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

  • Authors:
  • Jun Hosoda;Juraj Hromkovič;Taisuke Izumi;Hirotaka Ono;Monika Steinová;Koichi Wada

  • Affiliations:
  • Graduate School of Engineering, Nagoya Institute of Technology, Japan;Department of Computer Science, ETH Zurich, Switzerland;Graduate School of Engineering, Nagoya Institute of Technology, Japan;Department of Economic Engineering, Kyushu University, Japan;Department of Computer Science, ETH Zurich, Switzerland;Graduate School of Engineering, Nagoya Institute of Technology, Japan

  • Venue:
  • MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
  • Year:
  • 2011

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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(log t) 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.