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Equation 18 · Part 8 · Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

subscript

cquery(Q)=CindexQ+cmarginal.c_{\text{query}}(Q) = \frac{C_{\text{index}}}{Q} + c_{\text{marginal}}.
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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