@inproceedings{8287,
  abstract     = {Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous and discrete post operators to compute states reachable according to continuous and discrete dynamics, respectively. In this paper, we enhance both of these operators and make sure that most of the involved computations are performed in low-dimensional state space. In particular, we improve the continuous-post operator by performing computations in high-dimensional state space only for time intervals relevant for the subsequent application of the discrete-post operator. Furthermore, the new discrete-post operator performs low-dimensional computations by leveraging the structure of the guard and assignment of a considered transition. We illustrate the potential of our approach on a number of challenging benchmarks.},
  author       = {Bogomolov, Sergiy and Forets, Marcelo and Frehse, Goran and Potomkin, Kostiantyn and Schilling, Christian},
  booktitle    = {Proceedings of the International Conference on Embedded Software},
  keywords     = {reachability, hybrid systems, decomposition},
  location     = {Virtual },
  title        = {{Reachability analysis of linear hybrid systems via block decomposition}},
  year         = {2020},
}

@inproceedings{4097,
  abstract     = {Arrangements of curves in the plane are of fundamental significance in many problems of computational and combinatorial geometry (e.g. motion planning, algebraic cell decomposition, etc.). In this paper we study various topological and combinatorial properties of such arrangements under some mild assumptions on the shape of the curves, and develop basic tools for the construction, manipulation, and analysis of these arrangements. Our main results include a generalization of the zone theorem of [EOS], [CGL] to arrangements of curves (in which we show that the combinatorial complexity of the zone of a curve is nearly linear in the number of curves), and an application of (some weaker variant of) that theorem to obtain a nearly quadratic incremental algorithm for the construction of such arrangements.},
  author       = {Edelsbrunner, Herbert and Guibas, Leonidas and Pach, János and Pollack, Richard and Seidel, Raimund and Sharir, Micha},
  booktitle    = {15th International Colloquium on Automata, Languages and Programming},
  isbn         = {978-3-540-19488-0},
  keywords     = {line segment, computational geometry, Jordan curve, cell decomposition, vertical tangency},
  location     = {Tampere, Finland},
  pages        = {214 -- 229},
  publisher    = {Springer},
  title        = {{Arrangements of curves in the plane - topology, combinatorics, and algorithms}},
  doi          = {10.1007/3-540-19488-6_118},
  volume       = {317},
  year         = {1988},
}