set-theory   174

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The different types (not sizes!) of infinity
Cardinals, Ordinals, Poles/Limits, Hyperreals -- all different types of "infinity".
math  set-theory  infinity 
february 2018 by mcherm
[1711.02724] Algorithms to Approximate Column-Sparse Packing Problems
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation algorithms for some well-known families of such problems. As three main examples, we attain the integrality gap, up to lower-order terms, for known LP relaxations for k-column sparse packing integer programs (Bansal et al., Theory of Computing, 2012) and stochastic k-set packing (Bansal et al., Algorithmica, 2012), and go "half the remaining distance" to optimal for a major integrality-gap conjecture of Furedi, Kahn and Seymour on hypergraph matching (Combinatorica, 1993).
integer-programming  matrices  optimization  operations-research  set-theory  hypergraphs  to-write-about  approximation  algorithms 
november 2017 by Vaguery
Visualizing Intersecting Sets
Understanding relationships between sets is an important analysis task. The major challenge in this context is the combinatorial explosion of the number of set intersections if the number of sets exceeds a trivial threshold. To address this, we introduce UpSet, a novel visualization technique for the quantitative analysis of sets, their intersections, and aggregates of intersections.
visualization  set-theory  data-analysis  rather-interesting  to-write-about  to-do 
october 2017 by Vaguery

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