Consistency of Spectral Hypergraph Partitioning under Planted Partition Model

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received attention in the literature as compared to the extensive studies on the guarantees of graph partitioning. For instance, consistency results of spectral graph partitioning under the stochastic block model are well known. In this paper, we present a planted partition model for sparse random non-uniform hypergraphs that generalizes the stochastic block model. We derive an error bound for a spectral hypergraph partitioning algorithm under this model using matrix concentration inequalities. To the best of our knowledge, this is the first consistency result related to partitioning non-uniform hypergraphs.Comment: 35 pages, 2 figures, 1 tabl

Survey of partitioning techniques in silicon compilation

In the silicon compilation design process, partitioning is usually the first problem to be investigated because partitioning algorithms form the backbone of many algorithms including: system synthesis, processor synthesis, floorplanning, and placement. In this survey, several partitioning techniques will be examined. In addition, this paper will review the partitioning algorithms used by synthesis systems at different design levels

OPTIMIZING LARGE COMBINATIONAL NETWORKS FOR K-LUT BASED FPGA MAPPING

Optimizing by partitioning is a central problem in VLSI design automation, addressing circuit’s manufacturability. Circuit partitioning has multiple applications in VLSI design. One of the most common is that of dividing combinational circuits (usually large ones) that will not fit on a single package among a number of packages. Partitioning is of practical importance for k-LUT based FPGA circuit implementation. In this work is presented multilevel a multi-resource partitioning algorithm for partitioning large combinational circuits in order to efficiently use existing and commercially available FPGAs packagestwo-way partitioning, multi-way partitioning, recursive partitioning, flat partitioning, critical path, cutting cones, bottom-up clusters, top-down min-cut

Window-based Streaming Graph Partitioning Algorithm

In the recent years, the scale of graph datasets has increased to such a degree that a single machine is not capable of efficiently processing large graphs. Thereby, efficient graph partitioning is necessary for those large graph applications. Traditional graph partitioning generally loads the whole graph data into the memory before performing partitioning; this is not only a time consuming task but it also creates memory bottlenecks. These issues of memory limitation and enormous time complexity can be resolved using stream-based graph partitioning. A streaming graph partitioning algorithm reads vertices once and assigns that vertex to a partition accordingly. This is also called an one-pass algorithm. This paper proposes an efficient window-based streaming graph partitioning algorithm called WStream. The WStream algorithm is an edge-cut partitioning algorithm, which distributes a vertex among the partitions. Our results suggest that the WStream algorithm is able to partition large graph data efficiently while keeping the load balanced across different partitions, and communication to a minimum. Evaluation results with real workloads also prove the effectiveness of our proposed algorithm, and it achieves a significant reduction in load imbalance and edge-cut with different ranges of dataset