A set D of a graph G = (V,E) is a dominating set if every vertex in V −D is adjacent to some vertex in D. The domination number γ(G) of G is the minimum cardinality of a dominating set. A dominating set D is called a complementary tree dominating set if the induced subgraph < V −D > is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domina...

We introduce a complexity measure for decision trees called the soft rank, which measures how wellbalanced a given tree is. The soft rank is a somehow relaxed variant of the rank. Among all decision trees of depth d, the complete binary decision tree (the most balanced tree) has maximum soft rank d, the decision list (the most unbalanced tree) has minimum soft rank √ d, and any other trees have...

The method of minimum evolution reconstructs a phylogenetic tree T for n taxa given dissimilarity data d. In principle, for every tree W with these n leaves an estimate for the total length of W is made, and T is selected as the W that yields the minimum total length. Suppose that the ordinary least-squares formula S(W)(d) is used to estimate the total length of W. A theorem of Rzhetsky and Nei...

Consider a smart chimpanzee named M from a tribe afflicted with a form of Alzheimer’s disease. Think of M as a logspace-bounded Turing machine. M can do simple things like integer arithmetic and matrix multiplication, but M turns sullen and calls for help when asked to perform seemingly equally simple tasks, such as simulating deterministic tree and dag automata. Is M acting difficult or is she...

Answering connectivity queries is fundamental to fully dynamic graphs where edges and vertices are inserted deleted frequently. Existing work proposes data structures algorithms with worst case guarantees. We propose a new structure, the tree (D-tree), together construct maintain it. The D-tree first structure that scales millions of and, on average, answers much faster than

Abstract. A hyperplane search tree is a binary tree used to store a set S of n d-dimensional data points. In a random hyperplane search tree for S, the root represents a hyperplane defined by d data points drawn uniformly at random from S. The remaining data points are split by the hyperplane, and the definition is used recursively on each subset. We assume that the data are points in general p...

Results. In sham-injected and saline-injected MD tree shrews, 12 days of MD produced —13.2 D ± 0.8 D and —14.1 D ± 0.5 D of axial myopia, respectively. In pirenzepine-injected MD tree shrews, 12 days of MD induced an axial myopia of only —2.1 D ± 1.4 D. The significant reduction in myopia in pirenzepine-injected MD tree shrews was caused by significantly less vitreous chamber elongation of the ...

A new solution method to the Nearest Neighbour Problem is presented. The method is based upon the triangle inequality and works well for small point sets, where traditional solutions are particularly ineffective. Its performance is characterized experimentally and compared with k-d tree and Elias approaches. A hybrid approach is proposed wherein the triangle inequality method is applied to the ...

We present D-Tree, a dynamic deterministic structure for data management in decentralized networks, by engineering and further extending an existing decentralized structure. D-Tree achieves O(logN) worst-case search cost (N is the number of nodes in the network),O(logN) amortized load-balancing cost, and it is highly fault-tolerant. A particular strength of D-Tree is that it achieves O(logN) am...

We investigate Prim’s standard ‘tree-growing’ method for finding a minimum spanning tree, when applied to a network in which all degrees are about d and the edges e have independent identically distributed random weights w(e). We find that when the kth edge ek is added to the current tree, where k = o( √ d), the probability that this edge ek is incident to the node that was most recently added ...