550 research outputs found
Relaxation-Based Coarsening for Multilevel Hypergraph Partitioning
Multilevel partitioning methods that are inspired by principles of
multiscaling are the most powerful practical hypergraph partitioning solvers.
Hypergraph partitioning has many applications in disciplines ranging from
scientific computing to data science. In this paper we introduce the concept of
algebraic distance on hypergraphs and demonstrate its use as an algorithmic
component in the coarsening stage of multilevel hypergraph partitioning
solvers. The algebraic distance is a vertex distance measure that extends
hyperedge weights for capturing the local connectivity of vertices which is
critical for hypergraph coarsening schemes. The practical effectiveness of the
proposed measure and corresponding coarsening scheme is demonstrated through
extensive computational experiments on a diverse set of problems. Finally, we
propose a benchmark of hypergraph partitioning problems to compare the quality
of other solvers
Beyond pairwise clustering
We consider the problem of clustering in domains where the affinity relations are not dyadic (pairwise), but rather triadic, tetradic or higher. The problem is an instance of the hypergraph partitioning problem. We propose a two-step algorithm for solving this problem. In the first step we use a novel scheme to approximate the hypergraph using a weighted graph. In the second step a spectral partitioning algorithm is used to partition the vertices of this graph. The algorithm is capable of handling hyperedges of all orders including order two, thus incorporating information of all orders simultaneously. We present a theoretical analysis that relates our algorithm to an existing hypergraph partitioning algorithm and explain the reasons for its superior performance. We report the performance of our algorithm on a variety of computer vision problems and compare it to several existing hypergraph partitioning algorithms
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A survey of behavioral-level partitioning systems
Many approaches have been developed to partition a system's behavioral description before a structural implementation is synthesized. We highlight the foundations and motivations for behavioral partitioning. We survey behavioral partitioning approaches, discussing abstraction levels, goals, major steps, and key assumptions in each
A note on Pr\"ufer-like coding and counting forests of uniform hypertrees
This note presents an encoding and a decoding algorithms for a forest of
(labelled) rooted uniform hypertrees and hypercycles in linear time, by using
as few as integers in the range . It is a simple extension of
the classical Pr\"{u}fer code for (labelled) rooted trees to an encoding for
forests of (labelled) rooted uniform hypertrees and hypercycles, which allows
to count them up according to their number of vertices, hyperedges and
hypertrees. In passing, we also find Cayley's formula for the number of
(labelled) rooted trees as well as its generalisation to the number of
hypercycles found by Selivanov in the early 70's.Comment: Version 2; 8th International Conference on Computer Science and
Information Technologies (CSIT 2011), Erevan : Armenia (2011
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