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Aaron Quinlan
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@@ -60,7 +60,7 @@ \section{Results:} | |
| relationships between sets of genomic intervals. | ||
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| \section{Availability:} | ||
| \href{http://bedtools.googlecode.com}{http://bedtools.googlecode.com} | ||
| \href{https://github.com/arq5x/bits}{https://github.com/arq5x/bits} | ||
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| \section{Contact:} [email protected] | ||
| \end{abstract} | ||
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@@ -378,13 +378,13 @@ \subsection{Binary Interval Search (BITS) Algorithm} | |
| integer lists $B_S = [b_1.start, b_2.start, \dots, b_M.start]$ and $B_E = | ||
| [b_1.end, b_2.end, \dots, b_M.end]$, which are each sorted numerically in | ||
| ascending order. Next, two binary searches are performed, | ||
| $last=\textsc{ BSearch}(B_E, a_i.start)$ and | ||
| $first=\textsc{ BSearch}(B_S, a_i.end)$. Since $B_E$ is a sorted list of each | ||
| interval end coordinate in $B$, the elements less than or equal to $last$ in | ||
| $B_E$ correspond to the set of intervals in $B$ that end \emph{before} $a_i$ | ||
| starts (i.e., to the ``left'' of $a_i$). Similarly, the elements greater than | ||
| or equal to $first$ in $B_S$ correspond to the set of intervals in $B$ that | ||
| start \emph{after} $a_i$ ends (i.e., to the ``right'' of $a_i$). From these two | ||
| $last=\textsc{ BSearch}(B_E, a_i.start)$ and $first=\textsc{ BSearch}(B_S, | ||
| a_i.end)$. Since $B_E$ is a sorted list of each interval end coordinate in $B$, | ||
| the elements with indices less than or equal to $last$ in $B_E$ correspond to | ||
| the set of intervals in $B$ that end \emph{before} $a_i$ starts (i.e., to the | ||
| ``left'' of $a_i$). Similarly, the elements with indices greater than or equal | ||
| to $first$ in $B_S$ correspond to the set of intervals in $B$ that start | ||
| \emph{after} $a_i$ ends (i.e., to the ``right'' of $a_i$). From these two | ||
| values, we can directly infer the size of the intersection set | ||
| $\mathcal{I}(B,a_i)$ (i.e., the \emph{count} of intersections in $B$ for $a_i$): | ||
| \vspace{-.75em} | ||
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@@ -435,8 +435,8 @@ \subsection{Binary Interval Search (BITS) Algorithm} | |
| \BlankLine | ||
| \textbf{Function} \textsc{Counter}$(A,B)$ | ||
| \Begin { | ||
| $B_S \gets [b_1.start, \dots, b_{|B|}.start]$; | ||
| $B_E \gets [b_1.end, \dots, b_{|B|}.end]$; | ||
| $B_S \gets [b_1.start, \dots, b_{|B|}.start]$\; | ||
| $B_E \gets [b_1.end, \dots, b_{|B|}.end]$\; | ||
| \textsc{Sort}($B_S$)\; | ||
| \textsc{Sort}($B_E$)\; | ||
| $c \gets 0$\; | ||
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@@ -1042,7 +1042,7 @@ \subsection{Uncovering novel genomic relationships.} | |
| computational burden made feasible by the facility with which | ||
| the BITS algorithm could be applied to GPU architectures. Indeed, each | ||
| iteration of our Monte Carlo simulation tested for | ||
| intersections among 4,425,582,168 intervals among the 25,281 datasets, | ||
| intersections among 4 billion intervals among the 25 thousand datasets, | ||
| yielding over 44 trillion comparisons for the entire simulation. Whereas | ||
| this simulation took just over 6 days (9,069 minutes) on a single | ||
| computer with one GPU card, we estimate that it would take at least | ||
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@@ -1066,7 +1066,7 @@ \subsection{Uncovering novel genomic relationships.} | |
| % CONCLUSION | ||
| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
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| \vspace{-2em} | ||
| \section{Conclusion} | ||
| We have developed a novel algorithm for interval intersection that | ||
| is uniquely suited to scalable computing architectures such as GPUs. | ||
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