Ramified rectilinear polygons: coordinatization by dendrons

Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic $l_1$-metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexes that share this same embedding property are called ramified rectilinear polygons. The links of vertices in these cell complexes may be arbitrary bipartite graphs, in contrast to simple rectilinear polygons where the links of points are either 4-cycles or paths of length at most 3. Ramified rectilinear polygons are particular instances of rectangular complexes obtained from cube-free median graphs, or equivalently simply connected rectangular complexes with triangle-free links. The underlying graphs of finite ramified rectilinear polygons can be recognized among graphs in linear time by a Lexicographic Breadth-First-Search. Whereas the symmetry of a simple rectilinear polygon is very restricted (with automorphism group being a subgroup of the dihedral group $D_4$), ramified rectilinear polygons are universal: every finite group is the automorphism group of some ramified rectilinear polygon.Comment: 27 pages, 6 figure

Supporting Decision on Energy vs. Asset Cost Optimization in Drinking Water Distribution Networks

AbstractOne of the challenges for water utilities is the optimal asset design (i.e. maximum power of pump systems, tank volumes and pipe diameters) of water distribution networks (WDN) while optimizing operational efficiency (i.e. energy consumption and cost). Besides the classical minimization of capital cost while providing sufficient supply service, the operational sustainability is an emerging issue. As the reduction of each component of capital and energy costs are conflicting with each other, the optimization problem is multi-objective. This work presents the study of the robustness of solutions of the Pareto set as a further element to support the decision