\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}

\usepackage[utf8]{inputenc} % this is needed for umlauts
\usepackage[ngerman]{babel} % this is needed for umlauts
\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
\usepackage{amssymb,amsmath,amsfonts} % nice math rendering
\usepackage{braket} % needed for \Set
\usepackage{caption}
\usepackage{algorithm}
\usepackage[noend]{algpseudocode}

\DeclareCaptionFormat{myformat}{#3}
\captionsetup[algorithm]{format=myformat}

\begin{document}
\begin{preview}
    \begin{algorithm}[H]
        \begin{algorithmic}
        \Require
        \Statex Graph $G = (V, E)$
        \Statex Weight from node $i$ to node $j$: $g_{ij} \in \mathbb{R}_0^+$
        \Statex Starting node $s \in V$
        \Statex End node $t \in V$
        \Statex Lower bound to get from node $j$ to $t$: $h_j$ (default: $h_j = 0$)
        \Statex Upper bound to get from node $j$ to $t$: $m_j$ (default: $m_j = \infty$)
        \Procedure{LabelCorrection}{$G$, $s$, $t$, $h$, $m$}
            \State $d_s \gets 0$
            \State $d_i \gets \infty \quad \forall i \neq s$ \Comment{Distance of node $i$ from $s$}
            \State $u \gets \infty$ \Comment{Distance from $s$ to $t$}
            \State $K \gets \{s\}$ \Comment{Choose some datastructure here}
            \While{$K$ is not empty}
                \State $v \gets K.pop()$
                \For{child $c$ of $v$}
                    \If{$d_v + g_{vc} + h_c < \min(d_c, u)$}
                        \State $d_c \gets d_v + g_{vc}$
                        \State $c.parent \gets v$
                        \If{$c \neq t$ and $c \notin K$}
                            \State $K.insert(c)$
                        \EndIf
                        \If{$c = t$}
                            \State $u \gets d_v + g_{vt}$
                        \EndIf
                    \EndIf
                    \If{$d_c + m_c < u$}
                        \State $u \gets d_c + m_c$
                    \EndIf
                \EndFor
            \EndWhile
        \EndProcedure
        \end{algorithmic}
    \caption{Label correction algorithm}
    \label{alg:label-correction-algorithm}
    \end{algorithm}
\end{preview}
\end{document}
