arXiv subjects

Paolo Nobili

Publications and source records attributed to Paolo Nobili.

4 recordsLinked to original sources

arXiv2023

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.

math.OC↗

arXiv2019

An ${\cal O}(n^2 \log(n))$ algorithm for the weighted stable set problem in claw-free graphs

A graph $G(V, E)$ is \emph{claw-free} if no vertex has three pairwise non-adjacent neighbours. The Maximum Weight Stable Set (MWSS) Problem in a claw-free graph is a natural generalization of the Matching Problem and has been shown to be polynomially solvable by Minty and Sbihi in 1980. In a remarkable paper, Faenza, Oriolo and Stauffer have shown that, in a two-step procedure, a claw-free graph can be first turned into a quasi-line graph by removing strips containing all the irregular nodes and then decomposed into \emph{\{claw, net\}-free} strips and strips with stability number at most three. Through this decomposition, the MWSS Problem can be solved in ${\cal O}(|V|(|V| \log |V| + |E|))$ time. In this paper, we describe a direct decomposition of a claw-free graph into \emph{\{claw, net\}-free} strips and strips with stability number at most three which can be performed in ${\cal O}(|V|^2)$ time. In two companion papers we showed that the MWSS Problem can be solved in ${\cal O}(|E| \log |V|)$ time in claw-free graphs with $α(G) \le 3$ and in ${\cal O}(|V| \sqrt{|E|})$ time in \{claw, net\}-free graphs with $α(G) \ge 4$. These results prove that the MWSS Problem in a claw-free graph can be solved in ${\cal O}(|V|^2 \log |V|)$ time, the same complexity of the best and long standing algorithm for the MWSS Problem in \emph{line graphs}.

cs.DM↗

arXiv2015

An ${\cal O}(n\sqrt{m})$ algorithm for the weighted stable set problem in {claw, net}-free graphs with $α(G) \ge 4$

In this paper we show that a connected {claw, net}-free graph $G(V, E)$ with $α(G) \ge 4$ is the union of a strongly bisimplicial clique $Q$ and at most two clique-strips. A clique is strongly bisimplicial if its neighborhood is partitioned into two cliques which are mutually non-adjacent and a clique-strip is a sequence of cliques $\{H_0, \dots, H_p\}$ with the property that $H_i$ is adjacent only to $H_{i-1}$ and $H_{i+1}$. By exploiting such a structure we show how to solve the Maximum Weight Stable Set Problem in such a graph in time ${\cal O}(|V|\sqrt{|E|})$.

cs.DM↗

arXiv2015

An ${\cal O}(m\log n)$ algorithm for the weighted stable set problem in claw-free graphs with $α({G}) \le 3$

In this paper we show how to solve the \emph{Maximum Weight Stable Set Problem} in a claw-free graph $G(V, E)$ with $α(G) \le 3$ in time ${\cal O}(|E|\log|V|)$. More precisely, in time ${\cal O}(|E|)$ we check whether $α(G) \le 3$ or produce a stable set with cardinality at least $4$; moreover, if $α(G) \le 3$ we produce in time ${\cal O}(|E|\log|V|)$ a maximum stable set of $G$. This improves the bound of ${\cal O}(|E||V|)$ due to Faenza et al.

cs.DM↗