Several recent works have discussed tree structured sparse coding [8, 10, 7, 3], where N data points in R written as the d × N matrix X are approximately decomposed into the product of matrices WZ . HereW is a d×K dictionary matrix, and Z is a K×N matrix of coefficients. In tree structured sparse coding, the rows of Z correspond to nodes on a tree, and the columns of Z are encouraged to be nonz...

This paper presents a new processor allocation approach called “a generalized k-Tree-based model” to perform dynamic sub-system allocation/deallocation decision for partitionable multi-dimensional mesh-connected architectures. Time complexity of our generalized k-tree-based sub-system allocation algorithm is O(k42k(NA+NF)+k 2) for the partitionable k-D meshes and O(NA+NF) for the partitionable ...

We study the problem of approximating MST(P ), the Euclidean minimum spanning tree of a set P of n points in [0, 1], by a spanning tree of some subset Q ⊂ P . We show that if the weight of MST(P ) is to be approximated, then in general Q must be large. If the shape of MST(P ) is to be approximated, then this is always possible with a small Q. More specifically, for any 0 < ε < 1 we prove: (i) T...

Understanding how trees respond to global change drivers is central to predict changes in forest structure and functions. Although there is evidence on the mode of nitrogen (N) and drought (D) effects on tree growth, our understanding of the interplay of these factors is still limited. Simultaneously, as mixtures are expected to be less sensitive to global change as compared to monocultures, we...

This article is a continuation of an article on deening functions on trees (see 7]). In this article we develop terminology specialized for binary trees, rst deening binary trees and binary grammars. We recast the induction principle for the set of parse trees of binary grammars and the scheme of deening functions inductively with the set as domain. We conclude with deening the scheme of deenin...

We are dealing here with d-ary trees, which are amongst the most fundamental tree structures with applications, e.g., in combinatorics, computer science and biology, see, e.g., [1,3–5,9]. A d-ary tree is either an empty tree or it consists of a root node, to which an ordered sequence of exactly d subtrees is attached that are itself d-ary trees. We denote the family of d-ary trees by Td and the...

The k-Delaunay tree extends the Delaunay tree introduced in [1,2]. It is a hierarchical data structure that allows the semi-dynamic construction of the higher order Vorono diagrams of a nite set of n points in any dimension. In this paper, we prove that a randomized construction of the k-Delaunay tree, and thus, of all the order k Vorono diagrams, can be done in O(n logn + k 3 n) expected tim...

We consider a special variant of tree-decompositions, called domino treedecompositions, and the related notion of domino treewidth. In a domino tree-decomposition, each vertex of the graph belongs to at most two nodes of the tree. We prove that for every k, d, there exists a constant ck;d such that a graph with treewidth at most k and maximum degree at most d has domino treewidth at most ck;d. ...

We use the Lexicalised D-Tree Grammar (LDTG) formalism (Rambow et al. 95), which is based on the Lexicalized Tree Adjoining Grammar (LTAG) formalism. In LDTG, there are two types of edges between nodes: d-edges, represented with a broken line, and p-edges, represented by a solid line. Trees are combined by two substitution-like operations, both of which involve combining two descriptions, by eq...

We consider the K-satisfiability problem on a regular d-ary rooted tree. For this model, we demonstrate how we can calculate in closed form, the moments of the total number of solutions as a function of d and K, where the average is over all realizations, for a fixed assignment of the surface variables. We find that different moments pick out different ’critical’ values of d, below which they d...