Assume a biword index. Give an example of a document

which will be returned for a query of New York University

but is actually a false positive which should not be

returned.

Consider the following fragment of a positional

index with the format:

word: document: $$position$,$ position, $...$; document:

$$position$,...>$

cdots

Gates: $1$:$($:$3$:$)$;$2$:$($:$6$:$)$;$3$ : $($:$2,17$:$)$;$4$ : $($:$1$:$)$

IBM: $4$:$($:$3$:$)$;$7$:$($:$14$:$)$

Microsoft: $1$: $($:$1$:$)$;$2$ : $($:$1,21$:$)$;$3$ : $($:$3$:$)$;$5$ : $($:$16,22,51$:$)$

The $\frac{?}{k}$ operator, word $\frac{1}{k}$ word$2$ finds occurrences of

word $1$ within $k$ words of word$2($on either side$),$ where $k$ is

a positive integer argument. Thus $k=1$ demands that

word$1$ be adjacent to word$2.$

a$.$ Describe the set of documents that satisfy the query

Gates $/2$ Microsoft.

b$.$ Describe each set of values for $k$ for which the query

Gates $\frac{?}{k}$ Microsoft returns a different set of documents as

the answer.$(2)$ Consider the following fragment of a positional index with the format: word: document: ; document: $$ position, $...>...$ Gates: $1$:$3>$; $2$:: $3$:: $4$:: IBM: $4$:$3>$; $7$:$14>$ Microsoft: $1$:$1$ ; $2$:; $3$:; $5$:$16,22,51$ The $/$ k operator, word$1/$ k word$2$ finds occurrences of word$1$ within k words of word$2$ lon either side$),$ where k is a positive integer argument. Thus k$=1$ demands that word $1$ be adjacent to word$2.$ Describe the set of documents that satisfy the query Gates $/2$ Microsoft. $(1,2](1,3)(2,3)(4,5)$