Computing hypergraph width measures exactly

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, comp...

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Bibliographic Details
Published in:Information processing letters Vol. 112; no. 6; pp. 238 - 242
Main Authors: Moll, Lukas, Tazari, Siamak, Thurley, Marc
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 15.03.2012
Elsevier Sequoia S.A
Subjects:
Algorithms
Complexity
Complexity theory
Computation
Design of algorithms
Exact exponential algorithms
Exponents
Fractional hypertree-width
Generalized hypertree-width
Graph algorithms
Graph theory
Graphs
Optimization algorithms
Studies
Exact exponential algorithms
Graph algorithms
Design of algorithms
Fractional hypertree-width
Generalized hypertree-width
ISSN:0020-0190, 1872-6119
Online Access:Get full text
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Summary: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.
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ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2011.12.002