Search results
Results from the WOW.Com Content Network
Animated example of a depth-first search. For the following graph: a depth-first search starting at the node A, assuming that the left edges in the shown graph are chosen before right edges, and assuming the search remembers previously visited nodes and will not repeat them (since this is a small graph), will visit the nodes in the following ...
In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points ), together with a set of unordered pairs of these ...
The basic idea of the algorithm is this: a depth-first search (DFS) begins from an arbitrary start node (and subsequent depth-first searches are conducted on any nodes that have not yet been found). As usual with depth-first search, the search visits every node of the graph exactly once, refusing to revisit any node that has already been visited.
Several algorithms based on depth-first search compute strongly connected components in linear time.. Kosaraju's algorithm uses two passes of depth-first search. The first, in the original graph, is used to choose the order in which the outer loop of the second depth-first search tests vertices for having been visited already and recursively explores them if not.
Trémaux trees are named after Charles Pierre Trémaux, a 19th-century French author who used a form of depth-first search as a strategy for solving mazes. [1] [2] They have also been called normal spanning trees, especially in the context of infinite graphs. [3] [4] All depth-first search trees and all Hamiltonian paths are Trémaux
Let Y 1 be a minimum spanning tree of graph P. If Y 1 =Y then Y is a minimum spanning tree. Otherwise, let e be the first edge added during the construction of tree Y that is not in tree Y 1, and V be the set of vertices connected by the edges added before edge e. Then one endpoint of edge e is in set V and the other is not.
The depth is standard to maintain during a depth-first search. The lowpoint of v can be computed after visiting all descendants of v (i.e., just before v gets popped off the depth-first-search stack) as the minimum of the depth of v, the depth of all neighbors of v (other than the parent of v in the depth-first-search tree) and the lowpoint of ...
For general graphs, the best known algorithms for both undirected and directed graphs is a simple greedy algorithm: In the undirected case, the greedy tour is at most O(ln n)-times longer than an optimal tour. [1] The best lower bound known for any deterministic online algorithm is 10/3. [2]