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A Tree-Based Model for Addressing Sparsity and Taxa Covariance in Microbiome Compositional Count Data. [PDF]
Wang Z, Mao J, Ma L.
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2014
In the problem session of the ICFCA 2006, Sandor Radeleczki asked for the meaning of the smallest integer k such that a given poset can be decomposed as the union of k directed trees. The problem also asks for the connection of this number to the order dimension.
Sebastian Kerkhoff +1 more
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In the problem session of the ICFCA 2006, Sandor Radeleczki asked for the meaning of the smallest integer k such that a given poset can be decomposed as the union of k directed trees. The problem also asks for the connection of this number to the order dimension.
Sebastian Kerkhoff +1 more
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2020
In this chapter we review the most important algorithmic approaches to the following problem: given a graph G, compute a tree decomposition of G of (nearly) optimum width. We present the 4-approximation algorithm running in time \(\mathcal {O}(27^k\cdot k^2\cdot n^2)\), which was first proposed by Robertson and Seymour in the Graph Minors series, and ...
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In this chapter we review the most important algorithmic approaches to the following problem: given a graph G, compute a tree decomposition of G of (nearly) optimum width. We present the 4-approximation algorithm running in time \(\mathcal {O}(27^k\cdot k^2\cdot n^2)\), which was first proposed by Robertson and Seymour in the Graph Minors series, and ...
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2008 23rd Annual IEEE Symposium on Logic in Computer Science, 2008
We introduce a notion of definable tree decompositions of graphs. Actually, a definable tree decomposition of a graph is not just a tree decomposition, but a more complicated structure that represents many different tree decompositions of the graph. It is definable in the graph by a tuple of formulas of some logic.
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We introduce a notion of definable tree decompositions of graphs. Actually, a definable tree decomposition of a graph is not just a tree decomposition, but a more complicated structure that represents many different tree decompositions of the graph. It is definable in the graph by a tuple of formulas of some logic.
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Tree Decomposition of Multiclass Problems
2008 10th Brazilian Symposium on Neural Networks, 2008Several popular machine learning techniques are originally designed for the solution of two-class problems. However, several classification problems have more than two classes. One approach to deal with multiclass problems using binary classifiers is to decompose the multiclass problem into multiple binary subproblems disposed in a binary tree.
Ana Carolina Lorena +1 more
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Random Structures and Algorithms, 1998
Summary: Let \(H\) be a tree on \(h\geq 2\) vertices. It is shown that if \(G=(V,E)\) is a graph with \(\delta(G)\geq(| V|/2) +10h^4 \sqrt{| V| \log| V|}\), and \(h-1\) divides \(| E|\), then there is a decomposition of the edges of \(G\) into copies of \(H\). This result is asymptotically the best possible for all trees with at least three vertices.
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Summary: Let \(H\) be a tree on \(h\geq 2\) vertices. It is shown that if \(G=(V,E)\) is a graph with \(\delta(G)\geq(| V|/2) +10h^4 \sqrt{| V| \log| V|}\), and \(h-1\) divides \(| E|\), then there is a decomposition of the edges of \(G\) into copies of \(H\). This result is asymptotically the best possible for all trees with at least three vertices.
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Guiding VNS with Tree Decomposition
2011 IEEE 23rd International Conference on Tools with Artificial Intelligence, 2011Tree decomposition introduced by Robertson and Seymour aims to decompose a problem into clusters constituting an a cyclic graph. There are works exploiting tree decomposition for complete search methods. In this paper, we show how tree decomposition can be used to efficiently guide the exploration of local search methods that use large neighborhoods ...
Mathieu Fontaine 0001 +2 more
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Tree Decomposition with Function Filtering
2005Besides search, complete inference methods can also be used to solve soft constraint problems. Their main drawback is the high spatial complexity. To improve its practical usage, we present an approach to decrease memory consumtion in tree decomposition methods, a class of complete inference algorithms.
Martí Sánchez-Fibla +2 more
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