Advanced Flow-Based Multilevel Hypergraph Partitioning

The balanced hypergraph partitioning problem is to partition a hypergraph into k disjoint blocks of bounded size such that the sum of the number of blocks connected by each hyperedge is minimized. We present an improvement to the flow-based refinement framework of KaHyPar-MF, the current state-of-the-art multilevel k-way hypergraph partitioning algorithm for high-quality solutions. Our improvement is based on the recently proposed HyperFlowCutter algorithm for computing bipartitions of unweighted hypergraphs by solving a sequence of incremental maximum flow problems. Since vertices and hyperedges are aggregated during the coarsening phase, refinement algorithms employed in the multilevel setting must be able to handle both weighted hyperedges and weighted vertices - even if the initial input hypergraph is unweighted. We therefore enhance HyperFlowCutter to handle weighted instances and propose a technique for computing maximum flows directly on weighted hypergraphs. We compare the performance of two configurations of our new algorithm with KaHyPar-MF and seven other partitioning algorithms on a comprehensive benchmark set with instances from application areas such as VLSI design, scientific computing, and SAT solving. Our first configuration, KaHyPar-HFC, computes slightly better solutions than KaHyPar-MF using significantly less running time. The second configuration, KaHyPar-HFC*, computes solutions of significantly better quality and is still slightly faster than KaHyPar-MF. Furthermore, in terms of solution quality, both configurations also outperform all other competing partitioners

PACE solver description: KaPoCE: A heuristic cluster editing algorithm

The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the heuristic cluster editing algorithm of the Karlsruhe and Potsdam Cluster Editing (KaPoCE) framework, submitted to the heuristic track of the 2021 PACE challenge

PACE Solver Description: KaPoCE: A Heuristic Cluster Editing Algorithm

The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the heuristic cluster editing algorithm of the Karlsruhe and Potsdam Cluster Editing (KaPoCE) framework, submitted to the heuristic track of the 2021 PACE challenge

Technology of Storage and Processing of Electronic Documents with Intellectual Search Properties

The technology of record, storage and processing of the texts, based on creation of integer index cycles is discussed. Algorithms of exact-match search and search similar on the basis of inquiry in a natural language are considered. The software realizing offered approaches is described, and examples of the electronic archives possessing properties of intellectual search are resulted

The New Software Package for Dynamic Hierarchical Clustering for Circles Types of Shapes

In data mining, efforts have focused on finding methods for efficient and effective cluster analysis in large databases. Active themes of research focus on the scalability of clustering methods, the effectiveness of methods for clustering complex shapes and types of data, high-dimensional clustering techniques, and methods for clustering mixed numerical and categorical data in large databases. One of the most accuracy approach based on dynamic modeling of cluster similarity is called Chameleon. In this paper we present a modified hierarchical clustering algorithm that used the main idea of Chameleon and the effectiveness of suggested approach will be demonstrated by the experimental results

Алгоритмы разбиения логических схем на подсхемы

The problem of partitioning a logical circuit into subcircuits is considered. It is of great importance when performing optimization transformations in the process of circuit synthesis. The brief review of partitioning methods and algorithms is given, and two groups of algorithms are identified: constructive and iterative one. The interpretation of a logical circuit in the form of a graph is presented. The problem of partitioning in terms of a graph-theoretic model is defined and some algorithms for solving the partitioning problem are proposed. Logic circuit functions are defined by a system of logical equations. Algorithms perform the partitioning the system of logical equations into subsystems with the restrictions of the number of input and output variables. The data structures to execute the algorithms are defined. Various types of equations connections, obtaining better solutions for partitioning are described. The problems of the use of partitioning algorithms to improve the quality of the circuit at the stage of technology-independent optimization are investigated. The results of an experimental study carried out by the BDD optimization procedure for the functional description of the circuit and LeonardoSpectrum synthesis confirm the effectiveness of the developed algorithms. The algorithms are implemented as partitioning circuit procedures in the experimental FLC system for logical design.Рассматривается задача разбиения логической схемы на подсхемы, имеющая большое значение при выполнении оптимизационных преобразований в процессе синтеза схемы. Приводится краткий обзор методов и алгоритмов разбиения, выделяются две группы алгоритмов: конструктивные и итеративные. Представляется интерпретация логической схемы в виде графа, формулируется задача разбиения в теоретико-графовой модели и предлагается набор алгоритмов для ее решения. Функционирование логической схемы задается системой логических уравнений. Алгоритмы осуществляют разбиение системы логических уравнений на подсистемы с выполнением ограничений по числу входных и выходных переменных. Рассматриваются структуры данных, необходимых для выполнения алгоритмов. Описываются различные виды взаимосвязей уравнений, определяющих получение оптимальных решений. Исследуются вопросы применения алгоритмов разбиения для улучшения качества схемы на этапе технологически независимой оптимизации. Результаты экспериментального исследования, выполненного с помощью процедуры BDD-оптимизации функционального описания схемы и промышленного синтезатора LeonardoSpectrum  подтверждают  эффективность  разработанных  алгоритмов.  Алгоритмы  реализуются в виде набора процедур разбиения схемы в рамках экспериментальной системы логического проектирования FLC

Partitioning Complex Networks via Size-constrained Clustering

The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and edges until the graph is small enough to be partitioned by some other algorithm. A partition of the input graph is then constructed by successively transferring the solution to the next finer graph and applying a local search algorithm to improve the current solution. In this paper, we describe a novel approach to partition graphs effectively especially if the networks have a highly irregular structure. More precisely, our algorithm provides graph coarsening by iteratively contracting size-constrained clusterings that are computed using a label propagation algorithm. The same algorithm that provides the size-constrained clusterings can also be used during uncoarsening as a fast and simple local search algorithm. Depending on the algorithm's configuration, we are able to compute partitions of very high quality outperforming all competitors, or partitions that are comparable to the best competitor in terms of quality, hMetis, while being nearly an order of magnitude faster on average. The fastest configuration partitions the largest graph available to us with 3.3 billion edges using a single machine in about ten minutes while cutting less than half of the edges than the fastest competitor, kMetis