Recently, Graph Neural Networks (GNNs) achieve remarkable success in Recommendation. To reduce the influence of data sparsity, Graph Contrastive Learning (GCL) is adopted in GNN-based CF methods for enhancing performance. Most GCL methods consist of data augmentation and contrastive loss (e.g., InfoNCE). GCL methods construct the contrastive pairs by hand-crafted graph augmentations and maximize the agreement between different views of the same node compared to that of other nodes, which is known as the InfoMax principle. However, improper data augmentation will hinder the performance of GCL. InfoMin principle, that the good set of views shares minimal information and gives guidelines to design better data augmentation. In this paper, we first propose a new data augmentation (i.e., edge-operating including edge-adding and edge-dropping). Then, guided by InfoMin principle, we propose a novel theoretical guiding contrastive learning framework, named Learnable Data Augmentation for Graph Contrastive Learning (LDA-GCL). Our methods include data augmentation learning and graph contrastive learning, which follow the InfoMin and InfoMax principles, respectively. In implementation, our methods optimize the adversarial loss function to learn data augmentation and effective representations of users and items. Extensive experiments on four public benchmark datasets demonstrate the effectiveness of LDA-GCL.

We present NeuroLKH, a novel algorithm that combines deep learning with the strong traditional heuristic Lin-Kernighan-Helsgaun (LKH) for solving Traveling Salesman Problem. Specifically, we train a Sparse Graph Network (SGN) with supervised learning for edge scores and unsupervised learning for node penalties, both of which are critical for improving the performance of LKH. Based on the output of SGN, NeuroLKH creates the edge candidate set and transforms edge distances to guide the searching process of LKH. Extensive experiments firmly demonstrate that, by training one model on a wide range of problem sizes, NeuroLKH significantly outperforms LKH and generalizes well to much larger sizes. Also, we show that NeuroLKH can be applied to other routing problems such as Capacitated Vehicle Routing Problem (CVRP), Pickup and Delivery Problem (PDP), and CVRP with Time Windows (CVRPTW).

We study the computational complexity of candidate control in elections with few voters, that is, we consider the parameterized complexity of candidate control in elections with respect to the number of voters as a parameter. We consider both the standard scenario of adding and deleting candidates, where one asks whether a given candidate can become a winner (or, in the destructive case, can be precluded from winning) by adding or deleting few candidates, as well as a combinatorial scenario where adding/deleting a candidate automatically means adding or deleting a whole group of candidates. Considering several fundamental voting rules, our results show that the parameterized complexity of candidate control, with the number of voters as the parameter, is much more varied than in the setting with many voters.

Election control problems are concerned with affecting the result of an election by modifying the structure of the election. Such election modifications could be either introducing some new candidates or voters or removing some existing candidates or voters from the election or partitioning candidates or voters [2, 27, 32, 42, 56, 57, 34, 35, 62]. We focus on the computational complexity of election control by adding and deleting candidates (that is, candidate control), for the case where the election involves only a few voters. From the viewpoint of computational complexity, voter control with few voters has not received sufficient study. We focus on very simple, practical voting rules such as Plurality, Veto, andt-Approval, but discuss several more involved rules as well. To analyze the effect of allowing only a small number of voters, we use the formal tools of parameterized complexity theory [21, 23, 38, 60]. From the viewpoint of classical complexity theory, most of the candidate control problems for most of the typically studied voting rules are NPhard. Indeed, candidate control problems are NPhard even for the Plurality rule; nonetheless, there are some natural examples of candidate control problems with polynomialtime algorithms. It turns out that for the case of elections with few voters, that is, for control problems parameterized by the number of voters, the computational complexity landscape of candidate control is much more varied and sometimes quite surprising.

We study the computational complexity of candidate control in elections with few voters (that is, we take the number of voters as a parameter). We consider both the standard scenario of adding and deleting candidates, where one asks if a given candidate can become a winner (or, in the destructive case, can be precluded from winning) by adding/deleting some candidates, and a combinatorial scenario where adding/deleting a candidate automatically means adding/deleting a whole group of candidates. Our results show that the parameterized complexity of candidate control (with the number of voters as the parameter) is much more varied than in the setting with many voters.