A Correction to this paper has been published: https://doi.org/10.1007/s00224-021-10057-6

Abstract We investigate parameterized algorithms for the NP-hard problem Min-Power Asymmetric Connectivity (MinPAC) that has applications in wireless sensor networks. Given a directed arc-weighted graph, MinPAC asks for a strongly connected spanning subgraph minimizing the summed vertex costs. Here, the cost of each vertex is the weight of its heaviest outgoing arc in the chosen subgraph. We present linear-time algorithms for the cases where the number of strongly connected components in a so-called obligatory subgraph or the feedback edge number in the underlying undirected graph is constant. Complementing these results, we prove that the problem is W[2]-hard with respect to the solution cost, even on restricted graphs with one feedback arc and binary arc weights.

Programs in domain-­specific embedded languages (DSELs) can be represented in the host language in different ways, for instance implicitly as libraries, or explicitly in the form of abstract syntax trees. Each of these representations has its own strengths and weaknesses. The implicit approach has good composability properties, whereas the explicit approach allows more freedom in making syntactic program transformations.

Self-representation -- the ability to represent programs in their own language -- has important applications in reflective languages and many other domains of programming language design. Although approaches to designing typed program representations for sublanguages of some base language have become quite popular recently, the question whether a fully metacircular typed self-representation is possible is still open. This paper makes a big step towards this aim by defining the Fω* calculus, an extension of the higher-order polymorphic lambda calculus Fω that allows typed self-representations. While the usability of these representations for metaprogramming is still limited, we believe that our approach makes a significant step towards a new generation of reflective languages that are both safe and efficient.

The influential pure embedding methodology of embedding domain-specific languages (DSLs) as libraries into a general-purpose host language forces the DSL designer to commit to a single semantics. This precludes the subsequent addition of compilation, optimization or domain-specific analyses. We propose polymorphic embedding of DSLs, where many different interpretations of a DSL can be provided as reusable components, and show how polymorphic embedding can be realized in the programming language Scala. With polymorphic embedding, the static type-safety, modularity, composability and rapid prototyping of pure embedding are reconciled with the flexibility attainable by external toolchains.