Given the following:
"You are organizing a party and you want it to be as much fun as possible. You have $n$ friends to choose from, but the maximum number of people that you can invite into your flat — its capacity — is $C$. The fun at a party stems from pairwise interactions between guests, and you have the an $n \times n$ “fun table” $F$, such that for every pair $(i,j)$ of your friends, $F[i,j]$ is a number between 0 and 1 that specifies how much fun their mutual presence at the party would contribute. The DECENT-PARTY decision problem is—given an $n\times n$ array $F$ representing the fun table, a number $C$ and a number $T$ as inputs—to determine if there is a selection of $C$ guests such that the total fun contributed by all pairwise interactions between them is at least $T$."
How can I prove that if there is a polynomial time algorithm for solving DECENT-PARTY then there is also one for the INDEPENDENT-SET decision problem? In order to do this I want to show a polynomial time reduction from INDEPENDENT-SET to DECENT-PARTY, i.e. that DP is at least as hard as IS and thus it follows.
To do this, I think I need to instantiate IS, a graph and some integer $k$. Then somehow translate that to an instance of DP but I am not sure how as it seems that DP involves non-integer values.