scholarly journals Forming Probably Stable Communities with Limited Interactions

2019 ◽  
Vol 33 ◽  
pp. 2053-2060
Author(s):  
Ayumi Igarashi ◽  
Jakub Sliwinski ◽  
Yair Zick
Keyword(s):  
Interaction Network ◽  
Graph Structure ◽  
Interaction Graph ◽  
Community Needs ◽  
Underlying Graph ◽  
Coalition Structures ◽  
Stable Coalition ◽  
Hedonic Games ◽  
Connected Subgraphs ◽  
Stable Community

A community needs to be partitioned into disjoint groups; each community member has an underlying preference over the groups that they would want to be a member of. We are interested in finding a stable community structure: one where no subset of members S wants to deviate from the current structure. We model this setting as a hedonic game, where players are connected by an underlying interaction network, and can only consider joining groups that are connected subgraphs of the underlying graph. We analyze the relation between network structure, and one’s capability to infer statistically stable (also known as PAC stable) player partitions from data. We show that when the interaction network is a forest, one can efficiently infer PAC stable coalition structures. Furthermore, when the underlying interaction graph is not a forest, efficient PAC stabilizability is no longer achievable. Thus, our results completely characterize when one can leverage the underlying graph structure in order to compute PAC stable outcomes for hedonic games. Finally, given an unknown underlying interaction network, we show that it is NP-hard to decide whether there exists a forest consistent with data samples from the network.

scholarly journals Testing stability properties in graphical hedonic games

2021 ◽  
Vol 35 (2) ◽  
Author(s):  
Hendrik Fichtenberger ◽  
Anja Rey
Keyword(s):  
Time Complexity ◽  
Coalition Structure ◽  
Property Testing ◽  
Core Stability ◽  
Bounded Degree ◽  
Coalition Structures ◽  
Input Size ◽  
Stable Coalition ◽  
Hedonic Games ◽  
The Stability

AbstractIn hedonic games, players form coalitions based on individual preferences over the group of players they could belong to. Several concepts to describe the stability of coalition structures in a game have been proposed and analysed in the literature. However, prior research focuses on algorithms with time complexity that is at least linear in the input size. In the light of very large games that arise from, e.g., social networks and advertising, we initiate the study of sublinear time property testing algorithms for existence and verification problems under several notions of coalition stability in a model of hedonic games represented by graphs with bounded degree. In graph property testing, one shall decide whether a given input has a property (e.g., a game admits a stable coalition structure) or is far from it, i.e., one has to modify at least an $$\epsilon$$ ϵ -fraction of the input (e.g., the game’s preferences) to make it have the property. In particular, we consider verification of perfection, individual rationality, Nash stability, (contractual) individual stability, and core stability. While there is always a Nash-stable coalition structure (which also implies individually stable coalitions), we show that the existence of a perfect coalition structure is not tautological but can be tested. All our testers have one-sided error and time complexity that is independent of the input size.

scholarly journals Sequentially Stable Coalition Structures

2007 ◽  
Author(s):  
Yukihiko Funaki ◽  
Takehiko Yamato
Keyword(s):  
Coalition Structures ◽  
Stable Coalition

scholarly journals Graph Convolutional Neural Network for a Pharmacy Cross-Selling Recommender System

Information ◽  
2020 ◽  
Vol 11 (11) ◽  
pp. 525
Author(s):  
Franz Hell ◽  
Yasser Taha ◽  
Gereon Hinz ◽  
Sabine Heibei ◽  
Harald Müller ◽  
...  
Keyword(s):  
Recommender System ◽  
Network Optimization ◽  
Deep Neural Networks ◽  
Product Information ◽  
State Of The Art ◽  
Pharmaceutical Product ◽  
Structured Data ◽  
Graph Structure ◽  
Convolutional Network ◽  
Underlying Graph

Recent advancements in deep neural networks for graph-structured data have led to state-of-the-art performance in recommender system benchmarks. Adapting these methods to pharmacy product cross-selling recommendation tasks with a million products and hundreds of millions of sales remains a challenge, due to the intricate medical and legal properties of pharmaceutical data. To tackle this challenge, we developed a graph convolutional network (GCN) algorithm called PharmaSage, which uses graph convolutions to generate embeddings for pharmacy products, which are then used in a downstream recommendation task. In the underlying graph, we incorporate both cross-sales information from the sales transaction within the graph structure, as well as product information as node features. Via modifications to the sampling involved in the network optimization process, we address a common phenomenon in recommender systems, the so-called popularity bias: popular products are frequently recommended, while less popular items are often neglected and recommended seldomly or not at all. We deployed PharmaSage using real-world sales data and trained it on 700,000 articles represented as nodes in a graph with edges between nodes representing approximately 100 million sales transactions. By exploiting the pharmaceutical product properties, such as their indications, ingredients, and adverse effects, and combining these with large sales histories, we achieved better results than with a purely statistics based approach. To our knowledge, this is the first application of deep graph embeddings for pharmacy product cross-selling recommendation at this scale to date.

scholarly journals Constrained Coalition Formation on Valuation Structures: Formal Framework, Applications, and Islands of Tractability (Extended Abstract)

2018 ◽  
Author(s):  
Gianluigi Greco ◽  
Antonella Guzzo
Keyword(s):  
Coalition Structure ◽  
Interaction Graph ◽  
Topological Properties ◽  
Structure Generation ◽  
Coalition Structures ◽  
Formal Framework ◽  
Real World Applications ◽  
Feasible Coalition ◽  
Stability Issues ◽  
Coalition Structure Generation

Coalition structure generation is considered in a setting where feasible coalition structures must satisfy constraints of two different kinds modeled in terms of a valuation structure, which consists of a set of pivotal agents that are pairwise incompatible, plus an interaction graph prescribing that a coalition C can form only if the subgraph induced over the nodes/agents in C is connected. It is shown that valuation structures can be used to model a number of relevant problems in real-world applications. Moreover, complexity issues arising with them are studied, by focusing in particular on identifying islands of tractability based on topological properties of the underlying interaction graph. Stability issues on valuation structures are studied too.

scholarly journals Finite Controllability for Ontology-Mediated Query Answering of CRPQ

2020 ◽  
Author(s):  
Diego Figueira ◽  
Santiago Figueira ◽  
Edwin Pin Baque
Keyword(s):  
Query Answering ◽  
Graph Structure ◽  
First Order ◽  
Underlying Graph ◽  
Graph Classes ◽  
Regular Path ◽  
Order Constraints ◽  
Simple Recursion ◽  
Regular Path Queries ◽  
Path Queries

Finite ontology mediated query answering (FOMQA) is the variant of ontology mediated query answering (OMQA) where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. We study the property of finite-controllability, that is, whether FOMQA and OMQA are equivalent, for fragments of C2RPQ. C2RPQ is the language of conjunctive two-way regular path queries, which can be regarded as the result of adding simple recursion to Conjunctive Queries. For graph classes S, we consider fragments C2RPQ(S) of C2RPQ as the queries whose underlying graph structure is in S. We completely classify the finitely controllable and non-finitely controllable fragments under: inclusion dependencies, (frontier-)guarded rules, frontier-one rules (either with or without constants), and more generally under guarded-negation first-order constraints. For the finitely controllable fragments, we show a reduction to the satisfiability problem for guarded-negation first-order logic, yielding a 2EXPTIME algorithm (in combined complexity) for the corresponding (F)OMQA problem.

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