TY - GEN

T1 - Minimum-cost paths for electric cars

AU - Dorfman, Dani

AU - Kaplan, Haim

AU - Tarjan, Robert E.

AU - Thorup, Mikkel

AU - Zwick, Uri

N1 - Publisher Copyright:
Copyright © 2024 by SIAM.

PY - 2024

Y1 - 2024

N2 - An electric car equipped with a battery of a finite capacity travels on a road network with an infrastructure of charging stations. Each charging station has a possibly different cost per unit of energy. Traversing a given road segment requires a specified amount of energy that may be positive, zero or negative. The car can only traverse a road segment if it has enough charge to do so (the charge cannot drop below zero), and it cannot charge its battery beyond its capacity. To travel from one point to another the car needs to choose a travel plan consisting of a path in the network and a recharging schedule that specifies how much energy to charge at each charging station on the path, making sure of having enough energy to reach the next charging station or the destination. The cost of the plan is the total charging cost along the chosen path. We reduce the problem of computing plans between every two junctions of the network to two problems: Finding optimal energetic paths when no charging is allowed and finding standard shortest paths. When there are no negative cycles in the network, we obtain an O(n3)-time algorithm for computing all-pairs travel plans, where n is the number of junctions in the network. We obtain slightly faster algorithms under some further assumptions. We also consider the case in which a bound is placed on the number of rechargings allowed.

AB - An electric car equipped with a battery of a finite capacity travels on a road network with an infrastructure of charging stations. Each charging station has a possibly different cost per unit of energy. Traversing a given road segment requires a specified amount of energy that may be positive, zero or negative. The car can only traverse a road segment if it has enough charge to do so (the charge cannot drop below zero), and it cannot charge its battery beyond its capacity. To travel from one point to another the car needs to choose a travel plan consisting of a path in the network and a recharging schedule that specifies how much energy to charge at each charging station on the path, making sure of having enough energy to reach the next charging station or the destination. The cost of the plan is the total charging cost along the chosen path. We reduce the problem of computing plans between every two junctions of the network to two problems: Finding optimal energetic paths when no charging is allowed and finding standard shortest paths. When there are no negative cycles in the network, we obtain an O(n3)-time algorithm for computing all-pairs travel plans, where n is the number of junctions in the network. We obtain slightly faster algorithms under some further assumptions. We also consider the case in which a bound is placed on the number of rechargings allowed.

UR - http://www.scopus.com/inward/record.url?scp=85194196870&partnerID=8YFLogxK

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AN - SCOPUS:85194196870

T3 - 2024 Symposium on Simplicity in Algorithms, SOSA 2024

SP - 374

EP - 382

BT - 2024 Symposium on Simplicity in Algorithms, SOSA 2024

A2 - Parter, Merav

A2 - Pettie, Seth

PB - Society for Industrial and Applied Mathematics (SIAM)

T2 - 7th SIAM Symposium on Simplicity in Algorithms, SOSA 2024

Y2 - 8 January 2024 through 10 January 2024

ER -