\begin{algorithm} [tb!]
\footnotesize
\caption{\small {\sf HuGE-D} walking procedure}
\label{HuGE-D_walk}
\begin{algorithmic}[1]
\Require current node $u$, candidate node $v$, Walker $W$, {\sf HuGE} parameter $\mu$
\Ensure walker state updates
{\flushleft{{\bf sendStateQuery($u$, $v$, $W$)}}} %//{submit the walker-to-vertex query messages and process the state queries}
\State{$P(u,v) = Z\left(\frac{1}{deg(u)-Cm(u, v)}\cdot \max \left\{\frac{deg(u)}{deg(v)}, \frac{deg(v)}{deg(u)} \right\} \right)$} // Eq.~\ref{accept_CNHRW}

{\flushleft{{\bf getStateQueryResult($W, P(u,v)$)}}} %// {return results to querying walkers for retrieving the state and decide sampling outcome}
\State{generate a random number $\eta \in\left[0,1\right]$}
\If{$P(u,v)> \eta $}
\State{$W.path$.append($v$), $W.cur$ = $v$, $W.steps$ ++}
\State{$L$ = $W.steps$}
\State compute $H(W)$ and $R\left(H(W),L\right)$ // Eq.~\ref{path_entropy}, \ref{path_corr}
\If{$R^2(H(W),L) < \mu$}
\State terminate the walk
\Else
\State{generate another candidate node $t$ of $v$}
\State{sendStateQuery($v$, $t$, $W$)}
\EndIf
\Else
\State{backtrack to $u$ and generate another candidate node $v'$ of $u$}
\State{sendStateQuery($u$, $v'$, $W$)}
\EndIf
\end{algorithmic}
\end{algorithm}

\begin{algorithm}
[tb!]
\footnotesize
\caption{\small {\sf HuGE-D} walking procedure}
\begin{algorithmic}
[1]
\Require current node $u$, candidate node $v$, Walker $W$, {\sf HuGE} parameter $\mu$
\Ensure walker state updates
{\flushleft{{\bf sendStateQuery($u$, $v$, $W$)}}} %//{submit the walker-to-vertex query messages and process the state queries}
\State{$P(u,v) = Z\left(\frac{1}{deg(u)-Cm(u, v)}\cdot \max \left\{\frac{deg(u)}{deg(v)}, \frac{deg(v)}{deg(u)} \right\} \right)$} // Eq.~\ref{accept_CNHRW}
{\flushleft{{\bf getStateQueryResult($W, P(u,v)$)}}} %// {return results to querying walkers for retrieving the state and decide sampling outcome}
\State{generate a random number $\eta \in\left[0,1\right]$}
\If{$P(u,v)> \eta $}
\State{$W.path$.append($v$), $W.cur$ = $v$, $W.steps$ ++}
\State{$L$ = $W.steps$}
\State compute $H(W)$ and $R\left(H(W),L\right)$ // Eq.~\ref{path_entropy}, \ref{path_corr}
\If{$R^2(H(W),L) < \mu$}
\State terminate the walk
\Else
\State{generate another candidate node $t$ of $v$}
\State{sendStateQuery($v$, $t$, $W$)}
\EndIf
\Else
\State{backtrack to $u$ and generate another candidate node $v'$ of $u$}
\State{sendStateQuery($u$, $v'$, $W$)}
\EndIf
\end{algorithmic}
\end{algorithm}
{
    "title": "distributed graph embedding with information-oriented random walks",
    "id": "2303.15702",
    "abstract": "graph embedding maps graph nodes to low-dimensional vectors, and is widely adopted in machine learning tasks. the increasing availability of billion-edge graphs underscores the importance of learning efficient and effective embeddings on large graphs, such as link prediction on twitter with over one billion edges. most existing graph embedding methods fall short of reaching high data scalability. in this paper, we present a general-purpose, distributed, information-centric random walk-based graph embedding framework, distger, which can scale to embed billion-edge graphs. distger incrementally computes information-centric random walks. it further leverages a multi-proximity-aware, streaming, parallel graph partitioning strategy, simultaneously achieving high local partition quality and excellent workload balancing across machines. distger also improves the distributed skip-gram learning model to generate node embeddings by optimizing the access locality, cpu throughput, and synchronization efficiency. experiments on real-world graphs demonstrate that compared to state-of-the-art distributed graph embedding frameworks, including knightking, distdgl, and pytorch-biggraph, distger exhibits 2.33x-129x acceleration, 45% reduction in cross-machines communication, and > 10% effectiveness improvement in downstream tasks.",
    "categories": "cs.dc cs.lg",
    "doi": "",
    "created": "2023-03-27",
    "updated": "2024-02-25",
    "authors": [
        "peng fang",
        "arijit khan",
        "siqiang luo",
        "fang wang",
        "dan feng",
        "zhenli li",
        "wei yin",
        "yuchao cao"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2303.15702"
}
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