In the present work we investigate the effects of spatial constraints on the efficiency of task execution in systems underlain by geographical complex networks where the probability of connection decreases with the distance between the nodes. The investigation considers several configurations of the parameters defining the network connectivity, and the Barabási-Albert network model is also considered for comparisons. The results show that the effect of connectivity is significant only for shorter tasks, that the locality of connections implied by the spatial constraints reduces efficency, and that the addition of edges can improve the efficiency of the execution, although with increasing locality of the connections the improvement is small. 89.75.Fb, 89.20.Hh Great part of the current theoretical and applied research in physics relies on fast execution of relatively complex algorithms. Several problems of current interest can only be solved by using parallel or distributed computing systems. A recent trend, namely grid computing [1], often allows more cost-effective solutions to such problems, involving the combined use of several general purpose machines. Such an architecture promotes the natural scaling of the number of computing elements in terms of their availability and importance of specific problems (more elements can be assigned to more important problems). The interconnection of machines participating in grid computing systems involves not only local area networks, but mainly the Internet. The connectivity in grid computing is intrinsically dynamic because of its own nature, i.e. the fact that the availability of machines varies with time. In addition, as the interconnections between such machines are often implemented through the Internet, the connectivity of the latter inherently determines the grid architecture [2]. Although grid computing is inherently more flexible and scalable than traditional parallel and distributed systems the interconnectivity of the processing elements in a grid system, combined with specific properties of those elements, is fundamental for achieving efficiency [3]. Therefore, given a specific problem, one needs to select a suitable interconnectivity which, in the case of Internet-based grid computing, is inherently constrained by the Internet.Instead of implementing a specific problem and inferring the respective performance, a more reasonable and effective means is to model and simulate the execution of the given algorithms, which is not only cheaper but can be used to provide additional insights about the effect of modifying the interconnection and algorithms implementation. Because of their flexibility for representing almost any discrete structure, complex networks [4,5,6,7] represent a natural resource for modeling distributed computing systems, where the processing elements are denoted by nodes and their respective interconnections are represented by edges. Such a potential is especially relevant in the case of grid computing, which often involves interconnectiviti...
