Half-integrality, LP-branching, and FPT Algorithms
نویسندگان
چکیده
منابع مشابه
Half-integrality, LP-branching and FPT Algorithms
A recent trend in parameterized algorithms is the application of polytope tools (specifically, LPbranching) to FPT algorithms (e.g., Cygan et al., 2011; Narayanaswamy et al., 2012). Though the list of work in this direction is short, the results are already interesting, yielding significant speedups for a range of important problems. However, the existing approaches require the underlying polyt...
متن کاملHalf-integrality, Lp-branching and Fpt Algorithms∗
A recent trend in parameterized algorithms is the application of polytope tools to FPT algorithms (e.g., Cygan et al., 2011; Narayanaswamy et al., 2012). Although this approach has yielded significant speedups for a range of important problems, it requires the underlying polytope to have very restrictive properties, including half-integrality and Nemhauser-Trotter-style persistence properties. ...
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We give a combinatorial condition for the existence of efficient, LP-based FPT algorithms for a broad class of graph-theoretical optimisation problems. Our condition is based on the notion of biased graphs known from matroid theory. Specifically, we show that given a biased graph Ψ = (G,B), where B is a class of balanced cycles in G, the problem of finding a set X of at most k vertices in G whi...
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A recent trend in the design of FPT algorithms is exploiting the half-integrality of LP relaxations. In other words, starting with a half-integral optimal solution to an LP relaxation, we assign integral values to variables one-by-one by branch and bound. This technique is general and the resulting time complexity has a low dependency on the parameter. However, the time complexity often becomes...
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In structured prediction, a predictor optimizes an objective function over a combinatorial search space, such as the set of all image segmentations, or the set of all part-of-speech taggings. Unfortunately, finding the optimal structured labeling—sometimes referred to as maximum a posteriori (MAP) inference—is, in general, NP-hard [12], due to the combinatorial structure of the problem. Many in...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2016
ISSN: 0097-5397,1095-7111
DOI: 10.1137/140962838