In 1994, Telle introduced the following notion of domination, which generalizes many domination-type graph invariants. Let sigma and rho be two sets of non-negative integers. A vertex subset S subset of V of an undire...
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In 1994, Telle introduced the following notion of domination, which generalizes many domination-type graph invariants. Let sigma and rho be two sets of non-negative integers. A vertex subset S subset of V of an undirected graph G = (V, E) is called a (sigma, rho)-dominating set of G if |N(v) boolean AND S| is an element of sigma for all v is an element of S and |N(v) boolean AND S| is an element of rho for all v is an element of V \ S. In this paper, we prove that decision, optimization, and counting variants of ({p}, {q})-domination are solvable in time 2(|V|/2), |V|(0(1)). We also show how to extend these results for infinite sigma = {p + M . l: l is an element of N-0} and rho = {q + m . l: l is an element of N-0}. For the case |sigma| + |rho| = 3, these problems can be solved in time 3(|V|/2). |V|(0(1)), and similarly to the case |sigma| = |rho| = 1 it is possible to extend the algorithm for some infinite sets. (C) 2009 Elsevier B.V. All rights reserved.
Independent vector analysis (IVA), a multivariate extension of independent component analysis, tackles the convolutedly mixed blind source separation (BSS) problem in a way to avoid the permutation problem by employin...
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Independent vector analysis (IVA), a multivariate extension of independent component analysis, tackles the convolutedly mixed blind source separation (BSS) problem in a way to avoid the permutation problem by employing a multivariate source prior of the short-time Fourier transform (STFT) components. As the source prior in IVA, overall hyperspherical joint densities have been used, which imply that the dependence between the STFT components is invariant over bin difference. As a more effective source prior in the IVA framework, a dependence model is proposed that can be represented by chain-like overlaps of local cliques in graphical models. For convolutive BSS, the proposed method demonstrates consistently improved performance over using the overall hyperspherical joint density representation.
In this paper we present unified methods to solve the minus and signed total domination problems for chordal bipartite graphs and trees in O(n(2)) and O(n + m) time, respectively. We also prove that the decision probl...
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In this paper we present unified methods to solve the minus and signed total domination problems for chordal bipartite graphs and trees in O(n(2)) and O(n + m) time, respectively. We also prove that the decision problem for the signed total domination problem on doubly chordal graphs is NP-complete. Note that bipartite permutation graphs, biconvex bipartite graphs, and convex bipartite graphs are subclasses of chordal bipartite graphs. (c) 2009 Elsevier B.V. All rights reserved.
The k-clique problem is a cornerstone of NP-completeness and parametrized complexity. When k is a fixed constant, the asymptotically fastest known algorithm for finding a k-clique in an n-node graph runs in O (n(0.792...
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The k-clique problem is a cornerstone of NP-completeness and parametrized complexity. When k is a fixed constant, the asymptotically fastest known algorithm for finding a k-clique in an n-node graph runs in O (n(0.792k)) time (given by Nesetril and Poljak). However, this algorithm is infamously inapplicable, as it relies on Coppersmith and Winograd's fast matrix multiplication. We present good combinatorial algorithms for solving k-clique problems. These algorithms do not require large constants in their runtime, they can be readily implemented in any reasonable random access model. and are very space-efficient compared to their algebraic counterparts. Our results are the following: We give an algorithm for k-clique that runs in O(n(k)/(epsilon log n)(k-1)) time and O(n(epsilon)) space, for all epsilon > 0, on graphs with n nodes. This is the first algorithm to take o(n(k)) time and O(n(c)) space for c independent of k. Let k be even. Define a k-semiclique to be a k-node graph G that can be divided into two disjoint subgraphs U = {u(1),...,u(k/2)} and V = (v(1),...,v(k/2)} such that U and V are cliques, and for all i <= j, the graph G contains the edge {u(i), v(j)). We give an (O) over bar (k2(k)n(k/2+1)) time algorithm for determining if a graph has a k-semiclique. This yields an approximation algorithm for k-clique, in the following sense: if a given graph contains a k-clique, then our algorithm returns a subgraph with at least 3/4 of the edges in a k-clique. (C) 2008 Elsevier B.V. All rights reserved.
We present a novel approach to the problem of finding all subgraphs and induced subgraphs of a (target) graph which are isomorphic to another (pattern) graph. To attain efficiency we use a special representation of th...
