Satellites and Mirrors for Solving Independent Set on Sparse Graphs
نویسندگان
چکیده
We study the well-known Maximum Independent Set (MIS) problem and introduce the notion of satellites of a node. Branching on nodes with satellites is extremely simple. Nevertheless, satellites can be used to overcome a couple of hard cases in previous algorithms. Together with the notion of mirrors, introduced by Fomin, Grandoni, and Kratsch, they can be used to solve MIS in time bounded by O(1.1928), which is O(1.0922) for cubic graphs. This improves over previous results for sparse graphs.
منابع مشابه
On independent domination numbers of grid and toroidal grid directed graphs
A subset $S$ of vertex set $V(D)$ is an {em indpendent dominating set} of $D$ if $S$ is both an independent and a dominating set of $D$. The {em indpendent domination number}, $i(D)$ is the cardinality of the smallest independent dominating set of $D$. In this paper we calculate the independent domination number of the { em cartesian product} of two {em directed paths} $P_m$ and $P_n$ for arbi...
متن کاملIndependent domination in directed graphs
In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...
متن کاملA Fine-grained Analysis of a Simple Independent Set Algorithm
We present a simple exact algorithm for the INDEPENDENT SET problem with a runtime bounded by O(1.2132npoly(n)). This bound is obtained by, firstly, applying a new branching rule and, secondly, by a distinct, computer-aided case analysis. The new branching rule uses the concept of satellites and has previously only been used in an algorithm for sparse graphs. The computer-aided case analysis al...
متن کاملINDEPENDENT SETS OF SOME GRAPHS ASSOCIATED TO COMMUTATIVE RINGS
Let $G=(V,E)$ be a simple graph. A set $Ssubseteq V$ isindependent set of $G$, if no two vertices of $S$ are adjacent.The independence number $alpha(G)$ is the size of a maximumindependent set in the graph. In this paper we study and characterize the independent sets ofthe zero-divisor graph $Gamma(R)$ and ideal-based zero-divisor graph $Gamma_I(R)$of a commutative ring $R$.
متن کاملApproximations of Independent Set Variants and Hereditary Subset Problems
The focus of this study is to clarify the approximability of the important versions of the maximum independent set problem, and to apply, where possible, the technique to related hereditary subgraph and subset problem. We report improved performance ratios for the Independent Set problem in weighted general graphs, weighted bounded-degree graphs, and in sparse graphs. Other problems with better...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009