Polynomial-Time Approximation Schemes for Shortest Path with Alternatives

Nonner, Tim

doi:10.1007/978-3-642-33090-2_65

Cited by 7 publications

(11 citation statements)

References 12 publications

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“…A similar result for the recourse model for stochastic shortest paths and least expected arrival time utility was given by [24]. We prove NP-hardness for the continuous time case by extending the approach of Nonner [23]. Theorem 3.…”

Section: Theorem 2 There Always Exists An Optimal Policymentioning

confidence: 71%

“…. , s m arrive according to the construction of [23] where arriving probabilities are multiplied by 0 < 1 − p − q < 1. For sake of completeness, we give a description of Nonner's construction.…”

Section: Theorem 2 There Always Exists An Optimal Policymentioning

confidence: 99%

“…The difficulty of the problem therefore lies in selecting a set of 'alternatives' for each node instead of a single path. This framework was previously studied by Nonner [23] who proposed a method that computes a list of services for each stop depending on the waiting time distributions, and the user is recommended to take the service from the list that arrives first. As a respective model, Nonner suggested to determine the waiting time distributions as a function of the passing frequencies of the services at a given node.…”

Section: Introductionmentioning

confidence: 99%

“…The method is also able to use online data provided by monitoring devices, in order to replan and update the lists of alternatives for each stop whenever new information concerning delays, position of a vehicle, unexpected events, or level of congestion arrives. The notion of 'routing alternatives' of [23] was further developed by the first author et al [4]. They adopted the notion of 'policies' and provided current time dependent policies consisting of not only a single service but a set of services, so that the resulting travelling advice gets more robust to uncertainty.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Arrival time dependent routing policies in public transport

Bérczi

Jüttner

Laumanns

et al. 2018

Discrete Applied Mathematics

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We present a routing system that considers uncertainties, which are prevalent in any real transport system. Given desired departure or arrival times and a utility function representing the traveller's preferences, our method computes not just a single path through the network, but a more sophisticated and adaptive journey plan called routing policy. For each stop and time instance, a policy specifies the list of services that the passenger is recommended to take.We show that the problem of finding an optimal policy is NP-hard. We also give a polynomial-time algorithm for a relaxation of the problem when the number of recommended services is limited at each stop and time. A computational case study for the public transport network of Budapest shows that the obtained routing policies can lead to substantial travel time savings compared to deterministic plans, and that considering multiple service policies leads to an improvement compared to previous solutions using single-service policies.

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Section: Theorem 2 There Always Exists An Optimal Policymentioning

confidence: 71%

Section: Theorem 2 There Always Exists An Optimal Policymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Arrival time dependent routing policies in public transport

Bérczi

Jüttner

Laumanns

et al. 2018

Discrete Applied Mathematics

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show abstract

“…In its simplest form, journey planning is a shortest path problem: given a graph representation of a transportation network, find a shortest route between a start location and a destination. A more realistic modelling, such as considering uncertainty, can lead to problem variants that are computationally hard (Nikolova, Brand, & Karger, 2006;Nonner, 2012).…”

Section: Introductionmentioning

confidence: 99%

Computing Multi-Modal Journey Plans under Uncertainty

Botea¹,

Kishimoto²,

Nikolova³

et al. 2019

jair

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Multi-modal journey planning, which allows multiple types of transport within a single trip, is becoming increasingly popular, due to a strong practical interest and an increasing availability of data. In real life, transport networks feature uncertainty. Yet, most approaches assume a deterministic environment, making plans more prone to failures such as missed connections and major delays in the arrival. This paper presents an approach to computing optimal contingent plans in multi-modal journey planning. The problem is modeled as a search in an and/or state space. We describe search enhancements used on top of the AO* algorithm. Enhancements include admissible heuristics, multiple types of pruning that preserve the completeness and the optimality, and a hybrid search approach with a deterministic and a nondeterministic search. We demonstrate an NP-hardness result, with the hardness stemming from the dynamically changing distributions of the travel time random variables. We perform a detailed empirical analysis on realistic transport networks from cities such as Montpellier, Rome and Dublin. The results demonstrate the effectiveness of our algorithmic contributions, and the benefits of contingent plans as compared to standard sequential plans, when the arrival and departure times of buses are characterized by uncertainty.

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Multi-objective journey planning under uncertainty

Haqqani

2018

Proceedings of the Genetic and Evolutionary Computation Conference

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Polynomial-Time Approximation Schemes for Shortest Path with Alternatives

Cited by 7 publications

References 12 publications

Arrival time dependent routing policies in public transport

Arrival time dependent routing policies in public transport

Computing Multi-Modal Journey Plans under Uncertainty

Multi-objective journey planning under uncertainty

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