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Convex polyhedra are important objects in various areas of mathematics and other disciplines. A fundamental result, known as Minkowski-Weyl theorem, states that every polyhedron admits two types of representations, either as the solution set to a finite sy ...
Many complex networks erase parts of their geometry as they develop, so that their evolution is difficult to quantify and trace. Here we introduce entropy measures for quantifying the complexity of street orientations and length variations within planar ne ...
We present a method for the design of 3D constructions from planar pieces that can be cut easily and cheaply with laser cutters and similar Computer Numerical Control (CNC) machines. By cutting tight slits in intersecting pieces, they can be slid into each ...
Shortest paths are not always simple. In planar networks, they can be very different from those with the smallest number of turns - the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a non trivial and ...
The classical problem in network coding theory considers communication over multicast networks. Multiple transmitters send independent messages to multiple receivers which decode the same set of messages. In this work, computation over multicast networks i ...
Multilayered media with printed circuits embedded between their dielectric layers are one of the most successful technologies for manufacturing planar structures with a very promising performance-to-price ratio. These planar structures include many differe ...
Given a geometric hypergraph (or a range-space) H=(V,E), a coloring of its vertices is said to be conflict-free if for every hyperedge S∈E there is at least one vertex in S whose color is distinct from the colors of all other vertices i ...
The poser scheduling problem has been shown to be NP-complete in the general case but in P for a special case by Chang and Edmonds. In this paper, we extend the class of polynomially solvable cases and give some polyhedral characterizations. ...
We give a linear-time algorithm for single-source shortest paths in planar graphs with nonnegative edge-lengths. Our algorithm also yields a linear-time algorithm for maximum flow in a planar graph with the source and sink on the same face. For the case wh ...
