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Unformatted text preview: s ; v path. pred( v ) is the predecessor of v in the shortest s ; v path. We call an edge tense if dist( u ) + w ( u v ) < dist( v ). Our generic algorithm repeatedly nds a tense edge in the graph and relaxes it: Relax( u v ): dist( v ) dist( u ) + w ( u v ) pred( v ) u If there are no tense edges, our algorithm is nished, and we have our desired shortest path tree. The correctness of the relaxation algorithm follows directly from three simple claims. The rst of these is below. Prove it. When the algorithm halts, if dist( v ) 6 = , then dist( v ) is the total weight of the predecessor chain ending at v : s ( pred ( pred ( v )) pred ( v ) v. 3. Cant nd a Cut-edge A cut-edge is an edge which when deleted disconnects the graph. Prove or disprove the following. Every 3-regular graph has no cut-edge. (A common approach is induction.) 1...
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This note was uploaded on 10/14/2011 for the course ECON 101 taught by Professor Smith during the Spring '11 term at West Virginia University Institute of Technology.
- Spring '11