Advances in renewable and sustainable energy technologies critically depend on our ability to design and realize materials with optimal properties. Materials discovery and design efforts ideally involve close coupling between materials prediction, synthesis and characterization. The increased use of computational tools, the generation of materials databases, and advances in experimental methods have substantially accelerated these activities. It is therefore an opportune time to consider future prospects for materials by design approaches. The purpose of this Roadmap is to present an overview of the current state of computational materials prediction, synthesis and characterization approaches, materials design needs for various technologies, and future challenges and opportunities that must be addressed. The various perspectives cover topics on computational techniques, validation, materials databases, materials informatics, high-throughput combinatorial methods, advanced characterization approaches, and materials design issues in thermoelectrics, photovoltaics, solid state lighting, catalysts, batteries, metal alloys, complex oxides and transparent conducting materials. It is our hope that this Roadmap will guide researchers and funding agencies in identifying new prospects for materials design.

This paper introduces and studies the maximum k-plex problem, which arises in social network analysis, but can also be used in several other important application areas, including wireless networks, telecommunications, and graph-based data mining. We establish NP-completeness of the decision version of the problem on arbitrary graphs. An integer programming formulation is presented and basic polyhedral study of the problem is carried out. A branch-and-cut implementation is discussed and computational test results on the proposed benchmark instances and real-life scale-free graphs are also provided.

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