Memetic Multilevel Hypergraph Partitioning

Hypergraph partitioning has a wide range of important applications such as VLSI design or scientific computing. With focus on solution quality, we develop the first multilevel memetic algorithm to tackle the problem. Key components of our contribution are new effective multilevel recombination and mutation operations that provide a large amount of diversity. We perform a wide range of experiments on a benchmark set containing instances from application areas such VLSI, SAT solving, social networks, and scientific computing. Compared to the state-of-the-art hypergraph partitioning tools hMetis, PaToH, and KaHyPar, our new algorithm computes the best result on almost all instances

High-Quality Hypergraph Partitioning

This dissertation focuses on computing high-quality solutions for the NP-hard balanced hypergraph partitioning problem: Given a hypergraph and an integer $k$, partition its vertex set into $k$ disjoint blocks of bounded size, while minimizing an objective function over the hyperedges. Here, we consider the two most commonly used objectives: the cut-net metric and the connectivity metric. Since the problem is computationally intractable, heuristics are used in practice - the most prominent being the three-phase multi-level paradigm: During coarsening, the hypergraph is successively contracted to obtain a hierarchy of smaller instances. After applying an initial partitioning algorithm to the smallest hypergraph, contraction is undone and, at each level, refinement algorithms try to improve the current solution. With this work, we give a brief overview of the field and present several algorithmic improvements to the multi-level paradigm. Instead of using a logarithmic number of levels like traditional algorithms, we present two coarsening algorithms that create a hierarchy of (nearly) $n$ levels, where $n$ is the number of vertices. This makes consecutive levels as similar as possible and provides many opportunities for refinement algorithms to improve the partition. This approach is made feasible in practice by tailoring all algorithms and data structures to the $n$-level paradigm, and developing lazy-evaluation techniques, caching mechanisms and early stopping criteria to speed up the partitioning process. Furthermore, we propose a sparsification algorithm based on locality-sensitive hashing that improves the running time for hypergraphs with large hyperedges, and show that incorporating global information about the community structure into the coarsening process improves quality. Moreover, we present a portfolio-based initial partitioning approach, and propose three refinement algorithms. Two are based on the Fiduccia-Mattheyses (FM) heuristic, but perform a highly localized search at each level. While one is designed for two-way partitioning, the other is the first FM-style algorithm that can be efficiently employed in the multi-level setting to directly improve $k$-way partitions. The third algorithm uses max-flow computations on pairs of blocks to refine $k$-way partitions. Finally, we present the first memetic multi-level hypergraph partitioning algorithm for an extensive exploration of the global solution space. All contributions are made available through our open-source framework KaHyPar. In a comprehensive experimental study, we compare KaHyPar with hMETIS, PaToH, Mondriaan, Zoltan-AlgD, and HYPE on a wide range of hypergraphs from several application areas. Our results indicate that KaHyPar, already without the memetic component, computes better solutions than all competing algorithms for both the cut-net and the connectivity metric, while being faster than Zoltan-AlgD and equally fast as hMETIS. Moreover, KaHyPar compares favorably with the current best graph partitioning system KaFFPa - both in terms of solution quality and running time

A niching memetic algorithm for simultaneous clustering and feature selection

Clustering is inherently a difficult task, and is made even more difficult when the selection of relevant features is also an issue. In this paper we propose an approach for simultaneous clustering and feature selection using a niching memetic algorithm. Our approach (which we call NMA_CFS) makes feature selection an integral part of the global clustering search procedure and attempts to overcome the problem of identifying less promising locally optimal solutions in both clustering and feature selection, without making any a priori assumption about the number of clusters. Within the NMA_CFS procedure, a variable composite representation is devised to encode both feature selection and cluster centers with different numbers of clusters. Further, local search operations are introduced to refine feature selection and cluster centers encoded in the chromosomes. Finally, a niching method is integrated to preserve the population diversity and prevent premature convergence. In an experimental evaluation we demonstrate the effectiveness of the proposed approach and compare it with other related approaches, using both synthetic and real data

Evolutionary n-level hypergraph partitioning with adaptive coarsening

Hypergraph partitioning is an NP-hard problem that occurs in many computer science applications where it is necessary to reduce large problems into a number of smaller, computationally tractable sub-problems. Current techniques use a multilevel approach wherein an initial partitioning is performed after compressing the hypergraph to a predetermined level. This level is typically chosen to produce very coarse hypergraphs in which heuristic algorithms are fast and effective. This article presents a novel memetic algorithm which remains effective on larger initial hypergraphs. This enables the exploitation of information that can be lost during coarsening and results in improved final solution quality. We use this algorithm to present an empirical analysis of the space of possible initial hypergraphs in terms of its searchability at different levels of coarsening. We find that the best results arise at coarsening levels unique to each hypergraph. Based on this, we introduce an adaptive scheme that stops coarsening when the rate of information loss in a hypergraph becomes non-linear and show that this produces further improvements. The results show that we have identified a valuable role for evolutionary algorithms within the current state-of-the-art hypergraph partitioning framework

VLSI Design

This book provides some recent advances in design nanometer VLSI chips. The selected topics try to present some open problems and challenges with important topics ranging from design tools, new post-silicon devices, GPU-based parallel computing, emerging 3D integration, and antenna design. The book consists of two parts, with chapters such as: VLSI design for multi-sensor smart systems on a chip, Three-dimensional integrated circuits design for thousand-core processors, Parallel symbolic analysis of large analog circuits on GPU platforms, Algorithms for CAD tools VLSI design, A multilevel memetic algorithm for large SAT-encoded problems, etc

Recent Advances in Graph Partitioning

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