For each constant k, we present a linear time algorithm that, given a planar graph G, either finds a minimum odd cycle vertex transversal in G or guarantees that there is no transversal of size at most k. (C) 2007 Els...
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For each constant k, we present a linear time algorithm that, given a planar graph G, either finds a minimum odd cycle vertex transversal in G or guarantees that there is no transversal of size at most k. (C) 2007 Elsevier B.V. All rights reserved.
This paper is devoted to an octagonal cut algorithm and a hexadecagonal cut algorithm for finding the convex hull of n points in R-2, where some octagon and hexadecagon are used for discarding most of the given points...
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This paper is devoted to an octagonal cut algorithm and a hexadecagonal cut algorithm for finding the convex hull of n points in R-2, where some octagon and hexadecagon are used for discarding most of the given points interior to these polygons. In this way, the scope of the given problem can be reduced significantly. In particular, the convex hull of n points distributed b(least)-b(most)-boundedly in some rectangle can be determined with the complexity O (n). Computational experiments demonstrate that our algorithms outperform the Quickhull algorithm by a significant factor of up to 47 times when applied to the tested data sets. The speedup compared to the CGAL library is even more pronounced.
Let G be a finite undirected graph with edge set E. An edge set E'aS dagger E is an induced matching in G if the pairwise distance of the edges of E' in G is at least two;E' is dominating in G if every edg...
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Let G be a finite undirected graph with edge set E. An edge set E'aS dagger E is an induced matching in G if the pairwise distance of the edges of E' in G is at least two;E' is dominating in G if every edge eaEa-E' intersects some edge in E'. The Dominating Induced Matching Problem (DIM, for short) asks for the existence of an induced matching E' which is also dominating in G;this problem is also known as the Efficient Edge Domination Problem. The DIM problem is related to parallel resource allocation problems, encoding theory and network routing. It is -complete even for very restricted graph classes such as planar bipartite graphs with maximum degree three. However, its complexity was open for P (k) -free graphs for any ka parts per thousand yen5;P (k) denotes a chordless path with k vertices and k-1 edges. We show in this paper that the weighted DIM problem is solvable in lineartime for P (7)-free graphs in a robust way.
We consider the digitalization mapping dig: with othwerwise. For a given object one can obtain the so-called digitalization dig(s) of s. One problem of the image processing is the recognition of objects , whereγ=d...
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We consider the digitalization mapping dig: with othwerwise. For a given object one can obtain the so-called digitalization dig(s) of s. One problem of the image processing is the recognition of objects , whereγ=dig(s) is given. In case of dimension n = 2 we formulate necessary and sufficient conditions, that a given set γ⊂Z2 is the digitalization of a Euclidean circle s.
Multiclass probability estimation is the problem of estimating conditional probabilities of a data point belonging to a class given its covariate information. It has broad applications in statistical analysis and data...
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Let G be a finite undirected graph with edge set E. An edge set E' subset of E is an induced matching in G if the pairwise distance of the edges of E' in G is at least two;E' is dominating in G if every ed...
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ISBN:
(纸本)9783642255908
Let G be a finite undirected graph with edge set E. An edge set E' subset of E is an induced matching in G if the pairwise distance of the edges of E' in G is at least two;E' is dominating in G if every edge e is an element of E\E' intersects some edge in E'. The Dominating Induced Matching Problem (DIM, for short) asks for the existence of an induced matching E' which is also dominating in G;this problem is also known as the Efficient Edge Domination Problem. The DIM problem is related to parallel resource allocation problems, encoding theory and network routing. It is NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree three. However, its complexity was open for P-k-free graphs for any k >= 5;P-k denotes a chordless path with k vertices and k - 1 edges. We show in this paper that the weighted DIM problem is solvable in lineartime for P-7-free graphs in a robust way.
We show that for every fixed k, there is a linear time algorithm that decides whether or not a given graph has crossing number at most k, and if this is the case, computes a drawing of the graph in the plane with at m...
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ISBN:
(纸本)9781595936318
We show that for every fixed k, there is a linear time algorithm that decides whether or not a given graph has crossing number at most k, and if this is the case, computes a drawing of the graph in the plane with at most k crossings. This answers the question posed by Grohe (STOC'01 and JCSS 2004). Our algorithm can be viewed as a generalization of the seminal result by Hopcroft and Tarjan [26], which determines if a given graph is planar in lineartime. Our algorithm can also be compared to the algorithms by Mohar (STOC'96 and Siam J. Discrete Math 2001.), for testing the embeddability of an input graph in a fixed surface. For each surface S, Mohar describes an algorithm which yields either an embedding of G in S or a minor of G which is not embeddable in S and is minimal with this property. The same approach allows us to obtain linear time algorithms for the same question for a variety of other crossing numbers. We can also determine in lineartime if an input graph can be made planar by the deletion of k edges (for fixed k).
For every surface S (orientable or non-orientable), we give a linear time algorithm to test the graph isomorphism of two graphs, one of which admits at) embedding of face-width at least 3 into S. This improves a previ...
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ISBN:
(纸本)9781605580470
For every surface S (orientable or non-orientable), we give a linear time algorithm to test the graph isomorphism of two graphs, one of which admits at) embedding of face-width at least 3 into S. This improves a previously known algorithm whose time complexity is n(O(g)), where g is the genus of S. This is the first algorithm for which the degree of polynomial in the time complexity does not depend on g. The above result is based on two linear time algorithms, each of which solves a problem that is of independent;interest. The first of these problems is the following one. Let S be a fixed surface. Given a graph G and an integer k >= 3, we want to find art embedding of C in S of face-width at least k, or conclude that such an embedding does not exist. It is known that this problem is NP-hard when the surface is not fixed. Moreover, if there is an embedding, the algorithm can give all embeddings of face-width at least k, tip to Whitney equivalence. Here, the face-width of an embedded graph G is the minimum number of points of G in which some non-contractible closed curve in the surface intersects the graph. In the proof of the above algorithm, we give a simpler proof and a better bound for the theorem by Mohar and Robertson concerning the number of polyhedral embeddings of 3-connected graphs. The second ingredient is a linear time algorithm for map isomorphism and Whitney equivalence. This part generalizes the seminal result of Hopcroft and Wong that graph isomorphism can be decided in lineartime for planar graphs.
We give an explicit procedure for 5-list coloring a large class of toroidal 6-regular triangulations in lineartime. We also show that these graphs are not 3-choosable.
ISBN:
(纸本)9783031252105;9783031252112
We give an explicit procedure for 5-list coloring a large class of toroidal 6-regular triangulations in lineartime. We also show that these graphs are not 3-choosable.
A subset S of vertices in a graph G is a secure dominating set of G if S is a dominating set of G and, for each vertex u is not an element of S, there is a vertex v is an element of S such that uv is an edge and (S \ ...
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A subset S of vertices in a graph G is a secure dominating set of G if S is a dominating set of G and, for each vertex u is not an element of S, there is a vertex v is an element of S such that uv is an edge and (S \ {v}) boolean OR {u} is also a dominating set of G. The secure domination number gamma(s)(G) is the cardinality of a smallest secure dominating set of G. In this paper, we propose a linear-timealgorithm for finding the secure domination number of proper interval graphs. (C) 2018 Elsevier B.V. All rights reserved.
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