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 ...

First we modify the basic (binary) context-tree weighting method such that the past symbols x1 D; x2 D; ; x0 are not needed by the encoder and the decoder. Then we describe how to make the context-tree depth D infinite, which results in optimal redundancy behavior for all tree sources, while the number of records in the context tree is not larger than 2T 1: Here T is the length of the source se...

First we modify the basic (binary) context-tree weighting method such that the past symbols x1 D; x2 D; ; x0 are not needed by the encoder and the decoder. Then we describe how to make the context-tree depth D infinite, which results in optimal redundancy behavior for all tree sources, while the number of records in the context tree is not larger than 2T 1: Here T is the length of the source se...

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 sub graph < V −D > is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domin...

It is a fact simple to establish that the mixing time of random walk on d-regular graph $G_n$ with n vertices asymptotically bounded from below by $d/ ((d-2)\log (d-1))\log n$. Such bound obtained comparing infinite $d$-regular tree. If one can map another transitive onto $G_n$, then we improve strategy using comparison this (instead regular tree), and obtain lower form $1/h \log n$, where $h$ ...

The original description of the k -d tree recognized that rebalancing techniques, such as are used to build an AVL tree or a red-black tree, are not applicable to a k -d tree. Hence, in order to build a balanced k -d tree, it is necessary to find the median of the data for each recursive subdivision of those data. The sort or selection that is used to find the median for each subdivision strong...

We present a class of heuristics for the Euclidean Steiner tree problem in a d-dimensional space, d ≥ 3. These heuristics identify small subsets with few, geometrically close, terminals using Delaunay tessellations and minimum spanning trees. Low cost spanning trees of these subsets are determined by applying the exact algorithm for the Euclidean Steiner minimal tree in d-space as well as its h...