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Equation 18 · Part 5 · Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

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cquery(Q)=CindexQ+cmarginal.c_{\text{query}}(Q) = \frac{C_{\text{index}}}{Q} + c_{\text{marginal}}.
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

This is the one family among the five whose defining engineering trade-off is temporal rather than architectural: cost is shifted from query time to index time. Writing CindexC_{\text{index}} for the one-time cost of building the graph and its community summaries, and cmarginalc_{\text{marginal}} for the cost of answering a single query against the finished structure, the amortised cost of a query workload of size Q against one graph is cquery(Q)=CindexQ+cmarginalc_{\text{query}}(Q) = \frac{C_{\text{index}}}{Q} + c_{\text{marginal}}. When Q is small — a corpus queried rarely, or one still being explored — CindexC_{\text{index}} dominates and the naive or hybrid architectures are cheaper by a wide margin, because they pay nothing until a query arrives. When Q is large against a stable…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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