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zeekayandHanzo Dev
03c6289dfc
Design, prior art and a measurement protocol for a weighted inverted index over a mixed sparse basis and part-level routing before per-part HNSW in a ClickHouse-derived store. Each component is marked prior art or proposed. The protocol fits C(N) = aN^alpha to parts, granules and bytes touched per correct answer at a held recall. No numbers: every results cell is a placeholder read from results-data.tex until the baseline lane writes it. Co-authored-by: Hanzo Dev <[email protected]>
71 lines
2.4 KiB
TeX
71 lines
2.4 KiB
TeX
\section{Results}
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\label{sec:results}
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\emph{This section is a placeholder.} The lane that fills it is starting and
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has written no results file, so every cell below prints \ph{} and no sentence
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in this paper quotes a number. When the harness writes that file, these tables
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fill from it and the conditions of the run appear in the captions.
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\begin{table}[h]
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\centering
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\small
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\setlength{\tabcolsep}{5pt}
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\begin{tabular}{@{}lrrrrrrr@{}}
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\toprule
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& parts & granules & MiB & KiB/ans & recall@$k$ & p50 ms & p99 ms \\
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\midrule
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\multicolumn{8}{@{}l}{\textit{scan}} \\
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\costrow{scan/1e5}{\quad $10^5$}
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\costrow{scan/1e6}{\quad $10^6$}
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\costrow{scan/1e7}{\quad $10^7$}
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\midrule
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\multicolumn{8}{@{}l}{\textit{base} --- upstream ClickHouse 26.4} \\
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\costrow{base/1e5}{\quad $10^5$}
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\costrow{base/1e6}{\quad $10^6$}
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\costrow{base/1e7}{\quad $10^7$}
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\costrow{base/1e8}{\quad $10^8$}
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\costrow{base/1e9}{\quad $10^9$}
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\midrule
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\multicolumn{8}{@{}l}{\textit{route} --- sparse basis and part-level routing} \\
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\costrow{route/1e5}{\quad $10^5$}
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\costrow{route/1e6}{\quad $10^6$}
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\costrow{route/1e7}{\quad $10^7$}
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\costrow{route/1e8}{\quad $10^8$}
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\costrow{route/1e9}{\quad $10^9$}
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\midrule
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\multicolumn{8}{@{}l}{\textit{oracle} --- the parts and granules holding the exact top-$k$} \\
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\costrow{oracle/1e6}{\quad $10^6$}
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\costrow{oracle/1e9}{\quad $10^9$}
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\bottomrule
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\end{tabular}
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\caption{Cost at a held recall target, per query, averaged over the query set.
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Host \res{run/host}; store \res{run/version}; $k = \res{run/k}$; recall target
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\res{run/recall}; queries \res{run/queries}. Part counts at each size:
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\res{run/parts/1e6} at $10^6$ and \res{run/parts/1e9} at $10^9$. Every cell is
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empty until the harness writes it.}
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\label{tab:cost}
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\end{table}
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\begin{table}[h]
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\centering
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\small
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\begin{tabular}{@{}lllll@{}}
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\toprule
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& $\alpha$ parts & $\alpha$ granules & $\alpha$ bytes & $\alpha$ summaries \\
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& per answer & per answer & per answer & per query \\
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\midrule
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\fitrow{base}{base}
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\fitrow{route}{route}
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\fitrow{oracle}{oracle}
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\bottomrule
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\end{tabular}
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\caption{Fitted exponents of $C(N) = aN^{\alpha}$ for parts, granules and bytes
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touched per correct answer, and for routing summaries examined per query, with
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95\% bootstrap intervals over queries, at the recall target of
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Table~\ref{tab:cost}. The
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hypothesis of \S\ref{sec:setting} is a route row whose intervals lie below one
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and whose oracle ratio does not grow; the local slopes behind each fit are
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published with the run.}
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\label{tab:fit}
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\end{table}
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