Showing papers by "Nancy M. Amato published in 2013"

Scaling Techniques for Massive Scale-Free Graphs in Distributed (External) Memory

Abstract: We present techniques to process large scale-free graphs in distributed memory. Our aim is to scale to trillions of edges, and our research is targeted at leadership class supercomputers and clusters with local non-volatile memory, e.g., NAND Flash. We apply an edge list partitioning technique, designed to accommodate high-degree vertices (hubs) that create scaling challenges when processing scale-free graphs. In addition to partitioning hubs, we use ghost vertices to represent the hubs to reduce communication hotspots. We present a scaling study with three important graph algorithms: Breadth-First Search (BFS), K-Core decomposition, and Triangle Counting. We also demonstrate scalability on BG/P Intrepid by comparing to best known Graph500 results [1]. We show results on two clusters with local NVRAM storage that are capable of traversing trillion-edge scale-free graphs. By leveraging node-local NAND Flash, our approach can process thirty-two times larger datasets with only a 39% performance degradation in Traversed Edges Per Second (TEPS).

Fast approximate convex decomposition using relative concavity

Abstract: Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n"c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n"c+1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark by Chen et al. (2009) [31].

Provably optimal parallel transport sweeps on regular grids

Abstract: We have found provably optimal algorithms for full-domain discrete-ordinate transport sweeps on regular grids in 3D Cartesian geometry. We describe these algorithms and sketch a 'proof that they always execute the full eight-octant sweep in the minimum possible number of stages for a given P{sub x} x P{sub y} x P{sub z} partitioning. Computational results demonstrate that our optimal scheduling algorithms execute sweeps in the minimum possible stage count. Observed parallel efficiencies agree well with our performance model. An older version of our PDT transport code achieves almost 80% parallel efficiency on 131,072 cores, on a weak-scaling problem with only one energy group, 80 directions, and 4096 cells/core. A newer version is less efficient at present-we are still improving its implementation - but achieves almost 60% parallel efficiency on 393,216 cores. These results conclusively demonstrate that sweeps can perform with high efficiency on core counts approaching 10{sup 6}. (authors)

A scalable distributed RRT for motion planning

Abstract: Rapidly-exploring Random Tree (RRT), like other sampling-based motion planning methods, has been very successful in solving motion planning problems. Even so, sampling-based planners cannot solve all problems of interest efficiently, so attention is increasingly turning to parallelizing them. However, one challenge in parallelizing RRT is the global computation and communication overhead of nearest neighbor search, a key operation in RRTs. This is a critical issue as it limits the scalability of previous algorithms. We present two parallel algorithms to address this problem. The first algorithm extends existing work by introducing a parameter that adjusts how much local computation is done before a global update. The second algorithm radially subdivides the configuration space into regions, constructs a portion of the tree in each region in parallel, and connects the subtrees,i removing cycles if they exist. By subdividing the space, we increase computation locality enabling a scalable result. We show that our approaches are scalable. We present results demonstrating almost linear scaling to hundreds of processors on a Linux cluster and a Cray XE6 machine.

Adapting RRT growth for heterogeneous environments

Abstract: Rapidly-exploring Random Trees (RRTs) are effective for a wide range of applications ranging from kinodynamic planning to motion planning under uncertainty. However, RRTs are not as efficient when exploring heterogeneous environments and do not adapt to the space. For example, in difficult areas an expensive RRT growth method might be appropriate, while in open areas inexpensive growth methods should be chosen. In this paper, we present a novel algorithm, Adaptive RRT, that adapts RRT growth to the current exploration area using a two level growth selection mechanism. At the first level, we select groups of expansion methods according to the visibility of the node being expanded. Second, we use a cost-sensitive learning approach to select a sampler from the group of expansion methods chosen. Also, we propose a novel definition of visibility for RRT nodes which can be computed in an online manner and used by Adaptive RRT to select an appropriate expansion method. We present the algorithm and experimental analysis on a broad range of problems showing not only its adaptability, but efficiency gains achieved by adapting exploration methods appropriately.

