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Assume we have a path in an undirected cyclic weighted graph. Assuming we have an engine that can find a path from node A to node B in such a graph, is there an easy way/algorithm to figure out if the given path from A to B is at least X% better than any other disjoint path from A to B? By disjoint I mean two paths may not share any edges.

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When you mean cyclic, do you mean it's a cycle? –  mixedmath Oct 7 '11 at 23:14
    
I mean it has cycles. –  Schultz9999 Oct 7 '11 at 23:17
    
Perhaps this paper might be of use: dl.acm.org/citation.cfm?id=78636 –  Joseph Malkevitch Oct 8 '11 at 22:24
    
@JosephMalkevitch: we already have A* based search engine. –  Schultz9999 Oct 10 '11 at 22:46

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