106 research outputs found
Power Reduction in FM Networks by Mixed-Integer Programming. A Case Study
The climate change emergency calls for a reduction in energy consumption in
all human activities and production processes. The radio broadcasting industry
is no exception. However, reducing energy requirements by uniformly cutting the
radiated power at every transmitter can potentially impair the quality of
service. A careful evaluation and optimization study are in order. In this
paper, by analyzing the Italian frequency modulation analog broadcasting
service, we show that it is indeed possible to significantly reduce the energy
consumption of the broadcasters without sacrificing the quality of the service,
rather, even getting improvements
The Hirsch Conjecture for the fractional stable set polytope
The edge formulation of the stable set problem is defined by two-variable constraints, one for each edge of a graph G , expressing the simple condition that two adjacent nodes cannot belong to a stable set. We study the fractional stable set polytope, i.e. the polytope defined by the linear relaxation of the edge formulation. Even if this polytope is a weak approximation of the stable set polytope, its simple geometrical structure provides deep theoretical insight as well as interesting algorithmic opportunities. Exploiting a graphic characterization of the bases, we first redefine pivots in terms of simple graphic operations, that turn a given basis into an adjacent one. These results lead us to prove that the combinatorial diameter of the fractional stable set polytope is at most the number of nodes of the given graph. As a corollary, the Hirsch bound holds for this class of polytopes
- âŠ