Algorithmic aspects of broadcast independence
نویسندگان
چکیده
An independent broadcast on a connected graph G is function f:V(G)→N0 such that, for every vertex x of G, the value f(x) at most eccentricity in and f(x)>0 implies that f(y)=0 y within distance from x. The independence number αb(G) largest weight ∑x∈V(G)f(x) an f G. We describe efficient algorithm determines given tree. Furthermore, we show NP-hardness planar graphs maximum degree four, hardness approximation general graphs. Our results solve problems posed by Dunbar (2006), Hedetniemi Ahmane et al. (2018).
منابع مشابه
Girth, minimum degree, independence, and broadcast independence
An independent broadcast on a connected graph $G$is a function $f:V(G)to mathbb{N}_0$such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$,and $f(x)>0$ implies that $f(y)=0$ for every vertex $y$ of $G$ within distance at most $f(x)$ from $x$.The broadcast independence number $alpha_b(G)$ of $G$is the largest weight $sumlimits_{xin V(G)}f(x)$of an ind...
متن کاملAlgorithmic Aspects of Regularity
Szemer edi's celebrated regularity lemma proved to be a fundamental result in graph theory. Roughly speaking, his lemma states that any graph may be approximated by a union of a bounded number of bipartite graphs, each of which is`pseudorandom'. As later proved by Alon, Duke, Lefmann, RR odl, and Yuster, there is a fast deterministic algorithm for nding such an approximation, and therefore many...
متن کاملAlgorithmic Aspects of Boosting
We discuss algorithmic aspects of boosting techniques, such as Majority Vote Boosting [Fre95], AdaBoost [FS97], and MadaBoost [DW00a]. Considering a situation where we are given a huge amount of examples and asked to find some rule for explaining these example data, we show some reasonable algorithmic approaches for dealing with such a huge dataset by boosting techniques. Through this example, ...
متن کاملOn the Broadcast Independence Number of Caterpillars
Let G be a simple undirected graph. A broadcast on G is a function f : V (G) → N such that f(v) ≤ eG(v) holds for every vertex v of G, where eG(v) denotes the eccentricity of v in G, that is, the maximum distance from v to any other vertex of G. The cost of f is the value cost(f) = ∑ v∈V (G) f(v). A broadcast f on G is independent if for every two distinct vertices u and v in G, dG(u, v) > max{...
متن کاملDetecting quasiconvexity: Algorithmic aspects
The main result of this paper states that for any group G with an automatic structure L with unique representatives one can construct a uniform partial algorithm which detects L-rational subgroups and gives their preimages in L. This provides a practical, not just theoretical, procedure for solving the occurrence problem for such subgroups. 1. Generalized word problem and rational structures on...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2022
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2022.03.001