Yi Wu 9/17/2018

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 9/17/2018

Problem formulation 9/17/2018

Problem formulation Constraint: wait: rmax_time price: rmax_price 9/17/2018

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 9/17/2018

Algorithm Constraint: one rider rmax_time multiple drivers rmax_price assumption: $1/km input driver: CurrentLocation: mobile device Destination Driver trip 9/17/2018

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 9/17/2018

Phase 1. Euclidean Temporal Pruning Constraint: rmax_time = 15 rmax_price Euclidean distance as lower bound for Pickup time 9/17/2018

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: 7.3 + 2 * 12 + 9.1 – 8 = 32.4 RiderTrip = 12 9/17/2018

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 9/17/2018

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 9/17/2018 MAX rmax_price

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 9/17/2018

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 = 8.7 + 2 * 12 + 7.5 – 10 = 30.2 time cost rmax_time = 15 rmax_price = 30 MAX d c 9/17/2018

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 = 9.1 + 2 * 12 + 4.2 – 10 = 27.3 cost = 9.1 + 2*12 + 7.6 – 10 = 30.7 time cost rmax_time = 15 d c rmax_price = 30 9/17/2018 MAX

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 = 9.3 + 2*12 + 7.3 – 13.4 = 27.2 d2, MAX = 27.2 SEC = 9.4 + 2*12 + 5 – 9.2 = 29.2 > 27.2 d c rmax_price = 30 9/17/2018 MAX

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 E5-2637 3.50GHz, 8 GB RAM, Ubuntu 14.04 9/17/2018

Experiments phase 1 (ETP) temporal pruning phase 2 (ETP + ECP) Euclidean distance cost pruning phase 3 (SHAREK) skyline 9/17/2018

Experiments phase 1 temporal pruning phase 2 Euclidean distance cost pruning phase 3 skyline 9/17/2018

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 9/17/2018