Cost-Aware Deployment of Check-In Nodes in Complex Networks

It is challenging to deploy check-in nodes optimally in a complex network so as to perform specific check-in like services, e.g., fuel supplements etc., but crucial in many real-world applications. In this article, we propose and study the new optimization problem of placing check-in nodes with the minimum cost, i.e., the problem of finding the minimum-cost check-in nodes (MCCN), which is of great interests for real-world application situations, but even more difficult. We motivate the new algorithms through three typical worse cases by the often-used greedy-type algorithms, i.e., One-to-Many, Many-to-One, and Duplicate-Overrides. With this respect, the proposed novel optimization algorithms utilize a novel metric of contribution density for selecting check-in nodes iteratively, which successfully avoid the occurrence of the two worse cases of One-to-Many and Many-to-One. We also introduce an extra backward extraction step in one of new algorithms, which overcomes the crucial worse case of "duplicate overrides'' and largely improves the algorithmic performance in solving the introduced optimization problem of MCCN. Meanwhile, we extend the new contribution density metric to a more general class of functions and study their effectiveness to eliminate the two worse cases of One-to-Many and Many-to-One; also, a detailed analysis on complexity and performance of the proposed algorithms is presented to show their numerical efficiency and accuracy. Extensive experiments over two classical artificial networks, i.e., BA network and ER network, and ten real-world networks, under two typical cost setups, show the proposed algorithms significantly outperform the four state-of-the-art algorithms. We also demonstrate that our proposed algorithms are much reliable and robust with different experiment settings of deployment cost and network-type and scale.