In this paper, we propose HyperFlowCutter, an algorithm for balanced hypergraph bipartitioning. It is based on minimum S-T hyperedge cuts and maximum flows. It computes a sequence of bipartitions that optimize cut size and balance in the Pareto sense, being able to trade one for the other. HyperFlowCutter builds on the FlowCutter algorithm for partitioning graphs. We propose additional features, such as handling disconnected hypergraphs, novel methods for obtaining starting S,T pairs as well as an approach to refine a given partition with HyperFlowCutter. Our main contribution is ReBaHFC, a new algorithm which obtains an initial partition with the fast multilevel hypergraph partitioner PaToH and then improves it using HyperFlowCutter as a refinement algorithm. ReBaHFC is able to significantly improve the solution quality of PaToH at little additional running time. The solution quality is only marginally worse than that of the best-performing hypergraph partitioners KaHyPar and hMETIS, while being one order of magnitude faster. Thus ReBaHFC offers a new time-quality trade-off in the current spectrum of hypergraph partitioners. For the special case of perfectly balanced bipartitioning, only the much slower plain HyperFlowCutter yields slightly better solutions than ReBaHFC, while only PaToH is faster than ReBaHFC.
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 NP-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 [H. Meyerhenke, B. Monien, S. Schamberger, Accelerating shape optimizing load balancing for parallel FEM simulations by algebraic multigrid, in: Proceedings of the 20th IEEE International Parallel and Distributed Processing Symposium, IPDPS'06, IEEE Computer Society, 2006, p. 57 (CD)], which optimizes partition shapes by a diffusive mechanism. However, it is too slow for practical use, despite its high solution quality. In this paper, besides proving that Bubble-FOS C converges towards a local optimum of a potential function, we develop a much faster method for the improvement of partitionings. This faster method called TruncCons is based on a different diffusive process, which is restricted to local areas of the graph and also contains a high degree of parallelism. By coupling TruncCons with Bubble-FOS C in a multilevel framework based on two different hierarchy construction methods, we obtain our new graph partitioning heuristic DibaP. Compared to Bubble-FOS C, DibaP shows a considerable acceleration, while retaining the positive properties of the slower algorithm. Experiments with popular benchmark graphs show that DibaP computes consistently better results than the state-of-the-art libraries METIS and JOSTLE. Moreover, with our new algorithm, we have improved the best known edge-cut values for a significant number of partitionings of six widely used benchmark graphs.  A new heuristic algorithm, PROBE_BA, which is based on the recently introduced metaheuristic paradigm population- reinforced optimization-based exploration (PROBE), is proposed for solving the Graph Partitioning Problem. The "exploration" part of PROBE_BA is implemented by using the differential-greedy algorithm of Battiti and Bertossi and a modification of the Kernighan-Lin algorithm at the heart of Bui and Moon's genetic algorithm BFS _GBA. Experiments are used to investigate properties of PROBE and show that PROBE_BA compares favorably with other solution methods based on genetic algorithms, randomized reactive tabu search, or more specialized multilevel partitioning techniques. In addition, PROBE_BA finds new best cut values for 10 of the 34 instances in Walshaw's graph partitioning archive. Graph partitioning is one of the most studied NP-complete problems. Given a graph G=(V, E) , the task is to partition the vertex set V into k disjoint subsets of about the same size, such that the number of edges with endpoints in different subsets is minimized. In this paper, we present a highly effective multilevel memetic algorithm, which integrates a new multiparent crossover operator and a powerful perturbation-based tabu search algorithm. The proposed crossover operator tends to preserve the backbone with respect to a certain number of parent individuals, i.e., the grouping of vertices which is common to all parent individuals. Extensive experimental studies on numerous benchmark instances from the graph partitioning archive show that the proposed approach, within a time limit ranging from several minutes to several hours, performs far better than any of the existing graph partitioning algorithms in terms of solution quality. The balanced graph partitioning consists in dividing the vertices of an undirected graph into a given number of subsets of approximately equal size, such that the number of edges crossing the subsets is minimized. In this work, we present a multilevel memetic algorithm for this NP-hard problem that relies on a powerful grouping recombination operator and a dedicated local search procedure. The proposed operator tends to preserve the backbone with respect to a set of parent individuals, i.e. the grouping of vertices which is same throughout each parent individual. Although our approach requires significantly longer computing time compared to some current state-of-art graph partitioning algorithms such as SCOTCH, METIS, CHACO, JOSTLE, etc., it competes very favorably with these approaches in terms of solution quality. Moreover, it easily reaches or improves on the best partitions ever reported in the literature. Graph partitioning is one of the fundamental NP-complete problems which is widely applied in many domains, such as VLSI design, image segmentation, data mining, etc. Given a graph G=(V,E), the balanced k-partitioning problem consists in partitioning the vertex set V into k disjoint subsets of about the same size, such that the number of cutting edges is minimized. In this paper, we present a multilevel algorithm for balanced partition, which integrates a powerful refinement procedure based on tabu search with periodic perturbations. Experimental evaluations on a wide collection of benchmark graphs show that the proposed approach not only competes very favorably with the two well-known partitioning packages METIS and CHACO, but also improves more than two thirds of the best balanced partitions ever reported in the literature. We introduce new lower bounds for the minimum graph bisection problem. Within a branch-and-bound framework, they enable the solution of a wide variety of instances with tens of thousands of vertices to optimality. Our algorithm compares favorably with the best previous approaches, solving long-standing open instances in minutes.