The connectivity of networks has been widely studied in many highimpact applications, ranging from immunization, critical infrastructure analysis, social network mining, to bioinformatic system studies. Regardless of the end application domains, connectivity minimization has always been a fundamental task to effectively control the functioning of the underlying system. The combinatorial nature of the connectivity minimization problem imposes an exponential computational complexity to find the optimal solution, which is intractable in large systems. To tackle the computational barrier, greedy algorithm is extensively used to ensure a nearoptimal solution by exploiting the diminishing returns property of the problem. Despite the empirical success, the theoretical and algorithmic challenges of the problems still remain wide open. On the theoretical side, the intrinsic hardness and the approximability of the general connectivity minimization problem are still unknown except for a few special cases. On the algorithmic side, existing algorithms are hard to balance between the optimization quality and computational efficiency. In this article, we address the two challenges by (1) proving that the general connectivity minimization problem is NPhard and is the best approximation ratio for any polynomial algorithms, and (2) proposing the algorithm CONTAIN and its variant CONTAIN + that can well balance optimization effectivenessmore »
Network Connectivity Optimization: Fundamental Limits and Effective Algorithms
Network connectivity optimization, which aims to manipulate network connectivity by changing its underlying topology, is a fundamental task behind a wealth of highimpact data mining applications, ranging from immunization, critical infrastructure construction, social collaboration mining, bioinformatics analysis, to intelligent transportation system design. To tackle its exponential computation complexity, greedy algorithms have been extensively used for network connectivity optimization by exploiting its diminishing returns property. Despite the empirical success, two key challenges largely remain open. First, on the theoretic side, the hardness, as well as the approximability of the general network connectivity optimization problem are still nascent except for a few special instances. Second, on the algorithmic side, current algorithms are often hard to balance between the optimization quality and the computational efficiency. In this paper, we systematically address these two challenges for the network connectivity optimization problem. First, we reveal some fundamental limits by proving that, for a wide range of network connectivity optimization problems, (1) they are NPhard and (2) (11/e) is the optimal approximation ratio for any polynomial algorithms. Second, we propose an effective, scalable and general algorithm (CONTAIN) to carefully balance the optimization quality and the computational efficiency.
 Publication Date:
 NSFPAR ID:
 10099217
 Journal Name:
 KDD '18 Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining
 Page Range or eLocationID:
 1167 to 1176
 Sponsoring Org:
 National Science Foundation
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