Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

PT-Scotch: A tool for efficient parallel graph ordering

The parallel ordering of large graphs is a difficult problem, because on the one hand minimum degree algorithms do not parallelize well, and on the other hand the obtainment of high quality orderings with the nested dissection algorithm requires efficient graph bipartitioning heuristics, the best sequential implementations of which are also hard to parallelize. This paper presents a set of algorithms, implemented in the PT-Scotch software package, which allows one to order large graphs in parallel, yielding orderings the quality of which is only slightly worse than the one of state-of-the-art sequential algorithms. Our implementation uses the classical nested dissection approach but relies on several novel features to solve the parallel graph bipartitioning problem. Thanks to these improvements, PT-Scotch produces consistently better orderings than ParMeTiS on large numbers of processors

FPGA-based implementation of parallel graph partitioning

Graph partitioning is a very important application that can be found in numerous areas, from finite element methods to data processing and VLSI circuit design. Many algorithms have been developed to solve this problem. Of special interest is multilevel graph partitioning that provides a very efficient solution. This method can also be parallelized and implemented on various multiprocessor architectures. Unfortunately, the target of such implementations is often unavailable high-end multiprocessor systems. Here a parallel version of this method for an in-house developed multiprocessor system is implemented on an FPGA. The system designed provides a cost-effective solution. The design is based on two Altera soft IP Nios processors. They are synchronized using shared locks. Also, they communicate information by writing messages into buffers. These buffers are also implemented with shared memory. The design was tested for various graph sizes. The speedup was not attractive for the small graphs but becomes much better as the size of the graph increases. A speedup up to 22% was achieved compared to the single processor design. Larger graphs could yield better speedups. The quality of the partitions produced was also close to the numbers achieved by a single processor. Balance constraints were forced on the partitions and the variations were within 2% of the optimal ones

Open Problems in (Hyper)Graph Decomposition

Large networks are useful in a wide range of applications. Sometimes problem instances are composed of billions of entities. Decomposing and analyzing these structures helps us gain new insights about our surroundings. Even if the final application concerns a different problem (such as traversal, finding paths, trees, and flows), decomposing large graphs is often an important subproblem for complexity reduction or parallelization. This report is a summary of discussions that happened at Dagstuhl seminar 23331 on "Recent Trends in Graph Decomposition" and presents currently open problems and future directions in the area of (hyper)graph decomposition

Different approaches to community detection

A precise definition of what constitutes a community in networks has remained elusive. Consequently, network scientists have compared community detection algorithms on benchmark networks with a particular form of community structure and classified them based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different reasons for why we would want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community detection. This problem-driven classification is useful in applied network science, where it is important to select an appropriate algorithm for the given purpose. Moreover, highlighting the different approaches to community detection also delineates the many lines of research and points out open directions and avenues for future research.Comment: 14 pages, 2 figures. Written as a chapter for forthcoming Advances in network clustering and blockmodeling, and based on an extended version of The many facets of community detection in complex networks, Appl. Netw. Sci. 2: 4 (2017) by the same author

Web-site-based partitioning techniques for efficient parallelization of the PageRank computation

Cataloged from PDF version of article.Web search engines use ranking techniques to order Web pages in query results. PageRank is an important technique, which orders Web pages according to the linkage structure of the Web. The efficiency of the PageRank computation is important since the constantly evolving nature of the Web requires this computation to be repeated many times. PageRank computation includes repeated iterative sparse matrix-vector multiplications. Due to the enormous size of the Web matrix to be multiplied, PageRank computations are usually carried out on parallel systems. However, efficiently parallelizing PageRank is not an easy task, because of the irregular sparsity pattern of the Web matrix. Graph and hypergraphpartitioning-based techniques are widely used for efficiently parallelizing matrixvector multiplications. Recently, a hypergraph-partitioning-based decomposition technique for fast parallel computation of PageRank is proposed. This technique aims to minimize the communication overhead of the parallel matrix-vector multiplication. However, the proposed technique has a high prepropocessing time, which makes the technique impractical. In this work, we propose 1D (rowwise and columnwise) and 2D (fine-grain and checkerboard) decomposition models using web-site-based graph and hypergraph-partitioning techniques. Proposed models minimize the communication overhead of the parallel PageRank computations with a reasonable preprocessing time. The models encapsulate not only the matrix-vector multiplication, but the overall iterative algorithm. Conducted experiments show that the proposed models achieve fast PageRank computation with low preprocessing time, compared with those in the literature.Cevahir, AliM.S

Partitioning of Arterial Tree for Parallel Decomposition of Hemodynamic Calculations

AbstractModeling of fluid mechanics for the vascular system is of great value as a source of knowledge about development, progression, and treatment of cardiovascular disease. Full three-dimensional simulation of blood flow in the whole human body is a hard computational problem. We discuss parallel decomposition of blood flow simulation as a graph partitioning problem. The detailed model of full human arterial tree and some simpler geometries are discussed. The effectiveness of coarse-graining as well as pure spectral approaches is studied. Published data can be useful for development of parallel hemodynamic applications as well as for estimation of their effectiveness and scalability