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2.3 Window Freshness
In this section we define the window freshness, another quality measure for content-based
feed aggregation services. Window freshness evaluates item loss, but from a short-term
point of view. We consider item loss as being temporary, i.e. all items that have not been
already fetched by the aggregator can be retrieved as soon as it refreshes the source and
the window freshness takes the value 1.
Window freshness takes values in the interval [0, 1] and measures the quality of the aggregator
publication window by the fraction of items which are available both in the publication
window and in the corresponding source feed at the same time instant. It is defined in
two steps. The first step defines window freshness of a query feed f generated by filter
query q with respect to a single source feed s ∈ S(q), denoted by FW (f/s, t). The second
step defines window freshness with respect to all sources si ∈ S(q), denoted by FW (f, t).
Furthermore, we define window freshness with respect to all sources si ∈ S(q) computed
over a period of time, denoted by FW (f).
Definition 2.3.1. Window freshness with respect to a single source
Window freshness with respect to a single source feed s ∈ S(q) compares the number of
items relevant to query q available both on the publication window of the source feed s
and on the publication stream of the query feed f at time instant t, for |q(A(s, t))| > 0:
FW (f/s, t) =
By definition, FW (f/s, t) = 1 if |q(A(s, t))| = 0.
|F (f, t) ∩ q(A(s, t))|
|q(A(s, t))|
Definition 2.3.2. Window freshness with respect to all sources
The window freshness of a query feed f at time t with respect to all sources si ∈ S(q) is
defined as the average of all single-source freshness scores:
FW (f, t) = 1 �
∗ FW (f/si, t)
|S(q)|
si∈S(q)
We say that a query feed f is fresh and its window freshness with respect to all its sources
S(q) = {s1, ...sk} takes the maximum value FW (f, t) = 1 if f contains all the items that
are available at time instant t in the publication windows A(si, t) of all sources si ∈ S(q)
and that are relevant to query q.
Definition 2.3.3. Window freshness over a period of time
The window freshness of a query feed f with respect to all sources si ∈ S(q) computed
over a period of time ∆T is defined as:
FW (f) = 1
∆T ∗
� ∆T
FW (f, t)dt
0
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