1. Yi Wu
9/17/2018

2. Outlines Problem formulation and existing solutions Algorithm
Phase 1. Euclidean temporal pruning
Phase 2. Euclidean cost pruning
Phase 3. Semi-Euclidean skyline-aware pruning
Experiments
Future work
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3. Problem formulation
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4. Problem formulation Constraint: wait: rmax_time price: rmax_price
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5. Existing solutions Group trips by locations Slugging
No time constraint
Limited to similar trips
No cost constraint
Slugging
Pick-up and drop-off locations are pre- assigned by the driver
Inconvenient
NP-hard
Use historical data to predict driver locations
Pre-knowledge required
Big storage
Dial-a-ride
One driver vs multiple riders.
Riders specify the route
Multiple drivers vs one rider
Best driver vs best route
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6. Algorithm Constraint: one rider rmax_time multiple drivers rmax_price
assumption: $1/km
input
driver:
CurrentLocation: mobile device
Destination
Driver trip
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7. shortest path is expensive to compute
Algorithm
brutal force
Pickup + Return for each driver-rider pair
2d skyline over pickup time and cost
shortest path is expensive to compute
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8. Phase 1. Euclidean Temporal Pruning
Constraint:
rmax_time = 15
rmax_price
Euclidean distance as lower bound for Pickup time
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9. Phase 2. Euclidean Cost Pruning
Euclidean distance as lower bound for Pickup time
Constraint:
rmax_time
rmax_price = 30 EP
32.4
26.3 26
27.9
24.2
22.7
d1: * – 8 = 32.4
RiderTrip = 12
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10. Phase 3. Semi-Euclidean Skyline Pruning
find actual pickup cost Pickup(d,r)
sort matching table by EuclideanReturn(d,r) – DriverTrip(d)
check drivers by ascending Pickup(d,r)
SEC is still a lower bound for actual cost
Constraint:
rmax_time = 15
rmax_price = 30
visit order 4 3 5 1 2
ER-DT
-7.4
-5.8
-4.2
-2.5
-1.9
a driver can reach the rider faster than all drivers visited later
a driver has lower cost than all unvisited driver below in the table
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11. Phase 3. Semi-Euclidean Skyline Pruning
no need to update on max_time b/c visiting driver by ascending Pickup
initiate MAX = max_price, MAX = min(MAX, actual driver cost)
time
cost
rmax_time
skyline
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MAX
rmax_price

12. Phase 3. Semi-Euclidean Skyline Pruning
Case 1
Pickup(d,r) > rmax_time
Action:
terminate algorithm
report the current skyline
Reason:
visit drivers by ascending Pickup d
time
cost
rmax_time
MAX
rmax_price
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13. Phase 3. Semi-Euclidean Skyline Pruning
Case 2
Pickup(d,r) <= rmax_time
SEC(d,r) > MAX
Action:
prune d
prune all unvisited drivers D below d in the matching table
Reason:
d is dominated by c
D is dominated by c
d3, MAX = 30
SEC = * – 10 = 30.2
time
cost
rmax_time
= 15
rmax_price
= 30
MAX d c
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14. Phase 3. Semi-Euclidean Skyline Pruning
Case 3
Pickup(d,r) <= rmax_time
SEC(d,r) < MAX
cost(d,r) > MAX
Action:
prune d
Reason:
d is dominated by c
can not prune D b/c possible cost(d,r) > cost(D,r)
d5, MAX = 30
SEC = * – 10 = 27.3
cost = * – 10 = 30.7
time
cost
rmax_time
= 15 d c
rmax_price
= 30
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MAX

15. Phase 3. Semi-Euclidean Skyline Pruning
Case 4
Pickup(d,r) <= rmax_time
SEC(d,r) < MAX
cost(d,r) < MAX
Action:
add d to skyline
update MAX
time
cost
rmax_time
= 15
d6, MAX = 30
cost = * – 13.4 = 27.2
d2, MAX = 27.2
SEC = * – 9.2 = 29.2 > 27.2 d c
rmax_price
= 30
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MAX

16. Experiments data: mixture of real data and synthetic data real part
road network of San Francisco
223,606 edges and 175,343 nodes
synthetic data
drivers and riders on the road network
generated according to Brinkhoff road network generator
parameters
car speed = 40 km/hr
sharing cost = $1/km
Bidirectional Dijkstra shortest path
1000 rider requests and evaluate the average performance
Intel Xeon CPU E GHz, 8 GB RAM, Ubuntu 14.04
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17. Experiments phase 1 (ETP) temporal pruning phase 2 (ETP + ECP)
Euclidean distance cost pruning
phase 3 (SHAREK)
skyline
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18. Experiments phase 1 temporal pruning phase 2
Euclidean distance cost pruning
phase 3
skyline
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19. Comments need to compute the actual Pickup(d,r) for all drivers
prune by Semi-EuclideanCost by SEC > MAX
Pickup distance != pickup time
local vs freeway
customized sharing and detour cost
luxury car
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