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We present a novel approach to the problem of finding all subgraphs and induced subgraphs of a (target) graph which are isomorphic to another (pattern) graph. To attain efficiency we use a special representation of the pattern graph. We also combine our search algorithm with some known bisection algorithms. Experimental comparison with other algorithms was performed on several types of graphs. The comparison results suggest that the approach provided here is most effective when all instances of a subgraph need to be found.
graphical processing units (GPUs) have recently attracted attention for scientific applications such as particle simulations. This is partially driven by low commodity pricing of GPUs but also by recent toolkit and li...
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graphical processing units (GPUs) have recently attracted attention for scientific applications such as particle simulations. This is partially driven by low commodity pricing of GPUs but also by recent toolkit and library developments that make them more accessible to scientific programmers. We discuss the application of GPU programming to two significantly different paradigms-regular mesh field equations with unusual boundary conditions and graph analysis algorithms. The differing optimization techniques required for these two paradigms cover many of the challenges faced when developing GPU applications. We discuss the relevance of these application paradigms to simulation engines and games. GPUs were aimed primarily at the accelerated graphics market but since this is often closely coupled to advanced game products it is interesting to speculate about the future of fully integrated accelerator hardware for both visualization and simulation combined. As well as reporting the speed-up performance on selected simulation paradigms, we discuss suitable data-parallel algorithms and present code examples for exploiting GPU features like large numbers of threads and localized texture memory. We find a surprising variation in the performance that can be achieved on GPUs for our applications and discuss how these findings relate to past known effects in parallel computing such as memory speed-related super-linear speed up. Copyright (C) 2009 John Wiley & Sons, Ltd.
The class Of P-5-free graphs is the unique minimal class defined by a single connected forbidden induced subgraph for which the complexity status of the maximum independent set problem is unknown. In this paper, we pr...
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The class Of P-5-free graphs is the unique minimal class defined by a single connected forbidden induced subgraph for which the complexity status of the maximum independent set problem is unknown. In this paper, we prove polynomial-time solvability of the problem in two subclasses of P-5-free graphs generalizing several previously known results. (C) 2008 Elsevier B.V. All rights reserved.
The subgraph homeomorphism problem has been shown by Robertson and Seymour to be polynomial-time solvable for any fixed pattern graph H. The result, however, is not practical, involving constants that are worse than e...
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The subgraph homeomorphism problem has been shown by Robertson and Seymour to be polynomial-time solvable for any fixed pattern graph H. The result, however, is not practical, involving constants that are worse than exponential in |H|. Practical algorithms have only been developed for a few specific pattern graphs, the most recent of these being the wheels with four and five spokes. This paper looks at the subgraph homeomorphism problem where the pattern graph is a wheel with six spokes. The main result is a theorem characterizing graphs that do not contain subdivisions of W (6). We give an efficient algorithm for solving the subgraph homeomorphism problem for W (6). We also give a strengthening of the previous W (5) result.
We present a local algorithm (constant-time distributed algorithm) for finding a 3-approximate vertex cover in bounded-degree graphs. The algorithm is deterministic, and no auxiliary information besides port numbering...
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We present a local algorithm (constant-time distributed algorithm) for finding a 3-approximate vertex cover in bounded-degree graphs. The algorithm is deterministic, and no auxiliary information besides port numbering is required. (c) 2009 Elsevier B.V. All rights reserved.
A ranking on a graph is an assignment of positive integers to its vertices such that any path between two vertices of the same rank contains a vertex of strictly larger rank. A ranking is locally minimal if reducing t...
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A ranking on a graph is an assignment of positive integers to its vertices such that any path between two vertices of the same rank contains a vertex of strictly larger rank. A ranking is locally minimal if reducing the rank of any single vertex produces a non-ranking. A ranking is globally minimal if reducing the ranks of any set of vertices produces a non-ranking. A ranking is greedy if, for some ordering of the vertices, it is the ranking produced by assigning ranks in that order, always selecting the smallest possible rank. We will show that these three notions are equivalent. If a ranking satisfies one property it satisfies all three. As a consequence of this and known results on arank numbers of paths we improve known upper bounds for on-line ranking of paths and cycles. (C) 2009 Elsevier B.V. All rights reserved.
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