On the Approximability and Hardness of Minimum Topic Connected Overlay and Its Special Instances

TL;DR

This paper studies the computational complexity and approximation algorithms for the Minimum Topic-Connected Overlay problem, focusing on special cases with bounded user interest and topic sizes, providing new hardness results and a constant approximation algorithm.

Contribution

It introduces new hardness results for Min-TCO with bounded user interest and common topic interest, and presents the first constant approximation algorithm for certain instances.

Findings

Hardness results for instances with bounded user interest

Hardness results for instances with a constant number of users per topic

A constant approximation algorithm for specific cases

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 and a 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 topics in which an user is interested in is bounded by a constant, and also for the instances where the number of users interested in a common topic is constant. For the latter case, we present a first constant approximation algorithm. We also present some polynomial-time algorithms for very restricted instances of Min-TCO.