منابع مشابه
Bidimensionality
1 PROBLEM DEFINITION The theory of bidimensionality provides general techniques for designing efficient fixed-parameter algorithms and approximation algorithms for a broad range of NP-hard graph problems in a broad range of graphs. This theory applies to graph problems that are " bidi-mensional " in the sense that (1) the solution value for the k ×k grid graph and similar graphs grows with k, t...
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Bidimensionality theory was introduced by Demaine et al. [JACM 2005 ] as a framework to obtain algorithmic results for hard problems on minor closed graph classes. The theory has been sucessfully applied to yield subexponential time parameterized algorithms, EPTASs and linear kernels for many problems on families of graphs excluding a fixed graph H as a minor. In this paper we use several of th...
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We provide an exposition of the main results of the theory of bidimensionality in parameterized algorithm design. This theory applies to graph problems that are bidimensional in the sense that i) their solution value is not increasing when we take minors or contractions of the input graph and ii) their solution value for the (triangulated) (k × k)-grid graph grows as a quadratic function of k. ...
متن کاملBidimensionality of Geometric Intersection Graphs
Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric intersection graphs GB where each body of the collection B is represented by a vertex, and two vertices of GB are adjacent if the intersection of the correspon...
متن کاملContraction Bidimensionality: The Accurate Picture
We provide new combinatorial theorems on the structure of graphs that are contained as contractions in graphs of large treewidth. As a consequence of our combinatorial results we unify and significantly simplify contraction bidimensionality theory—the meta algorithmic framework to design efficient parameterized and approximation algorithms for contraction closed parameters.
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2020
ISSN: 0097-5397,1095-7111
DOI: 10.1137/16m1080264