text: One type of this structure proposed by Bentley quickly finds the nearest neighbor of an input, and its elements represent splitting planes.
full_question: One type of this structure proposed by Bentley quickly finds the nearest neighbor of an input, and its elements represent splitting planes. A proof of the n log(n) lower bound for comparison based sorting builds one of these structures, and notes it must have at least n factorial of a certain type of element. The inverse Ackermann function appears when analyzing an algorithm that uses a union-find data structure to find one of these structures. A greedy algorithm by Kruskal finds the minimum spanning type of this structure. For 10 points, name these acyclic graphs with root and leaf nodes.
first_sentence: One type of this structure proposed by Bentley quickly finds the nearest neighbor of an input, and its elements represent splitting planes.