Closures on partial partitions from closures on sets

MIR closures of polyhedral sets

We study the mixed-integer rounding (MIR) closures of polyhedral sets. The MIR closure of a polyhedral set is equal to its split closure and the associated separation problem is NP-hard. We describe a mixed-integer programming (MIP) model with linear constraints and a non-linear objective for separating an arbitrary point from the MIR closure of a given mixed-integer set. We linearize the objec...

Closures in Binary Partial Algebras

Two procedures for computing closures in binary partial algebras (BPA) are introduced: a Fibonacci-style procedure for closures in associative BPAs, and a multistage procedure for closures in associative, commutative and idempotent BPAs. Ramifications in areas such as resolution theorem proving, graph-theoretic algorithms, formal languages and formal concept analysis are discussed. In particula...

Closures of Discrete Sets in Compact Spaces

We consider the question of whether a compact space will always have a discrete subset whose closure has the same cardinality as the whole space. We obtain many positive results for compact spaces of countable tightness and a consistent negative result for a space of tightness and density ω1. Several authors have recently been investigating a notion called discretely reflexive where one seeks a...

Distance closures on complex networks

To expand the toolbox available to network science, we study the isomorphism between distance and Fuzzy (proximity or strength) graphs. Distinct transitive closures in Fuzzy graphs lead to closures of their isomorphic distance graphs with widely different structural properties. For instance, the All Pairs Shortest Paths (APSP) problem, based on the Dijkstra algorithm, is equivalent to a metric ...

Partial Commutation Closures of Recognizable Languages