How to indent a long sentence in an algorithm

You can use tabularx to figure out the width of a box that would fit until the end of the line:

\documentclass{article}

\usepackage{amsmath,algorithm,tabularx}
\usepackage[noend]{algpseudocode}

\makeatletter
\newcommand{\multiline}[1]{%
  \begin{tabularx}{\dimexpr\linewidth-\ALG@thistlm}[t]{@{}X@{}}
    #1
  \end{tabularx}
}
\makeatother

\begin{document}

\begin{algorithm}
  \caption{hello}
  \begin{algorithmic}[1]
    \Procedure{ASAPP}{}
      \State $i \gets 0$, $j \gets 0$, $k \gets 0$
      \While { $i \leq \text{nom}$ }
        \While {$j \leq C_i$ }
          \State \multiline{%
            Considering the $j$-th edge of the $i$-th metabolite,~$x$ and~$y$ 
            contains the vertices of the $j$-th edge}
          \State $k \gets j + 1$
          \While { $k \leq C_i$ }
            \State \multiline{%
              Considering the $k$-th edge of the $i$-th metabolite,~$x_1$ and~$y_1$ 
              contains the vertices of the $k$-th edge.}
          \EndWhile
        \EndWhile
      \EndWhile
    \EndProcedure
  \end{algorithmic}
\end{algorithm}

\end{document}

\multiline{<stuff>} sets its contents in a tabularx that is aligned at the [t]op inside an X-column. The width of this column is the difference of a regular \linewidth minus the current algorithm line indent.