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Unformatted text preview: target vertex t in Gk .)
Once we have a shortest path in G , we can convert it into the corresponding path in G by simply
replacing every vertex ui ∈ V with u ∈ V , and then removing any loop edges (vi , vi ) from the path
(resulting from the zero-weight edge (vi , vi +1 )). Intuitively, we just need to ﬂatten the k copies of
G down to the single copy.
Another solution to this problem, found by many students, is to replace the endpoints of the edges
instead of using zero-weight edges. For example, after making k copies of the graph G, we can
replace each edge (ui , vi ) with (ui , vi +1 ). This has the same effect as the zero-weight edges, and
removes the need to remove loops at the end. 6.006 Quiz 2 Solutions Name 12 Problem 6. Fill ’Er Up! [25 points]
You are traveling by car from one city to another city. Unfortunately, you have a hole in your
gas tank, and you have to reﬁll your gas tank to travel across more than two roads. In addition,
there is a toll booth on every road that charges you for...
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This document was uploaded on 03/17/2014 for the course ELECTRICAL 6.006 at MIT.
- Fall '11