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( 1 0 points ) True or False? For each of the statements below, determine whether it is True or False. Then, briefly explain your
points True or False?
For each of the statements below, determine whether it is True or False. Then, briefly explain
your answers or provide counterexamples. Incorrect answers or unanswered questions are worth
zero points. Each subproblem is worth point.
a Claim: algorithm runs faster than a algorithm for any input instance.
b Consider an instance of the Stable Matching Problem in which there exists a hospital
and a student such that is ranked first on the preference list of and is ranked first
on the preference list of
Claim: In every stable matching for this instance, the pair belongs to
c Consider the interval scheduling problem we discussed in the class, where we want to
maximize the number of compatible ie nonoverlapping intervals.
Claim: The lateststarttimefirst algorithm is optimal for the above problem.
d Consider a forest graph consisting of trees. Suppose has nodes.
Claim: Graph has edges.
e Let be a minimum spanning tree of a graph
Claim: for any pair of vertices and the shortest path from to in is the path from
to in
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