We study local well-posedness and orbital stability/instability of standing waves for a first order system associated with nonlinear Klein–Gordon equation on star graph. The proof the uses classical fixed point argument Hille–Yosida theorem. Stability relies linearization approach recent results NLS ?-interaction

In this paper, a parallel algorithm for data clustering is presented on a multi-computer with star topology. This algorithm is fast and requires a small amount of memory per processing element, which makes it even suitable for SIMD implementation. The proposed parallel algorithm completes in O(K+S T) steps for a clustering problem of N data patterns with M features per pattern and K clusters, w...

In this paper, we propose two one-to-all optimal broadcasting algorithms in incomplete star graphs. A n incomplete star graph with N nodes, where (n l ) ! < N < n! , is a subgraph of an n-star. Using a routing scheme to transmit a message to each substar composed of the incomplete star, our proposed broadcasting algorithm is optimal in O(n1ogn) on the single-port communication model. While broa...

Adaptive star grammars generalize well-known graph grammar formalisms based on hyperedge and node replacement while retaining, e.g., parseability and the commutativity and associativity of rule application. In this paper, we study how these grammars can be put to practical use for the definition of graph models. We show how to use adaptive star grammars to specify program graphs, models of obje...

In 1987, Akers, Harel and Krishnamurthy proposed the star graph Σ(n) as a new topology for interconnection networks. Hamiltonian properties of these graphs have been investigated by several authors. In this paper, we prove that Σ(n) contains bn/8c pairwise edge-disjoint Hamilton cycles when n is prime, and Ω(n/ log log n) such cycles for arbitrary n.

This paper introduces a parallel algorithm for computing an N=n!-point Lagrange interpolation on an n-star (n>2). It exploits several communication techniques on stars in a novel way which can be adapted for computing similar functions. The algorithm is optimal and consists of three phases: initialization, main and final. While there is no computation in the initialization phase, the main phase...

In this paper we develop a feasibility algorithm for preemptively scheduling a given set of jobs with dimension and time requirements on a star graph network of given size with a given deadline. We show that the algorithm runs in O(n log n) time where n is the number of jobs.