2005
DOI: 10.1590/s0101-74382005000200004
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Abstract: A minimum spanning tree of an undirected graph can be easily obtained using classical algorithms by Prim or Kruskal. A number of algorithms have been proposed to enumerate all spanning trees of an undirected graph. Good time and space complexities are the major concerns of these algorithms. Most algorithms generate spanning trees using some fundamental cut or circuit. In the generation process, the cost of the tree is not taken into consideration. This paper presents an algorithm to generate spanning trees of … Show more

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Cited by 29 publications
(18 citation statements)
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“…For any Steiner Minimal Tree T connecting the terminal set τ, it is proved that |R| ≤ |τ| − 2 ( [41]). Now, for each set of routers R, the algorithm constructs a complete graph G Rτ = (V Rτ , E Rτ ) with V Rτ = R τ and the weight of an edge uv ∈ E Rτ is equal to the minimum path length between two nodes u and v. In other words, it constructs a metric closure graph (complete graph) for the set V Rτ = R τ in the graph G. We then find all minimum spanning trees in the graph G Rτ , using the algorithm in [42]. We then consider each edge in that tree in turn and, if the end points are not yet connected in the new tree, select the corresponding shortest path from the original graph.…”
Section: Optimal Node Algorithm (N-opt)mentioning
confidence: 99%
See 1 more Smart Citation
“…For any Steiner Minimal Tree T connecting the terminal set τ, it is proved that |R| ≤ |τ| − 2 ( [41]). Now, for each set of routers R, the algorithm constructs a complete graph G Rτ = (V Rτ , E Rτ ) with V Rτ = R τ and the weight of an edge uv ∈ E Rτ is equal to the minimum path length between two nodes u and v. In other words, it constructs a metric closure graph (complete graph) for the set V Rτ = R τ in the graph G. We then find all minimum spanning trees in the graph G Rτ , using the algorithm in [42]. We then consider each edge in that tree in turn and, if the end points are not yet connected in the new tree, select the corresponding shortest path from the original graph.…”
Section: Optimal Node Algorithm (N-opt)mentioning
confidence: 99%
“…The algorithm firstly constructs the set R ⊆ V\τ such that |R| ≤ |τ| − 2. It then finds all spanning trees in the graph G Rτ , using the Algorithm in [42]. We then consider each edge in that tree in turn and, if the end points are not yet connected in the new tree, select the corresponding shortest path from the original graph.…”
Section: Algorithm 4: P-opt Algorithmmentioning
confidence: 99%
“…The algorithm is given by Sörensen and Janssens (2005) (who looked for lowest weight spanning trees, rather than highest weight spanning trees). Suppose that we are given an undirected connected graph on n vertices, in which each edge between a pair of vertices is given a non-negative weight value.…”
Section: Finding the K Best Spanning Trees Of A Graphmentioning
confidence: 99%
“…Note the first constraint (2a) is equivalent to removing the first e 2 1 edges from the list L, whilst for the other possible trees the search is started at the e 2 1 edge (2b -2d). The procedure may be repeated until the desired number k of maximum weight spanning trees is found, see Sörensen and Janssens (2005) for more details and proof. Note that if the procedure is repeated with no upper bound k specified, then the algorithm will generate all possible spanning trees ordered by weight.…”
Section: Finding the K Best Spanning Trees Of A Graphmentioning
confidence: 99%
“…P : List all the MSTs in graph G. Related to this problem are the algorithms to list all the spanning trees [5,9,11], do the same in non-decreasing order of cost [3,13] and find K-shortest spanning trees in a graph [2,8]. Indeed, P may be solved by finding all the spanning trees, or more preferably by applying a K-shortest 3176 T. Yamada et al spanning tree algorithm with sufficiently large K and truncating its execution as soon as we have a spanning tree of weight larger than z .…”
Section: Introductionmentioning
confidence: 99%