18,139 research outputs found
Domains via approximation operators
In this paper, we tailor-make new approximation operators inspired by rough
set theory and specially suited for domain theory. Our approximation operators
offer a fresh perspective to existing concepts and results in domain theory,
but also reveal ways to establishing novel domain-theoretic results. For
instance, (1) the well-known interpolation property of the way-below relation
on a continuous poset is equivalent to the idempotence of a certain
set-operator; (2) the continuity of a poset can be characterized by the
coincidence of the Scott closure operator and the upper approximation operator
induced by the way below relation; (3) meet-continuity can be established from
a certain property of the topological closure operator. Additionally, we show
how, to each approximating relation, an associated order-compatible topology
can be defined in such a way that for the case of a continuous poset the
topology associated to the way-below relation is exactly the Scott topology. A
preliminary investigation is carried out on this new topology.Comment: 17 pages; 1figure, Domains XII Worksho
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
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