Optimal paths in graphs with stochastic or multidimensional weights

Loui, Ronald P.

doi:10.1145/358172.358406

Cited by 201 publications

(95 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Run a multi-criteria variant of Dijkstra's algorithm [8,12,7] starting from labels of cost zero at all transfer nodes of station A.…”

Section: Transfer Patterns Precomputationmentioning

confidence: 99%

“…The stations being on the largest number of shortest paths are chosen as hubs. 7 Transfer patterns computation. The global search remains as described in Section 4.2.…”

Section: Hub Stationsmentioning

confidence: 99%

“…6 The number of global searches could be reduced further by introducing several levels of hubs, but in our implementation the total cost for the global searches is below the total cost for the local searches already with one level of hubs; see Section 8. 7 We experimented with a variety of hub selection strategies, but they showed only little difference with respect to preprocessing time and query graph sizes, and so we stuck with the simplest strategy. 8 Before that, inactive labels are needed to dominate non-optimal paths around hubs.…”

Section: Lemmamentioning

confidence: 99%

See 2 more Smart Citations

Fast Routing in Very Large Public Transportation Networks Using Transfer Patterns

Bast

Carlsson

Eigenwillig

et al. 2010

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. We show how to route on very large public transportation networks (up to half a billion arcs) with average query times of a few milliseconds. We take into account many realistic features like: traffic days, walking between stations, queries between geographic locations instead of a source and a target station, and multi-criteria cost functions. Our algorithm is based on two key observations: (1) many shortest paths share the same transfer pattern, i.e., the sequence of stations where a change of vehicle occurs; (2) direct connections without change of vehicle can be looked up quickly. We precompute the respective data; in practice, this can be done in time linear in the network size, at the expense of a small fraction of non-optimal results. We have accelerated public transportation routing on Google Maps with a system based on our ideas. We report experimental results for three data sets of various kinds and sizes.

show abstract

“…Run a multi-criteria variant of Dijkstra's algorithm [8,12,7] starting from labels of cost zero at all transfer nodes of station A.…”

Section: Transfer Patterns Precomputationmentioning

confidence: 99%

“…The stations being on the largest number of shortest paths are chosen as hubs. 7 Transfer patterns computation. The global search remains as described in Section 4.2.…”

Section: Hub Stationsmentioning

confidence: 99%

Section: Lemmamentioning

confidence: 99%

See 1 more Smart Citation

Fast Routing in Very Large Public Transportation Networks Using Transfer Patterns

Bast

Carlsson

Eigenwillig

et al. 2010

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…The second problem we present is a generalization of an optimal path problem in graphs with stochastic weights investigated by Loui [15]. The difference here is that the consequences of actions are stochastic.…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…Consequently, the sum of rewards obtained along a history and therefore the total reward obtained by applying a given policy are both Gaussian random variables. As underlined by [15], the expected utility of a Gaussian distribution N (µ, σ 2 ) is equal to d + cµ + bµ 2 + bσ 2 if the utility function u is quadratic, i.e., u(x) = bx 2 + cx + d. As u is a utility function, we restrict its domain of definition to an interval on which it is increasing. Then, on that interval, the function u : IR 2 → IR defined by u (x, y) = d + cx + bx 2 + by is increasing in its first argument.…”

Section: Illustrative Examplesmentioning

confidence: 99%

Markov Decision Processes with Functional Rewards

Spanjaard

Weng

2013

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Markov decision processes (MDP) have become one of the standard models for decision-theoretic planning problems under uncertainty. In its standard form, rewards are assumed to be numerical additive scalars. In this paper, we propose a generalization of this model allowing rewards to be functional. The value of a history is recursively computed by composing the reward functions. We show that several variants of MDPs presented in the literature can be instantiated in this setting. We then identify sufficient conditions on these reward functions for dynamic programming to be valid. In order to show the potential of our framework, we conclude the paper by presenting several illustrative examples.

show abstract