EMST meaning in General ?

Answer: What is Euclidean Minimum Spanning Tree mean?

The Euclidean minimum spanning tree or EMST is a minimum spanning tree of a set of n {\displaystyle n} points in the plane or higher-dimensional Euclidean space. It connects the points by a system of line segments, so that any two points can reach each other along a path through the line segments, and it selects line segments that minimize the sum of the Euclidean distances between directly-connected pairs of points.

In the plane, the Euclidean minimum spanning tree is a subgraph of the Delaunay triangulation. Using this fact, the Euclidean minimum spanning tree for a given set of planar points may be found in time O ( n log ⁡ n ) {\displaystyle O(n\log n)} (expressed in Big O notation), using algorithms based on comparisons of simple combinations of input coordinates. Faster randomized algorithms are known in models of computation allowing more powerful operations such as integer rounding.

In higher dimensions ( d ≥ 3 {\displaystyle d\geq 3} ), finding an optimal algorithm remains an open problem.

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