Concepts inEfficient data structures for range-aggregate queries on trees

Data structure

In computer science, a data structure is a particular way of storing and organizing data in a computer so that it can be used efficiently. Different kinds of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, B-trees are particularly well-suited for implementation of databases, while compiler implementations usually use hash tables to look up identifiers.
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Lattice graph

The terms lattice graph, mesh graph, or grid graph refer to a number of categories of graphs whose drawing corresponds to some grid/mesh/lattice, i.e. , its vertices correspond to the nodes of the mesh and its edges correspond to the ties between the nodes.
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Tree (graph theory)

In mathematics, more specifically graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one simple path. In other words, any connected graph without cycles is a tree. A forest is a disjoint union of trees. The various kinds of data structures referred to as trees in computer science are equivalent to trees in graph theory, although such data structures are commonly rooted trees, and may have additional ordering of branches.
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Tree (data structure)

In computer science, a tree is a widely used data structure that simulates a hierarchical tree structure with a set of linked nodes. Mathematically, it is an ordered directed tree, more specifically an arborescence: an acyclic connected graph where each node has zero or more children nodes and at most one parent node. Furthermore, the children of each node have a specific order.
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Directed graph

In mathematics, a directed graph or digraph is a graph, or set of nodes connected by edges, where the edges have a direction associated with them. In formal terms a digraph is a pair (sometimes) of: a set V, whose elements are called vertices or nodes, a set A of ordered pairs of vertices, called arcs, directed edges, or arrows (and sometimes simply edges with the corresponding set named E instead of A).
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DSPACE

In computational complexity theory, DSPACE or SPACE is the computational resource describing the resource of memory space for a deterministic Turing machine. It represents the total amount of memory space that a "normal" physical computer would need to solve a given computational problem with a given algorithm.
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Graph (mathematics)

In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics.
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