Can we use Floyd-Warshall to find the minimum weight cycle in a graph?

Правка en1, от felipeblassioli, 2015-10-08 04:54:23

Floyd-Warshall is initialized with dist[u][u] = 0 , can we do dist[u][u] = INF and run a default implementation of Floyd-Warshall hoping that dist[u][u] is the shortest distance from u to u? (i.e the minimum weight cycle)?

Does this works for both directed and undirected graphs?

I'm taking for a default implementation something like wikipedia:

1 let dist be a |V| × |V| array of minimum distances initialized to ∞ (infinity) 2 for each vertex v 3 dist[v][v] ← 0 4 for each edge (u,v) 5 dist[u][v] ← w(u,v) // the weight of the edge (u,v) 6 for k from 1 to |V| 7 for i from 1 to |V| 8 for j from 1 to |V| 9 if dist[i][j] > dist[i][k] + dist[k][j] 10 dist[i][j] ← dist[i][k] + dist[k][j] 11 end if

Теги algorithms, graphs, help me, cycle, cycle detection, floyd-warshall

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  Rev. Язык Кто Когда Δ Комментарий
en5 Английский felipeblassioli 2015-10-08 20:26:20 659 Explanation with problem with undirected graphs
en4 Английский felipeblassioli 2015-10-08 20:21:43 12 Trivial cycle for undirected graphs are not interesting
en3 Английский felipeblassioli 2015-10-08 05:11:44 90
en2 Английский felipeblassioli 2015-10-08 05:07:13 50 Tiny change: '\nFloyd-Wars' -
en1 Английский felipeblassioli 2015-10-08 04:54:23 834 Initial revision (published)