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Unformatted text preview: city sites (represented by vertices in V ). You’ve also written a history
of Boston, which would be best described by visiting sites v0 , v1 , . . . , vk in that order.
Your goal is to ﬁnd the shortest path in G that visits v0 , v1 , . . . , vk in order, possibly visiting other
vertices in between. (The path must have v0 , v1 , . . . , vk as a subsequence; the path is allowed to
visit a vertex more than once. For example, v0 , v2 , v1 , v2 , . . . , vk is legal.) To do the computation,
you’ve found an online service, Paths ’R Us, that will compute the shortest path from a given
source s to a given target t in a given weighted graph, for the bargain price of $1. You see how to
solve the problem by paying $k , calling Paths ’R Us with (v0 , v1 , G), (v1 , v2 , G), . . . , (vk−1 , vk , G)
and piecing together the paths. Describe how to solve the problem with only $1 by calling Paths
’R Us with (s, t, G ) for a newly constructed graph G = (V , E , w ), and converting the resulting
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This document was uploaded on 03/17/2014 for the course ELECTRICAL 6.006 at MIT.
- Fall '11