اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدParameterized complexity in multiple-interval graphs: domination, partition, separation, irredundancy
149
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We show that the problem k-Dominating Set and its several variants including k-Connected Dominating Set, k-Independent Dominating Set, and k-Dominating Clique, when parameterized by the solution size k, are W[1]-hard in either multiple-interval graphs or their complements or both. On the other hand, we show that these problems belong to W[1] when restricted to multiple-interval graphs and their complements. This answers an open question of Fellows et al. In sharp contrast, we show that d-Distance k-Dominating Set for d >= 2 is W[2]-complete in multiple-interval graphs and their complements. We also show that k-Perfect Code and d-Distance k-Perfect Code for d >= 2 are W[1]-complete even in unit 2-track interval graphs. In addition, we present various new results on the parameterized complexities of k-Vertex Clique Partition and k-Separating Vertices in multiple-interval graphs and their complements, and present a very simple alternative proof of the W[1]-hardness of k-Irredundant Set in general graphs.
قيم البحث
اقرأ أيضاً
Butman, Hermelin, Lewenstein, and Rawitz proved that Clique in t-interval graphs is NP-hard for t >= 3. We strengthen this result to show that Clique in 3-track interval graphs is APX-hard.
Best match graphs (BMGs) are vertex-colored directed graphs that were introduced to model the relationships of genes (vertices) from different species (colors) given an underlying evolutionary tree that is assumed to be unknown. In real-life applicat
ions, BMGs are estimated from sequence similarity data. Measurement noise and approximation errors usually result in empirically determined graphs that in general violate characteristic properties of BMGs. The arc modification problems for BMGs aim at correcting such violations and thus provide a means to improve the initial estimates of best match data. We show here that the arc deletion, arc completion and arc editing problems for BMGs are NP-complete and that they can be formulated and solved as integer linear programs. To this end, we provide a novel characterization of BMGs in terms of triples (binary trees on three leaves) and a characterization of BMGs with two colors in terms of forbidden subgraphs.
In this article, we study a variant of the minimum dominating set problem known as the minimum liars dominating set (MLDS) problem. We prove that the MLDS problem is NP-hard in unit disk graphs. Next, we show that the recent sub-quadratic time $frac{
11}{2}$-factor approximation algorithm cite{bhore} for the MLDS problem is erroneous and propose a simple $O(n + m)$ time 7.31-factor approximation algorithm, where $n$ and $m$ are the number of vertices and edges in the input unit disk graph, respectively. Finally, we prove that the MLDS problem admits a polynomial-time approximation scheme.
In this paper we study the problem of finding a small safe set $S$ in a graph $G$, i.e. a non-empty set of vertices such that no connected component of $G[S]$ is adjacent to a larger component in $G - S$. We enhance our understanding of the problem f
rom the viewpoint of parameterized complexity by showing that (1) the problem is W[2]-hard when parameterized by the pathwidth $pw$ and cannot be solved in time $n^{o(pw)}$ unless the ETH is false, (2) it admits no polynomial kernel parameterized by the vertex cover number $vc$ unless $mathrm{PH} = Sigma^{mathrm{p}}_{3}$, but (3) it is fixed-parameter tractable (FPT) when parameterized by the neighborhood diversity $nd$, and (4) it can be solved in time $n^{f(cw)}$ for some double exponential function $f$ where $cw$ is the clique-width. We also present (5) a faster FPT algorithm when parameterized by solution size.
A emph{2-interval} is the union of two disjoint intervals on the real line. Two 2-intervals $D_1$ and $D_2$ are emph{disjoint} if their intersection is empty (i.e., no interval of $D_1$ intersects any interval of $D_2$). There can be three different
relations between two disjoint 2-intervals; namely, preceding ($<$), nested ($sqsubset$) and crossing ($between$). Two 2-intervals $D_1$ and $D_2$ are called emph{$R$-comparable} for some $Rin{<,sqsubset,between}$, if either $D_1RD_2$ or $D_2RD_1$. A set $mathcal{D}$ of disjoint 2-intervals is $mathcal{R}$-comparable, for some $mathcal{R}subseteq{<,sqsubset,between}$ and $mathcal{R} eqemptyset$, if every pair of 2-intervals in $mathcal{R}$ are $R$-comparable for some $Rinmathcal{R}$. Given a set of 2-intervals and some $mathcal{R}subseteq{<,sqsubset,between}$, the objective of the emph{2-interval pattern problem} is to find a largest subset of 2-intervals that is $mathcal{R}$-comparable. The 2-interval pattern problem is known to be $W[1]$-hard when $|mathcal{R}|=3$ and $NP$-hard when $|mathcal{R}|=2$ (except for $mathcal{R}={<,sqsubset}$, which is solvable in quadratic time). In this paper, we fully settle the parameterized complexity of the problem by showing it to be $W[1]$-hard for both $mathcal{R}={sqsubset,between}$ and $mathcal{R}={<,between}$ (when parameterized by the size of an optimal solution); this answers an open question posed by Vialette [Encyclopedia of Algorithms, 2008].
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
