An analytic solution to the alibi query in the bead model for moving object data

Abstract

Moving objects produce trajectories, which are stored in databases by means of finite samples of time-stamped locations. When
also speed limitations in these sample points are known,
beads can be used to model the
uncertainty about the object's location in between sample points.

In this setting, a query of particular interest, that has been
studied in the literature of geographic information systems (GIS),
is the alibi query. This boolean query asks whether two
moving objects can have physically met. This adds up to deciding
whether the necklaces of beads of these objects intersect. This
problem can be reduced to deciding whether two beads intersect.
Since, existing software to solve this problem fails to answer this
question within a reasonable time, we propose an analytical solution
to the alibi query, which can be used to answer the alibi query in
constant time, a matter of milliseconds or less, for two single
beads and in time proportional to the product of their lengths for
necklaces of beads.