title: Best Performance-Critical Algorithm for Solving Nearest Neighbor
body: <p>We have a list of x,y pairs. Every pair represents a point on a 2D space. I want to find the closest point from this list, to a specific point xq,yq. What is the best performance-critical algorithm for this problem? Lisp of points is not going to change; which means I do not need to perform insertion and deletion. I want just to find the nearest neighbor of a target xq,yq point in this set.</p>
  
  <p>Edit 1: Thanks to all! As Stephan202 has guessed correctly, I want to do this repeatedly; like a function. An the list is not necessarily sorted (In fact I do not understand how can it be sorted? Like a table with a primary key of 2 columns a and y? If that helps then I will sort it).</p>
  
  <p>I will construct the data structure based on the list one time, and then I will use this generated data structure in the function (if this process itself is relevant).</p>
  
  <p>Thank you Jacob; It seems that KD-Tree data structure is a good candidate for being the answer (And I feel it is. I will update when I get some relevant results).</p>
  
  <p>Edit 2: I have found that, this problem is named "nearest neighbor"!</p>
  
  <p>Edit 3: First title was "In Search of an Algorithm (for Spatial-Querying and Spatial-Indexing) (Nearest Neighbor)"; I have chose a new title: "Best Performance-Critical Algorithm for Solving Nearest Neighbor". Since I do not want to perform insertion and deletion operation on my initial data and I want just the nearest one from them to a new point (which is not going to be inserted), I chose to (currently) working on KD-Trees. Thanks to all!</p>