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\title{\bf Assignment 7 \\[2ex]
\rm\normalsize Due: March 10, 2020}
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    \fbox{\fbox{\parbox{\textwidth}{\centering
    Your solutions must be typed (preferably typeset in \LaTeX) and submitted as a hard-copy at the beginning of
    class on the day its due.
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\paragraph{Problem 1: Partition [10 points]}
Show that the following problem is NP-Complete (Hint: reduce from SubsetSum).
\subparagraph{PARTITION:} Given a finite set $A$ and a positive integer $s(a)$ associated with each $a \in A$, is there a subset $A' \subseteq A$ such that $\sum_{a \in A'} s(a) = \sum_{a \in A-A'} s(a)$?

\paragraph{Problem 2: Fire Houses [10 points]}
Show that the following problem is NP-Complete (Hint: reduce from 3-SAT or Vertex Cover).
\subparagraph{FIREHOUSES:} Given an undirected graph $G$ with positive integer distances on the edges, and
two integers $f$ and $d$, is there a way to select $f$ vertices on $G$ on which to locate firehouses, so that
no vertex of $G$ is at distance more than $d$ from a firehouse?

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