A spanning tree is a subset of Graph G that has the fewest number of edges feasible connecting every vertex. A spanning tree cannot be detached and does not have cycles.How to implement in JAVA the following algorithm for finding a maximum spanning tree in G, which would maximize the bandwidth between two switching centers. Algorithm: Maximum Bandwidth(G,a)   Input: prompt the user for number of switching centers and number of edges/bandwidths, then prompt the user for bandwidth information, fill adjacency list with the following information starting switching centers --> destiantion center and its bandwidth.( starting and destination switching centers should be Character values and bandwidth is integer value, example A C 10, C D 7 etc. everything in one line). After prompt the user for finding maximum bandwidth between two switching centers (example A D --> 7) Output: Maximum bandwidth between two switching centers   Initialize empty queue Q; Start = a; for each vertex u of G do, D[u] = 0; for all vertices z adjacent to Start do{ ---- 1 If D[Start] => D[z] && w(start, z) > D[z] { Q.enqueue(z); D[z] = min(D[start], D[z]); } } If Q!=null { Start = Q.dequeue; Jump to 1 } else finish();

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Polynomial Time

The problems for which the deterministic polynomial-time algorithm exists belong to the complexity class (p) and it is central in the field of computational complexity theory. According to Cobham’s thesis, polynomial time is a synonym for “feasible”, “fast”, and “efficient”.