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In this paper we present novel algorithmic techniques with a O(H(N)+N/H(N))time complexity for performing several types of queries and updates on generalrooted trees, binary search trees and lists of size N. For rooted trees weintroduce a new compressed super-node tree representation which can be used forefficiently addressing a wide range of applications. For binary search trees wediscuss the idea of globally rebuilding the entire tree in a fully balancedmanner whenever the height of the tree exceeds the value of a convenientlychosen function of the number of tree nodes. In the end of the paper weintroduce the H-list data structure which supports concatenation, split andseveral types of queries. Note that when choosing H(N)=sqrt(N) we obtainO(H(N)+N/H(N))=O(sqrt(N)).

Novel O(H(N)+N/H(N)) Algorithmic Techniques for Several Types of Queries and Updates on Rooted Trees and Lists