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Pitchaya Boonsarngsuk
2018-03-23 13:45:16 +00:00
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@@ -215,18 +215,21 @@ Previous evaluations show that this method is faster than the Chalmers' 1996 alg
\section{Hybrid MDS with Pivot-Based Searching algorithm} \section{Hybrid MDS with Pivot-Based Searching algorithm}
\label{sec:bg_hybridPivot} \label{sec:bg_hybridPivot}
\begin{wrapfigure}{rh}{0.3\textwidth}
\centering
\includegraphics[width=0.3\textwidth]{images/pivotBucketsIllust.png}
\caption{Diagram of a pivot (dark shaded point) with five buckets, illustrated as discs between dotted circle. Each of the other points in $S$ are classified into buckets by the distances to the pivot.}
\label{fig:bg_pivotBuckets}
\end{wrapfigure}
The bottleneck of the Hybrid Layout Algorithm is the nearest-neighbour searching process during the interpolation. The previous brute-force method results in the time complexity of $O(N\sqrt{N})$. This improvement introduces pivot-based searching to approximate a near-neighbour and reduces the time complexity to $O(N^\frac{5}{4})$\cite{Algo2003}. The bottleneck of the Hybrid Layout Algorithm is the nearest-neighbour searching process during the interpolation. The previous brute-force method results in the time complexity of $O(N\sqrt{N})$. This improvement introduces pivot-based searching to approximate a near-neighbour and reduces the time complexity to $O(N^\frac{5}{4})$\cite{Algo2003}.
The main improvements is gained by pre-processing the set $S$ ($\sqrt{N}$ samples) so that each of the $N-\sqrt{N}$ other points can find the parent is faster. To begin, $k$ points were selected from $S$ as `parent'. Each pivot $p\in{k}$ have a number of buckets. Every other points in $S-\{p\}$ assigned a bucket number, based on the distance from to $p$ as illustrated in figure \ref{fig:bg_pivotBuckets}. The main improvements is gained by pre-processing the set $S$ ($\sqrt{N}$ samples) so that each of the $N-\sqrt{N}$ other points can find the parent is faster. To begin, $k$ points were selected from $S$ as `parent'. Each pivot $p\in{k}$ have a number of buckets. Every other points in $S-\{p\}$ assigned a bucket number, based on the distance from to $p$ as illustrated in figure \ref{fig:bg_pivotBuckets}.
To find a parent of an object, a distance calculation is first performed against each pivot to determine which bucket of each pivot is the object in. From this, the content of each bucket is searched for the nearest neighbor. To find a parent of an object, a distance calculation is first performed against each pivot to determine which bucket of each pivot is the object in. From this, the content of each bucket is searched for the nearest neighbour.
\break
\begin{wrapfigure}{Rh}{0.3\textwidth}
\vspace{-230pt}
\centering
\includegraphics[width=0.28\textwidth]{images/pivotBucketsIllust.png}
\caption{Diagram of a pivot (dark shaded point) with five buckets, illustrated as discs between dotted circle. Each of the other points in $S$ are classified into buckets by the distances to the pivot.}
\label{fig:bg_pivotBuckets}
\end{wrapfigure}
\begin{algorithmic} \begin{algorithmic}
\item Pre-processing: \item Pre-processing: