The k-tuple twin domination in generalized de Bruijn and Kautz networks

AbstractGiven a digraph (network) G=(V,A), a vertex u in G is said to out-dominate itself and all vertices v such that the arc (u,v)∈A; similarly, u in-dominates both itself and all vertices w such that the arc (w,u)∈A. A set D of vertices of G is a k-tuple twin dominating set if every vertex of G is out-dominated and in-dominated by at least k vertices in D, respectively. The k-tuple twin domination problem is to determine a minimum k-tuple twin dominating set for a digraph. In this paper we investigate the k-tuple twin domination problem in generalized de Bruijn networks GB(n,d) and generalized Kautz GK(n,d) networks when d divides n. We provide construction methods for constructing minimum k-tuple twin dominating sets in these networks. These results generalize previous results given by Araki [T. Araki, The k-tuple twin domination in de Bruijn and Kautz digraphs, Discrete Mathematics 308 (2008) 6406–6413] for de Bruijn and Kautz networks

Private Out-Domination Number of Generalized de Bruijn Digraphs

Dominating sets are widely applied in the design and efficient use of computer networks. They can be used to decide the placement of limited resources, so that every node has access to the resource through neighbouring node. The most efficient solution is one that avoids duplication of access to the resources. This more restricted version of minimum dominating set is called an private dominating set. A vertex v in a digraph D is called a private out-neighbor of the vertex u in S (subset of V(D)) if u is the only element in the intersection of in-neighborhood set of v and S. A subset S of the vertex set V (D) of a digraph D is called a private out-dominating set of D if every vertex of V − S is a private out-neighbor of some vertex of S. The minimum cardinality of a private out-dominating set is called the private out-domination number. In this paper, we investigate the private out-domination number of generalized de Bruijn digraphs. We estabilsh the bounds of private out-domination number. Finally, we present exact values and sharp upperbounds of private out-domination number of some classes of generalized de Bruijn digraphs

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp