Graph classification aims to categorize graphs based on their structural and attribute features, with applications in diverse fields such as social network analysis and bioinformatics. Among the methods proposed to solve this task, those relying on patterns (i.e., subgraphs) provide good explainability, as the patterns used for classification can be directly interpreted. To identify meaningful patterns, a standard approach is to use a quality measure, i.e., a function that evaluates the discriminative power of each pattern. However, the literature provides tens of such measures, making it difficult to select the most appropriate for a given application. Only a handful of surveys try to provide some insight by comparing these measures, and none of them specifically focuses on graphs. This typically results in the systematic use of the most widespread measures, without thorough evaluation. To address this issue, we present a comparative analysis of 38 quality measures from the literature. We characterize them theoretically, based on four mathematical properties. We leverage publicly available datasets to constitute a benchmark, and propose a method to elaborate a gold standard ranking of the patterns. We exploit these resources to perform an empirical comparison of the measures, both in terms of pattern ranking and classification performance. Moreover, we propose a clustering-based preprocessing step, which groups patterns appearing in the same graphs to enhance classification performance. Our experimental results demonstrate the effectiveness of this step, reducing the number of patterns to be processed while achieving comparable performance. Additionally, we show that some popular measures widely used in the literature are not associated with the best results.

In the context of community detection, correlation clustering (CC) provides a measure of balance for social networks as well as a tool to explore their structures. However, CC does not encompass features such as the mediation between the clusters, which could be all the more relevant with the recent rise of ideological polarization. In this work, we study correlation clustering under mediation (CCM), a new variant of CC in which a set of mediators is determined. This new signed graph clustering problem is proved to be NP-hard and formulated as an integer programming formulation. An extensive investigation of the mediation set structure leads to the development of two efficient exact enumeration algorithms for CCM. The first one exhaustively enumerates the maximal sets of mediators in order to provide several relevant solutions. The second algorithm implements a pruning mechanism, which drastically reduces the size of the exploration tree in order to return a single optimal solution. Computational experiments are presented on two sets of instances: signed networks representing voting activity in the European Parliament and random signed graphs. History: Accepted by Van Hentenryck, Area Editor for Pascal. Funding: This work was supported by Fondation Mathématique Jacques Hadamard [Grant P-2019-0031]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0129 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0129 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

The widespread adoption of 5G cellular technology will evolve as one of the major drivers for the growth of IoT-based applications. In this paper, we consider a Service Provider (SP) that launches a smart city service based on IoT data readings: in order to serve IoT data collected across different locations, the SP dynamically negotiates and rescales bandwidth and service functions. 5G network slicing functions are key to lease appropriate amount of resources over heterogeneous access technologies and different site types. Also, different infrastructure providers will charge slicing service depending on specific access technology supported across sites and IoT data collection patterns. We introduce a pricing mechanism based on Age of Information (AoI) to reduce the cost of SPs. It provides incentives for devices to smooth traffic by shifting part of the traffic load from highly congested and more expensive locations to lesser charged ones, while meeting QoS requirements of the IoT service. The proposed optimal pricing scheme comprises a two-stage decision process, where the SP determines the pricing of each location and devices schedule uploads of collected data based on the optimal uploading policy. Simulations show that the SP attains consistent cost reductions tuning the trade-off between slicing costs and the AoI of uploaded IoT data.

When adopting a novel mobile technology, a mobile network operator faces the dilemma of determining which is the best time to start the installation of next generation equipment onto the existing infrastructure. In a strategic context, the best possible time for deployment is also the best response to competitors’ actions, subject to normative and material constraints and to the customer’s adoption curve. We formulate in this paper a finite discrete-time game which captures the main features of the problem for a two-player game played over a prescribed finite horizon. Our numerical results provide insights on the possible optimal tradeoffs for an operator between fixed costs and installation strategies.

Abstract We consider the context of a telecommunication company that is at the same time an infrastructure operator and a service provider. When planning its network expansion, the company can leverage over its knowledge of the subscriber dynamic to better optimize the network dimensioning, therefore avoiding unnecessary costs. In this work, the network expansion represents the deployment and/or reinforcement of several technologies (e.g., 2G, 3G, 4G), assuming that subscribers to a given technology can be served by this technology or older ones. The operator can influence subscriber dynamic by subsidies. The planning is made over a discretized time horizon while some strategic guideline requirements are required at the end of the time horizon. Following classical models, we consider that the willingness of customers for shifting to a new technology follows an S‐shape piecewise constant function. We propose a mixed‐integer linear programming formulation, improved through several valid inequalities and a heuristic algorithm. We assess the formulation numerically on real instances.