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This work deals with a generalization of the minimum Target Set Selection (TSS) problem, a key algorithmic question in information diffusion research due to its potential commercial value. Firstly proposed by Kempe et al., the TSS problem is based on a linear threshold diffusion model defined on an input graph with node thresholds, quantifying the hardness to influence each node. The goal is to find the smaller set of items that can influence the whole network according to the diffusion model defined. This study generalizes the TSS problem on networks characterized by many-to-many relationships modeled via hypergraphs. Specifically, we introduce a linear threshold diffusion process on such structures, which evolves as follows. Let H=(V,E) be a hypergraph. At the beginning of the process, the nodes in a given set S⊆V are influenced. Then, at each iteration, (i) the influenced hyperedges set is augmented by all edges having a sufficiently large number of influenced nodes; (ii) consequently, the set of influenced nodes is enlarged by all the nodes having a sufficiently large number of already influenced hyperedges. The process ends when no new nodes can be influenced. Exploiting this diffusion model, we define the minimum Target Set Selection problem on hypergraphs (TSSH). Being the problem NP-hard (as it generalizes the TSS problem), we introduce four heuristics and provide an extensive evaluation on real-world networks.

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Despite the fact that many important problems (including clustering) can be described using hypergraphs, theoretical foundations as well as practical algorithms using hypergraphs are not well developed yet. In this paper, we propose a hypergraph modularity function that generalizes its well established and widely used graph counterpart measure of how clustered a network is. In order to define it properly, we generalize the Chung-Lu model for graphs to hypergraphs. We then provide the theoretical foundations to search for an optimal solution with respect to our hypergraph modularity function. A simple heuristic algorithm is described and applied to a few illustrative examples. We show that using a strict version of our proposed modularity function often leads to a solution where a smaller number of hyperedges get cut as compared to optimizing modularity of 2-section graph of a hypergraph.

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In the paper, we consider sequential decision problems with uncertainty, represented as decision trees. Sensitivity analysis is always a crucial element of decision making and in decision trees it often focuses on probabilities. In the stochastic model considered, the user often has only limited information about the true values of probabilities. We develop a framework for performing sensitivity analysis of optimal strategies accounting for this distributional uncertainty. We design this robust optimization approach in an intuitive and not overly technical way, to make it simple to apply in daily managerial practice. The proposed framework allows for (1) analysis of the stability of the expected-value-maximizing strategy and (2) identification of strategies which are robust with respect to pessimistic/optimistic/mode-favoring perturbations of probabilities. We verify the properties of our approach in two cases: (a) probabilities in a tree are the primitives of the model and can be modified independently; (b) probabilities in a tree reflect some underlying, structural probabilities, and are interrelated. We provide a free software tool implementing the methods described.