Parallel symbolic state-space exploration is difficult, but what is the alternative?

State-space exploration is an essential step in many modeling and analysis problems. Its goal is to find the states reachable from the initial state of a discrete-state model described. The state space can used to answer important questions, e.g., "Is there a dead state?" and "Can N become negative?", or as a starting point for sophisticated investigations expressed in temporal logic. Unfortunately, the state space is often so large that ordinary explicit data structures and sequential algorithms cannot cope, prompting the exploration of (1) parallel approaches using multiple processors, from simple workstation networks to shared-memory supercomputers, to satisfy large memory and runtime requirements and (2) symbolic approaches using decision diagrams to encode the large structured sets and relations manipulated during state-space generation. Both approaches have merits and limitations. Parallel explicit state-space generation is challenging, but almost linear speedup can be achieved; however, the analysis is ultimately limited by the memory and processors available. Symbolic methods are a heuristic that can efficiently encode many, but not all, functions over a structured and exponentially large domain; here the pitfalls are subtler: their performance varies widely depending on the class of decision diagram chosen, the state variable order, and obscure algorithmic parameters. As symbolic approaches are often much more efficient than explicit ones for many practical models, we argue for the need to parallelize symbolic state-space generation algorithms, so that we can realize the advantage of both approaches. This is a challenging endeavor, as the most efficient symbolic algorithm, Saturation, is inherently sequential. We conclude by discussing challenges, efforts, and promising directions toward this goal

Network Partitioning in Distributed Agent-Based Models

Agent-Based Models (ABMs) are an emerging simulation paradigm for modeling complex systems, comprised of autonomous, possibly heterogeneous, interacting agents. The utility of ABMs lies in their ability to represent such complex systems as self-organizing networks of agents. Modeling and understanding the behavior of complex systems usually occurs at large and representative scales, and often obtaining and visualizing of simulation results in real-time is critical. The real-time requirement necessitates the use of in-memory computing, as it is difficult and challenging to handle the latency and unpredictability of disk accesses. Combining this observation with the scale requirement emphasizes the need to use parallel and distributed computing platforms, such as MPI-enabled CPU clusters. Consequently, the agent population must be partitioned across different CPUs in a cluster. Further, the typically high volume of interactions among agents can quickly become a significant bottleneck for real-time or large-scale simulations. The problem is exacerbated if the underlying ABM network is dynamic and the inter-process communication evolves over the course of the simulation. Therefore, it is critical to develop topology-aware partitioning mechanisms to support such large simulations. In this dissertation, we demonstrate that distributed agent-based model simulations benefit from the use of graph partitioning algorithms that involve a local, neighborhood-based perspective. Such methods do not rely on global accesses to the network and thus are more scalable. In addition, we propose two partitioning schemes that consider the bottom-up individual-centric nature of agent-based modeling. The First technique utilizes label-propagation community detection to partition the dynamic agent network of an ABM. We propose a latency-hiding, seamless integration of community detection in the dynamics of a distributed ABM. To achieve this integration, we exploit the similarity in the process flow patterns of a label-propagation community-detection algorithm and self-organizing ABMs. In the second partitioning scheme, we apply a combination of the Guided Local Search (GLS) and Fast Local Search (FLS) metaheuristics in the context of graph partitioning. The main driving principle of GLS is the dynamic modi?cation of the objective function to escape local optima. The algorithm augments the objective of a local search, thereby transforming the landscape structure and escaping a local optimum. FLS is a local search heuristic algorithm that is aimed at reducing the search space of the main search algorithm. It breaks down the space into sub-neighborhoods such that inactive sub-neighborhoods are removed from the search process. The combination of GLS and FLS allowed us to design a graph partitioning algorithm that is both scalable and sensitive to the inherent modularity of real-world networks

Dynamic load balancing in parallel KD-tree k-means

One among the most influential and popular data mining methods is the k-Means algorithm for cluster analysis. Techniques for improving the efficiency of k-Means have been largely explored in two main directions. The amount of computation can be significantly reduced by adopting geometrical constraints and an efficient data structure, notably a multidimensional binary search tree (KD-Tree). These techniques allow to reduce the number of distance computations the algorithm performs at each iteration. A second direction is parallel processing, where data and computation loads are distributed over many processing nodes. However, little work has been done to provide a parallel formulation of the efficient sequential techniques based on KD-Trees. Such approaches are expected to have an irregular distribution of computation load and can suffer from load imbalance. This issue has so far limited the adoption of these efficient k-Means variants in parallel computing environments. In this work, we provide a parallel formulation of the KD-Tree based k-Means algorithm for distributed memory systems and address its load balancing issue. Three solutions have been developed and tested. Two approaches are based on a static partitioning of the data set and a third solution incorporates a dynamic load balancing policy