A k-disjoint path cover of a graph is a set of k internally vertex-disjoint paths which cover the vertex set with k paths and each of which runs between a source and a sink. Given that each source and sink v is associated with an integer-valued demand d(v) ≥ 1, we are concerned with general-demand k-disjoint path cover in which every source and sink v is contained in the d(v) paths. In this pap...

A many-to-many k-disjoint path cover of a graph joining two disjoint vertex sets S and T of equal size k is a set of k vertex-disjoint paths between S and T that altogether cover every vertex of the graph. The many-to-many k-disjoint path cover is classified as paired if each source in S is further required to be paired with a specific sink in T , or unpaired otherwise. In this paper, we first ...

Two-sided matchings are an important theoretical tool used to model markets and social interactions. In many real life problems the utility of an agent is influenced not only by their own choices, but also by the choices that other agents make. Such an influence is called an externality. Whereas fully expressive representations of externalities in matchings require exponential space, in this pa...

A new method for interpolating between presets is described. The interpolation algorithm called Intersecting N-Spheres Interpolation is simple to compute and its generalization to higher dimensions is straightforward. The current implementation in the SuperCollider environment is presented as a tool that eases the design of many-to-many mappings for musical interfaces. Examples of its uses, inc...