ZPTUSS
The Wikipedia Enthusiast Communication Group ( Telegram : @wikipedia_zh_n , IRC : #wikipedia-en link , both connected) welcome everyone to join.
| [ Close ] |
Hamiltonian
 | This entry does not list any references or sources . (March 24, 2014) |
Hamiltonian ( English: ON HAMILTONIAN path , or Traceable path ) is an undirected graph , the astronomer Hamiltonian proposed by the designated starting point to the designated end point, all the way through the other node and pass only once. In FIG theory refers FIG containing Hamiltonian circuit, called a closed Hamiltonian path Hamiltonian circuit ( the Hamiltonian Cycle ), all paths containing the vertices of the figure is referred Hamiltonian path .
The definition of the Hamilton graph: G = (V, E) is a graph. If a path in G passes through each vertex once and only once, it is called the Hamilton path. If a circle in G passes through each vertex once and only once, call this circle Hamiltonian. If a graph has a Hamiltonian circle, it is called a Hamilton map.
Necessary conditions for Hamiltonian graphs: If G=(V,E) is a Hamiltonian graph, for each non-empty subset S of V, there is W(G-S) ≤|S| where W(G-S) denotes Figure G wipes the vertices belonging to S, leaving the number of connected branches of the subgraph.
Sufficient conditions for the Hamilton graph: Let G = (V, E) be an undirected simple graph, |V|=n. n≥3. If for any two vertices u, v∊V,d(u)+d (v) ≥ n, then G is a Hamilton map.
The American graph theory mathematician Ole gave a sufficient condition for a graph to be a Hamilton graph in 1960 : For a graph with a number of vertices greater than 2, if the sum of any non-adjacent two points in the graph is greater than or equal to the total number of vertices, That map must be a Hamilton map.
Finding a Hamiltonian path is a typical NP-complete problem. Later, people also proved that finding an approximate algorithm with an approximate ratio of Hamilton Road is also NP-complete.
Although it is difficult to find the polynomial time for the determination algorithm for Hamiltonian roads, this does not mean that only the time complexity O(n!*n) can be used for brute force search. With state compression dynamic programming , the time complexity can be reduced to O(2^n*n^3). The specific algorithm is to establish the equation f[i][S][j], indicating that after i nodes, the nodes are Set S, the shortest path to node j. Every time the node connected by point j is transferred.
2 categories :
- NP complete problem
- Graph Theory
