices into block angular form, which reduces the problem to the well-known graph partitioning by vertex separator problem. We have experimented the validity of our proposed model with various LP problems selected from NETLIB and other sources. The results are very attractive both in terms of solution quality and running times. © Springer-Verlag Berlin Heidelberg 1996.
Open Access
Fast shared-memory streaming multilevel graph partitioning
(Elsevier, 2020-09-12) Jafari, N.; Selvitopi, O.; Aykanat, Cevdet
A fast parallel graph partitioner can benefit many applications by reducing data transfers. The online methods for partitioning graphs have to be fast and they often rely on simple one-pass streaming algorithms, while the offline methods for partitioning graphs contain more involved algorithms and the most successful methods in this category belong to the multilevel approaches. In this work, we assess the feasibility of using streaming graph partitioning algorithms within the multilevel framework. Our end goal is to come up with a fast parallel offline multilevel partitioner that can produce competitive cutsize quality. We rely on a simple but fast and flexible streaming algorithm throughout the entire multilevel framework. This streaming algorithm serves multiple purposes in the partitioning process: a clustering algorithm in the coarsening, an effective algorithm for the initial partitioning, and a fast refinement algorithm in the uncoarsening. Its simple nature also lends itself easily for parallelization. The experiments on various graphs show that our approach is on the average up to 5.1x faster than the multi-threaded MeTiS, which comes at the expense of only 2x worse cutsize.
Open Access
Multilevel cluster ensembling for histopathological image segmentation
(2011) Şimşek, Ahmet Çağrı
In cancer diagnosis and grading, histopathological examination of tissues by pathologists is accepted as the gold standard. However, this procedure has observer variability and leads to subjectivity in diagnosis. In order to overcome such problems, computational methods which use quantitative measures are proposed. These methods extract mathematical features from tissue images assuming they are composed of homogeneous regions and classify images. This assumption is not always true and segmentation of images before classification is necessary. There are methods to segment images but most of them are proposed for generic images and work on the pixel-level. Recently few algorithms incorporated medical background knowledge into segmentation. Their high level feature definitions are very promising. However, in the segmentation step, they use region growing approaches which are not very stable and may lead to local optima. In this thesis, we present an efficient and stable method for the segmentation of histopathological images which produces high quality results. We use existing high level feature definitions to segment tissue images. Our segmentation method significantly improves the segmentation accuracy and stability, compared to existing methods which use the same feature definition. We tackle image segmentation problem as a clustering problem. To improve the quality and the stability of the clustering results, we combine different clustering solutions. This approach is also known as cluster ensembles. We formulate the clustering problem as a graph partitioning problem. In order to obtain diverse and high quality clustering results quickly, we made modifications and improvements on the well-known multilevel graph partitioning scheme. Our method clusters medically meaningful components in tissue images into regions and obtains the final segmentation. Experiments showed that our multilevel cluster ensembling approach performed significantly better than existing segmentation algorithms used for generic and tissue images. Although most of the images used in experiments, contain noise and artifacts, the proposed algorithm produced high quality results.