[Verse 1]
Ford-Fulkerson had the vision, maximum flow through networks
But which path to pick was fuzzy, inefficient workers
Edmonds-Karp stepped up with clarity, BFS to guide the way
Shortest augmenting paths only, no backtrack delay
Queue up vertices level by level, breadth before depth
Polynomial time guaranteed, O-V-E squared kept
[Chorus]
Breadth first search, shortest paths persist
Augment the flow, capacity can't resist
Queue the neighbors, level by level rise
Edmonds-Karp optimizes, polynomial prize
Maximum flow, minimum time to find
BFS structure keeps complexity defined
[Verse 2]
Residual graph construction, forward edges minus reverse
Capacity remaining matters, bottlenecks disperse
Start from source, explore adjacent, mark each vertex seen
Queue expands horizontally, systematic and clean
When sink appears in BFS tree, augmenting path revealed
Minimum capacity traced back, flow increment sealed
[Chorus]
Breadth first search, shortest paths persist
Augment the flow, capacity can't resist
Queue the neighbors, level by level rise
Edmonds-Karp optimizes, polynomial prize
Maximum flow, minimum time to find
BFS structure keeps complexity defined
[Bridge]
No more exponential nightmares
Shortest paths eliminate despair
V times E squared complexity
Graph algorithms harmony
[Verse 3]
Saturated edges vanish, residual capacity zero
New paths emerge dynamically, algorithm's hero
Termination guaranteed certain, no more paths exist
Maximum flow achieved completely, efficiency's twist
Networks optimize transmission, pipes and cables flow
Edmonds-Karp delivers answers computer science should know
[Outro]
Breadth first search, the secret key
Polynomial bounds, complexity free
Maximum flow, problem solved clean
Edmonds-Karp reigns supreme