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In several domains, the flow of data is governed by an underlying network. Reduction of delays in end-to-end data flow is an important network optimization task. Reduced delays enable shorter travel times for vehicles in road networks, faster information flow in social networks, and increased rate of packets in communication networks. While techniques for network delay minimization have been proposed, they fail to provide any noticeable reduction in individual data flows. Furthermore, they treat all nodes as equally important, which is often not the case in real-world networks. In this paper, we incorporate these practical aspects and propose a network design problem where the goal is to perform k network upgrades such that it maximizes the number of flows in the network with a noticeable reduction in delay. We show that the problem is NP-hard, APX-hard, and non-submodular. We overcome these computational challenges by designing an importance sampling based algorithm with provable quality guarantees. Through extensive experiments on real and synthetic data sets, we establish that importance sampling imparts up to 1000 times speed-up over the greedy approach, and provides up to 70 times the improvement achieved by the state-of-the-art technique.

Graph Neural Networks (GNNs), a generalization of deep neural networks on graph data have been widely used in various domains, ranging from drug discovery to recommender systems. However, GNNs on such applications are limited when there are few available samples. Meta-learning has been an important framework to address the lack of samples in machine learning, and in recent years, researchers have started to apply meta-learning to GNNs. In this work, we provide a comprehensive survey of different metalearning approaches involving GNNs on various graph problems showing the power of using these two approaches together. We categorize the literature based on proposed architectures, shared representations, and applications. Finally, we discuss several exciting future research directions and open problems.

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