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dc.contributor.authorZou, Peng
dc.contributor.authorQingge, Letu
dc.contributor.authorYang, Qing
dc.contributor.authorZhu, Binhai
dc.identifier.citationZou, P., Qingge, L., Yang, Q., & Zhu, B. (2022). Computing a consensus trajectory in a vehicular network. Journal of Combinatorial Optimization, 44(5), 3575-3594.en_US
dc.descriptionThis version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at:
dc.description.abstractIn this paper, we study the problem of computing a consensus trajectory of a vehicle given the history of Points of Interest visited by the vehicle over a certain period of time. The problem arises when a system tries to establish the social connection between two vehicles in a vehicular network, where three versions of the problem are studied. Formally, given a set of m trajectories, the first version of the problem is to compute a target (median) sequence T over Σ such that the sum of similarity measure (i.e., number of adjacencies) between T and all Si’s is maximized. For this version, we show that the problem is NP-hard and we present a simple factor-2 approximation based on a greedy method. We implement the greedy algorithm and a variation of it which is based on a more natural greedy search on a new data structure called adjacency map. In the second version of the problem where the sequence T is restricted to be a permutation, we show that the problem remains NP-hard but the approximation factor can be improved to 1.5. In the third version where the sequence T has to contain all letters of Σ, we again prove that it is NP-hard. We implement a simple greedy algorithm and a variation of the 1.5-approximation algorithm for the second version, and which are used to construct solution for the third version. Our algorithms are tested on the simulation data and the empirical results are very promising.en_US
dc.publisherSpringer Science and Business Media LLCen_US
dc.rightscopyright Springer Science and Business Media LLC 2022en_US
dc.subjectConsensus Trajectoryen_US
dc.subjectApproximation Algorithmen_US
dc.subjectHeuristic Algorithmen_US
dc.titleComputing a consensus trajectory in a vehicular networken_US
mus.citation.journaltitleJournal of Combinatorial Optimizationen_US
mus.relation.collegeCollege of Engineeringen_US
mus.relation.departmentComputer Science.en_US
mus.relation.universityMontana State University - Bozemanen_US

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