Algorithm mashing into definitions and overfull / underfull warnings

Question

In a long latex doc I have I get my algorithm inserted into my definition for some reason. I apologize for not having a small working example I could not get one to work. Have a bunch of overfull and underfull errors can that actually cause a problem? And what would be the easiest way to fix such? See here:

\begin{algorithm}
\caption{Primal-dual}
\begin{algorithmic}
 \STATE $ c \leftarrow  w.$
 \STATE $S = \{u \in V : w(u) = 0 \}$.
\WHILE{$S$ is not a hitting set for $C$} 
\STATE  $\mathcal{M} $  a collection of cycles returned by a violation oracle Violation$(G, C, S)$.
\STATE $c_{ \mathcal{M} (u) } \leftarrow |{M _ M : u _ M}|, \forall u \in V $.
 \STATE $ \alpha 
\leftarrow min_ {u \in V \backslash S} | w(u)| /
c_{\mathcal{M} (u) } $
$\bar{
w(u) } \leftarrow  w(u) - \alpha cM (u),$ for all u in V.
$ S \leftarrow \{u _ V : w(u) = 0 \}. $
\ENDWHILE 
%end
return a minimal hitting set $ H \subset S $ of $\mathcal{C}$.
\end{algorithmic}
\end{algorithm}


\begin{definition}
For $p \geq 3$ a $p$-pocket for a planar graph G(V; E) and a cycle collection $\mathcal{C}$, is a set U $\subset$ V such that: \\
 1. The set U contains at most $p$ nodes  with neighbors outside U. (we call these contact nodes) \\
 2. The induced subgraph $G_S [U]$ has at least p faces in $\mathcal{C}$.
\end{definition}

Answer 1

I know that is a bad practive to copy-paste the answer from the manual but there is a subsection that is clearly the answer to your question.

4.4.1 Placement of Algorithms

One important fact that many users may not have noticed is that the algorithm environment is actually built with the float package and float, in turn, uses David Carlisle’s here style option. This means that the floats generated by the algorithm environment accept a special option, namely, [H], with a capital ‘H’, instead of the usual ‘h’ offered by plain LaTeX. This option works as a stronger request of “please put the float here”: instead of just a suggestion for LaTeX, it actually means “put this float HERE”, which is something desired by many. [...]

Warning You can’t use the ‘H’ positioning option together with the usual ‘h’ (for “here”), ‘b’ (for “bottom”) etc. This is a limitation (as far as I know) of the float.sty package.