Cartesian product of hypergraphs: properties and algorithms

Cartesian products of graphs have been studied extensively since the 1960s. They make it possible to decrease the algorithmic complexity of problems by using the factorization of the product. Hypergraphs were introduced as a generalization of graphs and the definition of Cartesian products extends naturally to them. In this paper, we give new properties and algorithms concerning coloring aspects of Cartesian products of hypergraphs. We also extend a classical prime factorization algorithm initially designed for graphs to connected conformal hypergraphs using 2-sections of hypergraphs

Factorization of products of hypergraphs: Structure and algorithms

International audienceOn the one hand Cartesian products of graphs have been extensively studied since the 1960s. On the other hand hypergraphs are a well-known and useful generalization of graphs. In this article, we present an algorithm able to factorize into its prime factors any bounded-rank and bounded-degree hypergraph in O(nm), where n is the number of vertices and m is the number of hyperedges of the hypergraph. First the algorithm applies a graph factorization algorithm to the 2-section of the hypergraph. Then the 2-section factorization is used to build the factorization of the hypergraph via the factorization of its L2-section. The L2-section is a recently introduced way to interpret a hypergraph as a labeled-graph. The graph factorization algorithm used in this article is due to Imrich and Peterin and is linear in time and space. Nevertheless any other such algorithm could be extended to a hypergraph factorization algorithm similar to the one presented here

Un algorithme pour la factorisation des hypergraphes conformes

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Coupling small batteries and PV generation: A review

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Concevoir un cours en ligne, c'est du bricolage

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Rate design with distributed energy resources and electric vehicles: A Californian case study

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Is one meter enough? Assessing the impacts of domestic electric vehicle-only rate adoption via submetering.

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Unlocking Flexible Electric Vehicle Charging via New Rate Design

International audienceTo reduce CO2, electric vehicles (EVs) are required to substitute Internal Combustion Engine (ICE) vehicles to achieve the decarbonisation goals established during international environmental summits. Between 150 and 230 million vehicles are expected to be on the world’s roads by 2030, potentially causing future issues for power systems. EV charging should not drastically increase consumption in already existing peak periods neither create new ones which may exceed grid maximum capacity. To avoid costly grid reinforcements and to ensure proper guidance for EV charging, a solution allowing customers to access EV-only rates without installing a separate meter, which we refer to as submetering, is an attractive option for EV owners and grid operators.We develop a game-theoretic model is presented to capture the interaction between a national regulatory authority (NRA) designing EV-only tariffs and dwellings to address this question. The model consists of two levels, the lower level represents the dwellings and the upper level stands for the regulatory authority, both casted as an optimization problem and modelled as a mathematical program with equilibrium constraint.Results show a fair energy cost reduction with an EV-only tariff for the adopter while keeping network charges fixed. However, by recovering grid costs via a three-part tariff that contains capacity charges, the increase in network costs offsets the gains brought by energy savings. With a pure volumetric tariff, fairness issues are nuanced, resulting in well-allocated network costs distribution in which consumers experience a higher decrease in their charges. In addition, we show that submetering can bring yearly gains varying from $64 to$125 with this type of tariff.The integrated assessment of submetering exploring the variations in energy and network charge has shown that this solution can bring significant added value to EV charging. Policymakers would not need to deplete their political capital to implement complex TOU pricing and capacity-based tariffs across jurisdictions. To help deal with problems coming from ill-designed tariffs in an emerging technology context, submetering can be a straightforward solution with low transaction costs to be implemented