Recent Advances in Graph Partitioning

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

Scalable High-Quality Graph and Hypergraph Partitioning

The balanced hypergraph partitioning problem (HGP) asks for a partition of the node set of a hypergraph into $k$ blocks of roughly equal size, such that an objective function defined on the hyperedges is minimized. In this work, we optimize the connectivity metric, which is the most prominent objective function for HGP. The hypergraph partitioning problem is NP-hard and there exists no constant factor approximation. Thus, heuristic algorithms are used in practice with the multilevel scheme as the most successful approach to solve the problem: First, the input hypergraph is coarsened to obtain a hierarchy of successively smaller and structurally similar approximations. The smallest hypergraph is then initially partitioned into $k$ blocks, and subsequently, the contractions are reverted level-by-level, and, on each level, local search algorithms are used to improve the partition (refinement phase). In recent years, several new techniques were developed for sequential multilevel partitioning that substantially improved solution quality at the cost of an increased running time. These developments divide the landscape of existing partitioning algorithms into systems that either aim for speed or high solution quality with the former often being more than an order of magnitude faster than the latter. Due to the high running times of the best sequential algorithms, it is currently not feasible to partition the largest real-world hypergraphs with the highest possible quality. Thus, it becomes increasingly important to parallelize the techniques used in these algorithms. However, existing state-of-the-art parallel partitioners currently do not achieve the same solution quality as their sequential counterparts because they use comparatively weak components that are easier to parallelize. Moreover, there has been a recent trend toward simpler methods for partitioning large hypergraphs that even omit the multilevel scheme. In contrast to this development, we present two shared-memory multilevel hypergraph partitioners with parallel implementations of techniques used by the highest-quality sequential systems. Our first multilevel algorithm uses a parallel clustering-based coarsening scheme, which uses substantially fewer locking mechanisms than previous approaches. The contraction decisions are guided by the community structure of the input hypergraph obtained via a parallel community detection algorithm. For initial partitioning, we implement parallel multilevel recursive bipartitioning with a novel work-stealing approach and a portfolio of initial bipartitioning techniques to compute an initial solution. In the refinement phase, we use three different parallel improvement algorithms: label propagation refinement, a highly-localized direct $k$-way FM algorithm, and a novel parallelization of flow-based refinement. These algorithms build on our highly-engineered partition data structure, for which we propose several novel techniques to compute accurate gain values of node moves in the parallel setting. Our second multilevel algorithm parallelizes the $n$-level partitioning scheme used in the highest-quality sequential partitioner KaHyPar. Here, only a single node is contracted on each level, leading to a hierarchy with approximately $n$ levels where $n$ is the number of nodes. Correspondingly, in each refinement step, only a single node is uncontracted, allowing a highly-localized search for improvements. We show that this approach, which seems inherently sequential, can be parallelized efficiently without compromises in solution quality. To this end, we design a forest-based representation of contractions from which we derive a feasible parallel schedule of the contraction operations that we apply on a novel dynamic hypergraph data structure on-the-fly. In the uncoarsening phase, we decompose the contraction forest into batches, each containing a fixed number of nodes. We then uncontract each batch in parallel and use highly-localized versions of our refinement algorithms to improve the partition around the uncontracted nodes. We further show that existing sequential partitioning algorithms considerably struggle to find balanced partitions for weighted real-world hypergraphs. To this end, we present a technique that enables partitioners based on recursive bipartitioning to reliably compute balanced solutions. The idea is to preassign a small portion of the heaviest nodes to one of the two blocks of each bipartition and optimize the objective function on the remaining nodes. We integrated the approach into the sequential hypergraph partitioner KaHyPar and show that our new approach can compute balanced solutions for all tested instances without negatively affecting the solution quality and running time of KaHyPar. In our experimental evaluation, we compare our new shared-memory (hyper)graph partitioner Mt-KaHyPar to $25$ different graph and hypergraph partitioners on over $800$ (hyper)graphs with up to two billion edges/pins. The results indicate that already our fastest configuration outperforms almost all existing hypergraph partitioners with regards to both solution quality and running time. Our highest-quality configuration ($n$-level with flow-based refinement) achieves the same solution quality as the currently best sequential partitioner KaHyPar, while being almost an order of magnitude faster with ten threads. In addition, we optimize our data structures for graph partitioning, which improves the running times of both multilevel partitioners by almost a factor of two for graphs. As a result, Mt-KaHyPar also outperforms most of the existing graph partitioning algorithms. While the shared-memory graph partitioner KaMinPar is still faster than Mt-KaHyPar, its produced solutions are worse by $10\%$ in the median. The best sequential graph partitioner KaFFPa-StrongS computes slightly better partitions than Mt-KaHyPar (median improvement is $1\%$), but is more than an order of magnitude slower on average

Exploiting Latent Features of Text and Graphs

As the size and scope of online data continues to grow, new machine learning techniques become necessary to best capitalize on the wealth of available information. However, the models that help convert data into knowledge require nontrivial processes to make sense of large collections of text and massive online graphs. In both scenarios, modern machine learning pipelines produce embeddings --- semantically rich vectors of latent features --- to convert human constructs for machine understanding. In this dissertation we focus on information available within biomedical science, including human-written abstracts of scientific papers, as well as machine-generated graphs of biomedical entity relationships. We present the Moliere system, and our method for identifying new discoveries through the use of natural language processing and graph mining algorithms. We propose heuristically-based ranking criteria to augment Moliere, and leverage this ranking to identify a new gene-treatment target for HIV-associated Neurodegenerative Disorders. We additionally focus on the latent features of graphs, and propose a new bipartite graph embedding technique. Using our graph embedding, we advance the state-of-the-art in hypergraph partitioning quality. Having newfound intuition of graph embeddings, we present Agatha, a deep-learning approach to hypothesis generation. This system learns a data-driven ranking criteria derived from the embeddings of our large proposed biomedical semantic graph. To produce human-readable results, we additionally propose CBAG, a technique for conditional biomedical abstract generation

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Abusing a hypergraph partitioner for unweighted graph partitioning

Abstract. We investigate using the Mondriaan matrix partitioner for unweighted graph partitioning in the communication volume and edgecut metrics. By converting the unweighted graphs to appropriate matrices, we measure Mondriaan’s performance as a graph partitioner for the 10th DIMACS challenge on graph partitioning and clustering. We find that Mondriaan can effectively be used as a graph partitioner: w.r.t. the edge-cut metric, Mondriaan’s average results are within 21 % of the best known results as listed in Chris Walshaw’s partitioning archive.