### Abstract

We introduce the concept of compactly representing a large number of state sequences, e.g., sequences of activities, as a flow diagram. We argue that the flow diagram representation gives an intuitive summary that allows the user to detect patterns among large sets of state sequences. Simplified, our aim is to generate a small flow diagram that models the flow of states of all the state sequences given as input. For a small number of state sequences we present efficient algorithms to compute a minimal flow diagram. For a large number of state sequences we show that it is unlikely that efficient algorithms exist. More specifically, the problem is W[1]-hard if the number of state sequences is taken as a parameter. We thus introduce several heuristics for this problem. We argue about the usefulness of the flow diagram by applying the algorithms to two problems in sports analysis. We evaluate the performance of our algorithms on a football data set and generated data.

Original language | English |
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Title of host publication | Experimental Algorithms |

Subtitle of host publication | 15th International Symposium, SEA 2016, St. Petersburg, Russia, June 5-8, 2016, Proceedings |

Place of Publication | Cham |

Publisher | Springer |

Pages | 89-104 |

ISBN (Electronic) | 978-3-319-38851-9 |

ISBN (Print) | 978-3-319-38850-2 |

DOIs | |

Publication status | Published - 2016 |

Event | International Symposium on Experimental Algorithms: 15th International Symposium - St. Petersburg, Russian Federation Duration: 5 Jun 2016 → 8 Jun 2016 http://link.springer.com/book/10.1007/978-3-319-38851-9 |

### Publication series

Name | Lecture Notes in Computer Science |
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Volume | 9685 |

### Conference

Conference | International Symposium on Experimental Algorithms |
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Abbreviated title | SEA 2016 |

Country | Russian Federation |

City | St. Petersburg |

Period | 5/06/16 → 8/06/16 |

Internet address |

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## Cite this

Buchin, K. A., Buchin, M. E., Gudmundsson, J., Horton, M. J., & Sijben, S. (2016). Compact flow diagrams for state sequences. In

*Experimental Algorithms: 15th International Symposium, SEA 2016, St. Petersburg, Russia, June 5-8, 2016, Proceedings*(pp. 89-104). (Lecture Notes in Computer Science; Vol. 9685). Springer. https://doi.org/10.1007/978-3-319-38851-9_7