10 9 Consider this statement: if a graph G contains a cycle C,and C contains an

Question

10 9 Consider this statement: if a graph G contains a cycle C,and C contains an edge e whose weight is less than the weight of all other edges in C, then e is in an MST for G. Is this true or false? HINT-consider how Kruskal's algorithm would contruct the MST for relevant examples. ii) To find the shortest paths containing at most Q edges from a vertex s to all other vertices of a directed graph G with positively weighted edges, you are told to modify either the Dijkstra or the Bellman-Ford algorithm. You limit the main loop to run exactly Q times. In iteration i, your modified RELAX procedure: c 1: procedure RELAX((u, v), i) 2: if distuli-1+ w(u,v)

Explanation / Answer

Solution:

ii)

The given statement is true, because:

c)

In this case Bellman ford will perform best. because:

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