Computing hypergraph width measures exactly - Moll, Lukas; Tazari, Siamak; Thurley, Marc (Information processing letters, 2012)
Hypergraph width measures are important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. As a consequence, we obtain algorithms which, for a hypergraph H on n vertices and m hyperedges, compute its generalized hypertree-width in time O ⁎ ( 2 n ) and its fractional hypertree-width in time O ( 1.734601 n ⋅ m ) . 3 3 We omit factors polynomial in n whenever the base of the exponent is rounded. This is justified as c n ⋅ n O ( 1 ) = O ( ( c + ϵ ) n ) for every ϵ > 0 . We also use the notation O ⁎ to suppress polynomial factors. ► We present a general exact exponential algorithm for the f-width of a hypergraph. ► Our algorithm works for any monotone width function f. ► This results in the currently fastest algorithm for generalized hypertree-width. ► Also this results in the currently fastest algorithm for fractional hypertree-width.