furthest$30503$ - meaning and definition. What is furthest$30503$
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What (who) is furthest$30503$ - definition

TYPE OF DIRECTED GRAPH
Nearest neighbour graph; Nearest-neighbour graph; Farthest neighbor graph; Furthest neighbor graph; Nearest-neighbor graph; Farthest-neighbor graph; Furthest-neighbor graph
  • A nearest neighbor graph of 100 points in the [[Euclidean plane]].

Farthest South         
  • Sir Francis Drake
  • The [[Amundsen–Scott South Pole Station]], photographed in 2006
  • Roald Amundsen, leader of the first expedition to reach the South Pole, 15 December 1911
  • Positions of Farthest South records from 1521 to 1911
  • Carsten Borchgrevink, who led the Southern Cross Expedition, 1898–1900
  • 20px
  • Captain Sir James Clark Ross
  • Captain James Cook
  • Weddell's ships, ''Jane'' and ''Beaufoy'', under full sail
  • Ferdinand Magellan
  • From left to right: Jameson Adams, Frank Wild and Eric Marshall (photographed by Shackleton) plant the Union flag at their southernmost position, 88°23', on 9 January 1909.
A RECORD HELD FOR MOST SOUTHERLY LATITUDE REACHED, BEFORE THE SOUTH POLE ITSELF WAS REACHED.
Furthest South; Farthest south
Farthest South refers to the most southerly latitude reached by explorers before the first successful expedition to the South Pole in 1911. Significant steps on the road to the pole were the discovery of lands south of Cape Horn in 1619, Captain James Cook's crossing of the Antarctic Circle in 1773, and the earliest confirmed sightings of the Antarctic mainland in 1820.
Further than the Furthest Thing         
PLAY IN TWO ACTS BY THE SCOTTISH PLAYWRIGHT ZINNIE HARRIS
Draft:Further than the Furthest Thing
Further than the Furthest Thing is a play in two acts by the Scottish playwright Zinnie Harris, set in 1961 on a remote island based loosely on Tristan da Cunha, and in the English city of Southampton. It was inspired by Harris' mother's memories of her childhood, during which she lived on Tristan for a few years; the Faber edition of the play includes two poems written by Harris' grandfather, Reverend Dennis Wilkinson.
Farthest North         
  • The North Pole, at the center of the Arctic Ocean. The inner circle shows 75° N.
  • 3 August 1958}}
MOST NORTHERLY LATITUDE REACHED BY EXPLORERS BEFORE THE CONQUEST OF THE NORTH POLE
Furthest North
Farthest North describes the most northerly latitude reached by explorers, before the first successful expedition to the North Pole rendered the expression obsolete. The Arctic polar regions are much more accessible than those of the Antarctic, as continental land masses extend to high latitudes and sea voyages to the regions are relatively short.

Wikipedia

Nearest neighbor graph

The nearest neighbor graph (NNG) is a directed graph defined for a set of points in a metric space, such as the Euclidean distance in the plane. The NNG has a vertex for each point, and a directed edge from p to q whenever q is a nearest neighbor of p, a point whose distance from p is minimum among all the given points other than p itself.

In many uses of these graphs, the directions of the edges are ignored and the NNG is defined instead as an undirected graph. However, the nearest neighbor relation is not a symmetric one, i.e., p from the definition is not necessarily a nearest neighbor for q. In theoretical discussions of algorithms a kind of general position is often assumed, namely, the nearest (k-nearest) neighbor is unique for each object. In implementations of the algorithms it is necessary to bear in mind that this is not always the case. For situations in which it is necessary to make the nearest neighbor for each object unique, the set P may be indexed and in the case of a tie the object with, e.g., the largest index may be taken as the nearest neighbor.

The k-nearest neighbor graph (k-NNG) is a graph in which two vertices p and q are connected by an edge, if the distance between p and q is among the k-th smallest distances from p to other objects from P. The NNG is a special case of the k-NNG, namely it is the 1-NNG. k-NNGs obey a separator theorem: they can be partitioned into two subgraphs of at most n(d + 1)/(d + 2) vertices each by the removal of O(k1/dn1 − 1/d) points.

Another variation is the farthest neighbor graph (FNG), in which each point is connected by an edge to the farthest point from it, instead of the nearest point.

NNGs for points in the plane as well as in multidimensional spaces find applications, e.g., in data compression, motion planning, and facilities location. In statistical analysis, the nearest-neighbor chain algorithm based on following paths in this graph can be used to find hierarchical clusterings quickly. Nearest neighbor graphs are also a subject of computational geometry.

The method can be used to induce a graph on nodes with unknown connectivity.