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Tour recommendation for groups

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Abstract

Consider a group of people who are visiting a major touristic city, such as NY, Paris, or Rome. It is reasonable to assume that each member of the group has his or her own interests or preferences about places to visit, which in general may differ from those of other members. Still, people almost always want to hang out together and so the following question naturally arises: What is the best tour that the group could perform together in the city? This problem underpins several challenges, ranging from understanding people’s expected attitudes towards potential points of interest, to modeling and providing good and viable solutions. Formulating this problem is challenging because of multiple competing objectives. For example, making the entire group as happy as possible in general conflicts with the objective that no member becomes disappointed. In this paper, we address the algorithmic implications of the above problem, by providing various formulations that take into account the overall group as well as the individual satisfaction and the length of the tour. We then study the computational complexity of these formulations, we provide effective and efficient practical algorithms, and, finally, we evaluate them on datasets constructed from real city data.

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Notes

  1. We remind that a problem is APX-hard if there exists a polynomial-time approximation scheme (PTAS) reduction to it from any problem in APX. Practically, it means that unless \(P=NP\), there exists a constant c such that it is impossible to design a polynomial-time algorithm that solves the problem with approximation ratio better than c.

  2. This is without loss of generality, since if T visits fewer than \(B-1\) useful vertices, we can obviously return a shorter tour \(T'\) achieving the same value of the objective.

  3. The datasets are available at http://wadam.dis.uniroma1.it/datasets/Tour_Recommendation_for_Groups_Dataset.tgz.

  4. We attempted to also use the Wikipedia categories; however they turned out not to be appropriate for our purpose: they tend to be very specific and they refer mostly to the architectural features or the historical era of construction. For instance, it is common to find two churches belonging to completely different categories, even at higher levels of the Wikipedia ontology.

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Acknowledgements

We thank Fabrizio Grandoni for useful discussions on the problem complexity. We also thank Microsoft for awarding us with credits on their Azure cloud-computing platform, providing us in this way the required infrastructure to run our experiments. Finally, we want to thank the anonymous reviewers, whose comments helped to improve significantly our paper. This research was partially supported by the Google Focused Research Award “Algorithms for Large-Scale Data Analysis” and by the EU FET project MULTIPLEX 317532.

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Authors and Affiliations

  1. Sapienza University of Rome, Rome, Italy

    Aris Anagnostopoulos, Reem Atassi, Luca Becchetti & Adriano Fazzone

  2. ISTI CNR, Pisa, Italy

    Fabrizio Silvestri

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  1. Aris Anagnostopoulos
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  2. Reem Atassi
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Correspondence to Reem Atassi.

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Responsible editors: Thomas Gärtner, Mirco Nanni, Andrea Passerini and Celine Robardet.

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Anagnostopoulos, A., Atassi, R., Becchetti, L. et al. Tour recommendation for groups. Data Min Knowl Disc 31, 1157–1188 (2017). https://doi.org/10.1007/s10618-016-0477-7

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