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    3-coloring in time script O sign(1.3289<sup>n</sup>)

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    Genre
    Pre-print
    Date
    2005-02-01
    Author
    Beigel, R
    Eppstein, D
    Subject
    cs.DS
    cs.DS
    F.2.2
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/4216
    
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    DOI
    10.1016/j.jalgor.2004.06.008
    Abstract
    We consider worst case time bounds for several NP-complete problems, based on a constraint satisfaction (CSP) formulation of these problems: (a,b)-CSP instances consist of a set of variables, each with up to a possible values, and constraints disallowing certain b-tuples of variable values; a problem is solved by assigning values to all variables satisfying all constraints, or by showing that no such assignment exist. 3-SAT is equivalent to (2,3)-CSP while 3-coloring and various related problems are special cases of (3,2)-CSP; there is also a natural duality transformation from (a,b)-CSP to (b,a)-CSP. We show that n-variable (3,2)-CSP instances can be solved in time O(1.3645n), that satisfying assignments to (d,2)-CSP instances can be found in randomized expected time O((0.4518d)n); that 3-coloring of n-vertex graphs can be solved in time O(1.3289n); that 3-list-coloring of n-vertex graphs can be solved in time O(1.3645n); that 3-edge-coloring of n-vertex graphs can be solved in time O(2n/2), and that 3-satisfiability of a formula with t 3-clauses can be solved in time O(nO(1)+1.3645t). © 2004 Elsevier Inc. All rights reserved.
    Citation to related work
    Elsevier BV
    Has part
    Journal of Algorithms
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    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/4198
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