123,166 research outputs found
Coxeter Decompositions of Hyperbolic Tetrahedra
We classify Coxeter decompositions of hyperbolic tetrahedra, i.e. simplices
in the hyperbolic space H^3. The paper completes the classification of Coxeter
decompositions of hyperbolic simplices.Comment: 14 pages, 4 figures, 3 table
Computing hypergraph width measures exactly
Hypergraph width measures are a class of hypergraph invariants important in
studying the complexity of constraint satisfaction problems (CSPs). We present
a general exact exponential algorithm for a large variety of these measures. A
connection between these and tree decompositions is established. This enables
us to almost seamlessly adapt the combinatorial and algorithmic results known
for tree decompositions of graphs to the case of hypergraphs and obtain fast
exact algorithms.
As a consequence, we provide algorithms which, given a hypergraph H on n
vertices and m hyperedges, compute the generalized hypertree-width of H in time
O*(2^n) and compute the fractional hypertree-width of H in time
O(m*1.734601^n).Comment: 12 pages, 1 figur
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