minor phrasing

circuits-model-runtime.tex

@@ -41,7 +41,8 @@ For a more detailed discussion of why~\Cref{lem:approx-alg} holds for a lineage
 So far our analysis of $\approxq$ has been in terms of the size of the compressed lineage polynomial.
 We now show that this model corresponds to the behavior of a deterministic database by proving that for any union of conjunctive queries, we can construct a compressed lineage polynomial for a query $Q$ and \bi $\pxdb$ of size (and in runtime) linear in the runtime of a general class of query processing algorithms for the same query $Q$ on a deterministic database $\db$.
 We assume a linear relationship between input sizes $|\pxdb|$ and $|\db|$ (i.e., $\exists c, \db \in \pxdb$ s.t. $\abs{\pxdb} \leq c \cdot \abs{\db})$).
-This is a reasonable assumption because each block of a \bi represents entities with uncertain attributes --- in practice there is a limited number of alternatives for each block (e.g., which of five conflicting data sources to trust). Note that all \tis trivially fulfill this condition for $c = 1$.
+This is a reasonable assumption because each block of a \bi represents entities with uncertain attributes. 
+In practice there is often a limited number of alternatives for each block (e.g., which of five conflicting data sources to trust). Note that all \tis trivially fulfill this condition (i.e., $c = 1$).
 %That is for \bis that fulfill this restriction approximating the expectation of results of SPJU queries is only has a constant factor overhead over deterministic query processing (using one of the algorithms for which we prove the claim).
 % with the same complexity as it would take to evaluate the query on a deterministic \emph{bag} database of the same size as the input PDB.
 We adopt a minimalistic compute-bound model of query evaluation drawn from the worst-case optimal join literature~\cite{skew,ngo-survey}.