step 2 structure of shortest

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Unformatted text preview: is the distance from to . So our aim 444 565¥ ! ¥ © ¡ % for 5 ¥     1 32 ¤£¡  Subproblems: compute . ¨ 1 32   ¤£¡ is to compute   ) ¤ Claim: be the '% (&¥ ¤£¡  Let is set to be Step 2: Structure of shortest paths Observation 1: A shortest path does not contain the same vertex twice. Proof: A path containing the same vertex twice contains a cycle. Removing cycle gives a shorter path.  Observation 2: For a shortest path from to such that any intermediate vertices on the path are chosen , there are two possibilities: from...
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