For a positive integer k, a radio k-coloring of a simple connected graph G = (V (G), E(G)) is a mapping | f(u) - f(v)| ≥ k +1-d (u , v ) such that f :V (G)→{0,1, 2,...} for each pair of distinct vertices u and v of G, where d(u, v) is the distance between u and v in G. The span of a radio k-coloring f, rck(f), is the maximum integer it assigns to some vertex of G. The radio k-chromatic number, rck(G) of G is min{rck(f)}, where the minimum is taken over all radio k-colorings f of G. If k is the diameter of G, then rck(G) is known as the radio number of G. In this work, we propose four algorithms (two serial algorithms and their parallel versions) which related to the radio k-coloring problem. One of them is an approximate algorithm that determines an upper bound of the radio number of a given graph. The other is an exact algorithm which finds the radio number of a graph G. The approximate algorithm is a polynomial time algorithm while the exact algorithm is an exponential time algorithm. The parallel algorithms are parallelized using the Message Passing Interface (MPI) standard. The experimental results prove the ability of the proposed algorithms to achieve a speedup 7 for 8 processors.

A parallel shallow water flow model is introduced in this paper. The explicit-time finite volume approach is adopted to solve the 2D shallow water equations on an unstructured triangular mesh. The proposed scheme is second-order accurate in temporal and spatial terms using the two-stage Runge-Kutta and the monotone upwind scheme for conservation law (MUSCL) methods, respectively. Based on Message Passing Interface (MPI) and OpenACC, a multi-GPU model is presented with the METIS library to produce the domain decomposition. A CUDA-aware MPI library through GPUDirect for peer-to-peer (P2P) transfer between two GPUs and overlapping computation and MPI communication are used to speed up MPI memory exchange and the performance of the code. A 2D circular dam break test with wet and dry downstream beds and grid resolutions of about 2 million cells is considered to verify the accuracy of the code, and good results were achieved compared to the numerical simulations of published studies. Compared with the multi-CPU version of the 6-core CPU, maximum speedups of 56.18 and 331.51 were obtained using the single-GPU and multi-GPU versions, respectively. Results indicate that acceleration performance improves as the mesh resolution increases.

Consider a robot that is navigating in a space modeled by a graph, and that wants to know its current location. It can send a signal to determine how far it is from each landmark among a set of fixed landmarks. We study the problem of computing the minimum required number of landmarks, and where they should be placed so that the robot can always determine its location. Since the problem is an NP-complete problem, the robot's responses to the actions are slow. To accelerate this response, we can use the parallel version of this problem. In this work, we introduce a new parallel implementation for determining the metric dimension of a given graph. We run the proposed algorithm on a symmetric multi-processing (SMP) cluster using C programming language and the Message Passing Interface (MPI) library. Finally, we run our implementation on four categories of graphs (the tracks in which the robot moves): a cycle graph Cn, a path graph Pn, a triangular snake graph and a ladder graph Ln. Preliminary computational results indicate that the metric dimension problem is an NP-complete problem and prove the ability of the proposed algorithm to achieve a speedup of 6 for 8 processors.