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Label each split component with a P (a two-vertex split component with multiple edges), an S (a split component in the form of a triangle), or an R (any other split component). While there exist two split components that share a linked pair of virtual edges, and both components have type S or both have type P, merge them into a single larger ...
A recursive tree is a labeled rooted tree where the vertex labels respect the tree order (i.e., if u < v for two vertices u and v, then the label of u is smaller than the label of v). In a rooted tree, the parent of a vertex v is the vertex connected to v on the path to the root; every vertex has a unique parent, except the root has no parent. [24]
The business model canvas is a strategic management template that is used for developing new business models and documenting existing ones. [2] [3] It offers a visual chart with elements describing a firm's or product's value proposition, [4] infrastructure, customers, and finances, [1] assisting businesses to align their activities by illustrating potential trade-offs.
A cutpoint, cut vertex, or articulation point of a graph G is a vertex that is shared by two or more blocks. The structure of the blocks and cutpoints of a connected graph can be described by a tree called the block-cut tree or BC-tree. This tree has a vertex for each block and for each articulation point of the given graph.
In either case, one can form a spanning tree by connecting each vertex, other than the root vertex v, to the vertex from which it was discovered. This tree is known as a depth-first search tree or a breadth-first search tree according to the graph exploration algorithm used to construct it. [ 18 ]
A graph with eight vertices, and a tree decomposition of it onto a tree with six nodes. Each graph edge connects two vertices that are listed together at some tree node, and each graph vertex is listed at the nodes of a contiguous subtree of the tree. Each tree node lists at most three vertices, so the width of this decomposition is two.
To split a tree into two trees, those smaller than key x, and those larger than key x, we first draw a path from the root by inserting x into the tree. After this insertion, all values less than x will be found on the left of the path, and all values greater than x will be found on the right.
In particular, we can adjust it to merge (link) and split (cut) in O(log(n)) amortized time. Link/cut trees divide each tree in the represented forest into vertex-disjoint paths, where each path is represented by an auxiliary data structure (often splay trees, though the original paper predates splay trees and thus uses biased binary search ...