Accompanying Vehicles
Qitong Wang
Contents
• Question
• Method
• Discussion
Intuition
• Vehicles are tracked by monitors set up at landmarks, i.e., crossings.
• With all the vehicles in an area are tracked during a period of time,
accompanying vehicles finding is to extract which vehicles follow each
other.
• In criminal investigation, a common scenario is that a criminal has
some partners.
• They tended to drive together, especially during the crime’s committing.
• If two (or more) vehicles drove together, their drivers are more likely to be a
criminal gang than others, especially some of them have been identified as
suspects.
Explanatory Chart
Spots
Spot 5
Spot 4
Spot 3
Spot 2
𝒕
Spot 1
Time
Key Issue
Pair Count
𝒄
•4
•2
•1
• We need to know how many accompanying pairs
every vehicle pair makes.
• Numb. of total accompanying pairs =
𝑁𝑣
× 𝐴𝑣𝑔𝑝𝑎𝑖𝑟 ≈ 𝑚 × 𝑁𝑣
2
•
•
•
•
𝑁𝑣 denotes numb. of vehicles
𝑁𝑟 denotes numb. of records
𝑚 denotes numb. of records during 𝒕
𝐴𝑣𝑔𝑝𝑎𝑖𝑟 denotes average accompanying pair each
vehicle pair makes
• 9 million records and 2.5 million vehicles per day
in Beijing
• Makes roughly billions of accompanying pairs!
Method
• Bottle: Pairs are too many to be cached in memory.
• Generate only the accompanying pairs likely to make an
accompanying vehicle pair
• Prune
• How to recognize the potential/impossible vehicle pair?
• Split the accompanying pairs into groups
• Find an upper bound for any two pairs
Matrix
• Scatter different
pairs into different
cells of a statistics
matrix uniformly
• Store counters only
• The pairs falling into
a cell with a
counter ≥ 𝒄 are
potential candidate
vehicle pairs
4
=4≥𝒄
2
+
1
=3<𝒄
Time
Explanatory
Chart
𝒕
Spots
Spot 5
Spot 4
Spot 3
Spot 2
Spot 1
Sketches
Vehicle
Spot 1
Spot 2
Spot 3
Spot 4
Spot 5
1
1
2
0
1
1
1
2
0
1
0
1
0
0
1
• How many pairs two vehicle can make at most at each spot?
• The smaller number of appearances in this spot of the two vehicles
•
and
can make at most 1 pair at spot 1, while and
will never make a pair at spot 1.
• How many pairs two vehicle can make at most?
• Sum over the upper bound at each spot
•
and
can make at most 5 pairs, while and
can make 2 pairs.
• and is a potential candidate vehicle pair
Discussion
• Strength of the two methods?
• Any other optimizations?
Thanks
Accompanying Vehicles by Qitong Wang