Efficiency in exponential time for domination-type problems
نویسنده
چکیده
Wedesign fast exponential time algorithms for some intractable graph-theoretic problems. Ourmain result states that aminimum optional dominating set in a graph of order n can be found in time O∗(1.8899n). Ourmethods to obtain this result involvematching techniques. The list of the considered problems includes Minimum Maximal Matching, 3Colourability, Minimum Dominating Edge Set, Minimum Connected Dominating Set (∼Maximum Leaf Spanning Tree), Minimum Independent Dominating Set andMinimum Dominating set. © 2008 Elsevier B.V. All rights reserved.
منابع مشابه
On exponential domination and graph operations
An exponential dominating set of graph $G = (V,E )$ is a subset $Ssubseteq V(G)$ such that $sum_{uin S}(1/2)^{overline{d}{(u,v)-1}}geq 1$ for every vertex $v$ in $V(G)-S$, where $overline{d}(u,v)$ is the distance between vertices $u in S$ and $v in V(G)-S$ in the graph $G -(S-{u})$. The exponential domination number, $gamma_{e}(G)$, is the smallest cardinality of an exponential dominating set....
متن کاملOptimal Dynamic Program for r-Domination Problems over Tree Decompositions
There has been recent progress in showing that the exponential dependence on treewidth in dynamic programming algorithms for solving NP-hard problems is optimal under the Strong Exponential Time Hypothesis (SETH). We extend this work to r-domination problems. In rdominating set, one wishes to find a minimum subset S of vertices such that every vertex of G is within r hops of some vertex in S. I...
متن کاملBeyond O*(2^n) in domination-type problems
In this paper we provide algorithms faster thanO(2) for several NP-complete dominationtype problems. More precisely, we provide: • an algorithm for CAPACITATED DOMINATING SET that solves it in O(1.89), • a branch-and-reducealgorithm solving LARGEST IRREDUNDANT SET inO(1.9657) time, • and a simple iterative-DFS algorithm for SMALLEST INCLUSION-MAXIMAL IRREDUNDANT SET that solves it in O(1.999956...
متن کاملAn Efficient Numerical Method for a Class of Boundary Value Problems, Based on Shifted Jacobi-Gauss Collocation Scheme
We present a numerical method for a class of boundary value problems on the unit interval which feature a type of exponential and product nonlinearities. Also, we consider singular case. We construct a kind of spectral collocation method based on shifted Jacobi polynomials to implement this method. A number of specific numerical examples demonstrate the accuracy and the efficiency of the propos...
متن کاملExponential Domination in Subcubic Graphs
As a natural variant of domination in graphs, Dankelmann et al. [Domination with exponential decay, Discrete Math. 309 (2009) 5877-5883] introduced exponential domination, where vertices are considered to have some dominating power that decreases exponentially with the distance, and the dominated vertices have to accumulate a sufficient amount of this power emanating from the dominating vertice...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 156 شماره
صفحات -
تاریخ انتشار 2008