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Load balancing is one of the central problems that have to be solved in parallel computation. Here, the problem of distributed, dynamic load balancing for massive parallelism is addressed. A new local method, which realizes a physical analogy to equilibrating liquids in multi-dimensional tori or hypercubes, is presented. It is especially suited for communication mechanisms with low set-up to transfer ratio occurring in tightly-coupled or SIMD systems. By successive shifting single load elements to the direct neighbors, the load is automatically transferred to lightly loaded processors. Compared to former methods, the proposed Liquid model has two main advantages. First, the task of load sharing is combined with the task of load balancing, where the former has priority. This property is valuable in many applications and important for highly dynamic load distribution. Second, the Liquid model has high efficiency. Asymptotically, it needs O(D . K . Ldiff ) load transfers to reach the balanced state in a D-dimensional torus with K processors per dimension and a maximum initial load difference of Ldiff . The Liquid model clearly outperforms an earlier load balancing approach, the nearest-neighbor-averaging. Besides a survey of related research, analytical results within a formal framework are derived. These results are validated by worst-case simulations in one-and two-dimensional tori with up to two thousand processors.
One of the many features needed to support the activities of autonomous systems is the ability of motion planning. It enables robots to move in their environment securely and to accomplish given tasks. Unfortunately, the control loop comprising sensing, planning, and acting has not yet been closed for robots in dynamic environments. One reason involves the long execution times of the motion planning component. A solution for this problem is offered by the use of highly computational parallelism. Thus, an important task is the parallelization of existing motion planning algorithms for robots so that they are suitable for highly computational parallelism. In several cases, completely new algorithms have to be designed, so that a parallelization is feasible. In this survey, we review recent approaches to motion planning using parallel computation. As a classification scheme, we use the structure given by the different approaches to the robot's motion planning. For each approach, the available parallel processing methods are discussed. Each approach is uniquely assigned a class. Finally, for each referenced research work, a list of keywords is given.