An Efficient Algorithm for Maximum Trajectory Coverage Query With Approximation Guarantee
In this paper, we study the <inline-formula> <tex-math notation="LaTeX">k</tex-math> </inline-formula> Maximum Trajectory Coverage Query, which aims to find <inline-formula> <tex-math notation="LaTeX">k</tex-math> </inline-formula>...
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| Published in: | IEEE transactions on intelligent transportation systems Vol. 23; no. 12; pp. 1 - 13 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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IEEE
01.12.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1524-9050, 1558-0016 |
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| Abstract | In this paper, we study the <inline-formula> <tex-math notation="LaTeX">k</tex-math> </inline-formula> Maximum Trajectory Coverage Query, which aims to find <inline-formula> <tex-math notation="LaTeX">k</tex-math> </inline-formula> routes in a public transport system that can serve the maximum number of users with given journey trajectories. In existing studies, they only consider independent service that includes no transfers, but overlooks the aggregative service that includes transfer of multiple routes, resulting in inferior results. In our study, we consider both independent and aggregative services, which can help provide more meaningful results. However, the problem is NP-hard and non-submodular. To address this problem, we propose a greedy algorithm that iteratively selects the route with the maximum marginal gain considering both independent and aggregative services, and show that it outperforms the competitor by up to 60% in terms of accuracy. Since the problem is non-submodular, the greedy algorithm typically does not provide any approximation guarantee. By a mild assumption, we show that our proposed solution provides a constant approximation with respect to the optimal one. Moreover, since we need to consider both the independent and aggregative service, our greedy algorithm becomes more complicated and brings additional time overheads. To overcome such a deficiency, we further accelerate our solution using several heuristics and present an efficient method for spatially associating trajectories and routes. Extensive experiments on real-world datasets demonstrate that our optimisation brings up to an order of magnitude speedup and even outperforms existing solutions (that consider no aggregative service) by 2-3 times. |
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| AbstractList | In this paper, we study the [Formula Omitted] Maximum Trajectory Coverage Query, which aims to find [Formula Omitted] routes in a public transport system that can serve the maximum number of users with given journey trajectories. In existing studies, they only consider independent service that includes no transfers, but overlooks the aggregative service that includes transfer of multiple routes, resulting in inferior results. In our study, we consider both independent and aggregative services, which can help provide more meaningful results. However, the problem is NP-hard and non-submodular. To address this problem, we propose a greedy algorithm that iteratively selects the route with the maximum marginal gain considering both independent and aggregative services, and show that it outperforms the competitor by up to 60% in terms of accuracy. Since the problem is non-submodular, the greedy algorithm typically does not provide any approximation guarantee. By a mild assumption, we show that our proposed solution provides a constant approximation with respect to the optimal one. Moreover, since we need to consider both the independent and aggregative service, our greedy algorithm becomes more complicated and brings additional time overheads. To overcome such a deficiency, we further accelerate our solution using several heuristics and present an efficient method for spatially associating trajectories and routes. Extensive experiments on real-world datasets demonstrate that our optimisation brings up to an order of magnitude speedup and even outperforms existing solutions (that consider no aggregative service) by 2–3 times. In this paper, we study the <inline-formula> <tex-math notation="LaTeX">k</tex-math> </inline-formula> Maximum Trajectory Coverage Query, which aims to find <inline-formula> <tex-math notation="LaTeX">k</tex-math> </inline-formula> routes in a public transport system that can serve the maximum number of users with given journey trajectories. In existing studies, they only consider independent service that includes no transfers, but overlooks the aggregative service that includes transfer of multiple routes, resulting in inferior results. In our study, we consider both independent and aggregative services, which can help provide more meaningful results. However, the problem is NP-hard and non-submodular. To address this problem, we propose a greedy algorithm that iteratively selects the route with the maximum marginal gain considering both independent and aggregative services, and show that it outperforms the competitor by up to 60% in terms of accuracy. Since the problem is non-submodular, the greedy algorithm typically does not provide any approximation guarantee. By a mild assumption, we show that our proposed solution provides a constant approximation with respect to the optimal one. Moreover, since we need to consider both the independent and aggregative service, our greedy algorithm becomes more complicated and brings additional time overheads. To overcome such a deficiency, we further accelerate our solution using several heuristics and present an efficient method for spatially associating trajectories and routes. Extensive experiments on real-world datasets demonstrate that our optimisation brings up to an order of magnitude speedup and even outperforms existing solutions (that consider no aggregative service) by 2-3 times. |
| Author | Kim, Jiwon He, Dan Zhou, Xiaofang Zhou, Thomas |
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| References | ref13 ref12 ref15 ref14 ref31 ref30 ref11 ref10 ref2 chao (ref9) 2017 ref1 ref17 ref16 pfoser (ref18) 2000 ref24 ref23 ref25 ref22 ref21 tao (ref20) 2001 tao (ref19) 2001 ref27 ref29 potts (ref28) 2010 ref8 ref7 ref4 ref3 ref6 manurangsi (ref26) 2018 bian (ref5) 2017; 70 |
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| SubjectTerms | Algorithms Approximation Approximation algorithms check-in trajectory Greedy algorithms location-based applications Mathematical analysis maximum coverage Optimization Public transportation Route selection Spatial database Spatial databases STEM Trajectory Transportation systems Urban areas |
| Title | An Efficient Algorithm for Maximum Trajectory Coverage Query With Approximation Guarantee |
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