### Abstract

In the context of designing a scalable overlay network to support decentralized topic-based pub/sub communication, the Minimum Topic-Connected Overlay problem (Min-TCO in short) has been investigated: Given a set of t topics, collection of n users together with the lists of topics they are interested in, the aim is to connect these users to a network by a minimum number of edges such that every graph induced by users interested in a common topic is connected. It is known that Min-TCO is NP-hard and approximable within O(logt) in polynomial time. In this paper, we further investigate the problem and some of its special instances. We give various hardness results for instances where the number of users interested in a common topic is constant, and also for the instances where the number of topics in which an user is interested in is bounded by a constant. Furthermore, we close the gap of hardness of Min-TCO by showing its LOGAPX-completeness. We also present a few polynomial-time algorithms for very restricted instances of Min-TCO.

Original language | English |
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Title of host publication | Mathematical Foundations of Computer Science 2011 - 36th International Symposium, MFCS 2011, Proceedings |

Pages | 376-387 |

Number of pages | 12 |

DOIs | |

Publication status | Published - Sep 1 2011 |

Event | 36th International Symposium on Mathematical Foundations of Computer Science, MFCS 2011 - Warsaw, Poland Duration: Aug 22 2011 → Aug 26 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6907 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 36th International Symposium on Mathematical Foundations of Computer Science, MFCS 2011 |
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Country | Poland |

City | Warsaw |

Period | 8/22/11 → 8/26/11 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Mathematical Foundations of Computer Science 2011 - 36th International Symposium, MFCS 2011, Proceedings*(pp. 376-387). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6907 LNCS). https://doi.org/10.1007/978-3-642-22993-0_35

**On the approximability of minimum topic connected overlay and its special instances.** / Hosoda, Jun; Hromkovič, Juraj; Izumi, Taisuke; Ono, Hirotaka; Steinová, Monika; Wada, Koichi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Mathematical Foundations of Computer Science 2011 - 36th International Symposium, MFCS 2011, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6907 LNCS, pp. 376-387, 36th International Symposium on Mathematical Foundations of Computer Science, MFCS 2011, Warsaw, Poland, 8/22/11. https://doi.org/10.1007/978-3-642-22993-0_35

}

TY - GEN

T1 - On the approximability of minimum topic connected overlay and its special instances

AU - Hosoda, Jun

AU - Hromkovič, Juraj

AU - Izumi, Taisuke

AU - Ono, Hirotaka

AU - Steinová, Monika

AU - Wada, Koichi

PY - 2011/9/1

Y1 - 2011/9/1

N2 - In the context of designing a scalable overlay network to support decentralized topic-based pub/sub communication, the Minimum Topic-Connected Overlay problem (Min-TCO in short) has been investigated: Given a set of t topics, collection of n users together with the lists of topics they are interested in, the aim is to connect these users to a network by a minimum number of edges such that every graph induced by users interested in a common topic is connected. It is known that Min-TCO is NP-hard and approximable within O(logt) in polynomial time. In this paper, we further investigate the problem and some of its special instances. We give various hardness results for instances where the number of users interested in a common topic is constant, and also for the instances where the number of topics in which an user is interested in is bounded by a constant. Furthermore, we close the gap of hardness of Min-TCO by showing its LOGAPX-completeness. We also present a few polynomial-time algorithms for very restricted instances of Min-TCO.

AB - In the context of designing a scalable overlay network to support decentralized topic-based pub/sub communication, the Minimum Topic-Connected Overlay problem (Min-TCO in short) has been investigated: Given a set of t topics, collection of n users together with the lists of topics they are interested in, the aim is to connect these users to a network by a minimum number of edges such that every graph induced by users interested in a common topic is connected. It is known that Min-TCO is NP-hard and approximable within O(logt) in polynomial time. In this paper, we further investigate the problem and some of its special instances. We give various hardness results for instances where the number of users interested in a common topic is constant, and also for the instances where the number of topics in which an user is interested in is bounded by a constant. Furthermore, we close the gap of hardness of Min-TCO by showing its LOGAPX-completeness. We also present a few polynomial-time algorithms for very restricted instances of Min-TCO.

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U2 - 10.1007/978-3-642-22993-0_35

DO - 10.1007/978-3-642-22993-0_35

M3 - Conference contribution

AN - SCOPUS:80052111219

SN - 9783642229923

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 376

EP - 387

BT - Mathematical Foundations of Computer Science 2011 - 36th International Symposium, MFCS 2011, Proceedings

ER -