34,424 research outputs found
Covering pairs by q2 + q + 1 sets
AbstractFor given k and s let n(k, s) be the largest cardinality of a set whose pairs can be covered by sk-sets. We determine n(k, q2 + q + 1) if a PG(2, q) exists, k > q(q + 1)2, and the remainder of k divided by (q + 1) is at least √q. Asymptotic results are also given for n(k, s) whenever s is fixed and k → ∞. Our main tool is the theory of fractional matchings of hypergraphs
Disproving the normal graph conjecture
A graph is called normal if there exist two coverings, and
of its vertex set such that every member of induces a
clique in , every member of induces an independent set in
and for every and . It has been conjectured by De Simone and K\"orner in 1999 that a
graph is normal if does not contain , and
as an induced subgraph. We disprove this conjecture
Interactive Submodular Set Cover
We introduce a natural generalization of submodular set cover and exact
active learning with a finite hypothesis class (query learning). We call this
new problem interactive submodular set cover. Applications include advertising
in social networks with hidden information. We give an approximation guarantee
for a novel greedy algorithm and give a hardness of approximation result which
matches up to constant factors. We also discuss negative results for simpler
approaches and present encouraging early experimental results.Comment: 15 pages, 1 figur
Quantum causal histories
Quantum causal histories are defined to be causal sets with Hilbert spaces
attached to each event and local unitary evolution operators. The reflexivity,
antisymmetry, and transitivity properties of a causal set are preserved in the
quantum history as conditions on the evolution operators. A quantum causal
history in which transitivity holds can be treated as ``directed'' topological
quantum field theory. Two examples of such histories are described.Comment: 16 pages, epsfig latex. Some clarifications, minor corrections and
references added. Version to appear in Classical and Quantum Gravit
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