Lazy Toggle PRM: A single-query approach to motion planning

Abstract: Probabilistic RoadMaps (PRMs) are quite successful in solving complex and high-dimensional motion planning problems. While particularly suited for multiple-query scenarios and expansive spaces, they lack efficiency in both solving single-query scenarios and mapping narrow spaces. Two PRM variants separately tackle these gaps. Lazy PRM reduces the computational cost of roadmap construction for single-query scenarios by delaying roadmap validation until query time. Toggle PRM is well suited for mapping narrow spaces by mapping both Cfree and Cobst, which gives certain theoretical benefits. However, fully validating the two resulting roadmaps can be costly. We present a strategy, Lazy Toggle PRM, for integrating these two approaches into a method which is both suited for narrow passages and efficient single-query calculations. This simultaneously addresses two challenges of PRMs. Like Lazy PRM, Lazy Toggle PRM delays validation of roadmaps until query time, but if no path is found, the algorithm augments the roadmap using the Toggle PRM methodology. We demonstrate the effectiveness of Lazy Toggle PRM in a wide range of scenarios, including those with narrow passages and high descriptive complexity (e.g., those described by many triangles), concluding that it is more effective than existing methods in solving difficult queries.

Adaptive neighbor connection for PRMs: A natural fit for heterogeneous environments and parallelism

Abstract: Probabilistic Roadmap Methods (PRMs) are widely used motion planning methods that sample robot configurations (nodes) and connect them to form a graph (roadmap) containing feasible trajectories. Many PRM variants propose different strategies for each of the steps and choosing among them is problem dependent. Planning in heterogeneous environments and/or on parallel machines necessitates dividing the problem into regions where these choices have to be made for each one. Hand-selecting the best method for each region becomes infeasible. In particular, there are many ways to select connection candidates, and choosing the appropriate strategy is input dependent. In this paper, we present a general connection framework that adaptively selects a neighbor finding strategy from a candidate set of options. Our framework learns which strategy to use by examining their success rates and costs. It frees the user of the burden of selecting the best strategy and allows the selection to change over time. We perform experiments on rigid bodies of varying geometry and articulated linkages up to 37 degrees of freedom. Our results show that strategy performance is indeed problem/region dependent, and our adaptive method harnesses their strengths. Over all problems studied, our method differs the least from manual selection of the best method, and if one were to manually select a single method across all problems, the performance can be quite poor. Our method is able to adapt to changing sampling density and learns different strategies for each region when the problem is partitioned for parallelism.

Blind RRT: A probabilistically complete distributed RRT

Abstract: Rapidly-Exploring Random Trees (RRTs) have been successful at finding feasible solutions for many types of problems. With motion planning becoming more computationally demanding, we turn to parallel motion planning for efficient solutions. Existing work on distributed RRTs has been limited by the overhead that global communication requires. A recent approach, Radial RRT, demonstrated a scalable algorithm that subdivides the space into regions to increase the computation locality. However, if an obstacle completely blocks RRT growth in a region, the planning space is not covered and is thus not probabilistically complete. We present a new algorithm, Blind RRT, which ignores obstacles during initial growth to efficiently explore the entire space. Because obstacles are ignored, free components of the tree become disconnected and fragmented. Blind RRT merges parts of the tree that have become disconnected from the root. We show how this algorithm can be applied to the Radial RRT framework allowing both scalability and effectiveness in motion planning. This method is a probabilistically complete approach to parallel RRTs. We show that our method not only scales but also overcomes the motion planning limitations that Radial RRT has in a series of difficult motion planning tasks.

Optimizing aspects of pedestrian traffic in building designs

Abstract: In this work, we investigate aspects of building design that can be optimized. Architectural features that we explore include pillar placement in simple corridors, doorway placement in buildings, and agent placement for information dispersement in an evacuation. The metrics utilized are tuned to the specific scenarios we study, which include continuous flow pedestrian movement and building evacuation. We use Multidimensional Direct Search (MDS) optimization with an extreme barrier criteria to find optimal placements while enforcing building constraints.

Rigidity analysis for protein motion and folding core identification

Abstract: Protein folding plays an essential role in protein function and stability. Despite the explosion in our knowledge of structural and functional data, our understanding of protein folding is still very limited. In addition, methods such as folding core identification are gaining importance with the increased desire to engineer proteins with particular functions and efficiencies. However, defining the folding core can be challenging for both experiment and simulation. In this work, we use rigidity analysis to effectively sample and model the protein's energy landscape and identify the folding core. Our results show that rigidity analysis improves the accuracy of our approximate landscape models and produces landscape models that capture the subtle folding differences between protein G and its mutants, NuG1 and NuG2. We then validate our folding core identification against known experimental data and compare to other simulation tools. In addition to correlating well with experiment, our method can suggest other components of structure that have not been identified as part of the core because they were not previously measured experimentally.

Multi-robot caravanning

Abstract: We study multi-robot caravanning, which is loosely defined as the problem of a heterogeneous team of robots visiting specific areas of an environment (waypoints) as a group. After formally defining this problem, we propose a novel solution that requires minimal communication and scales with the number of waypoints and robots. Our approach restricts explicit communication and coordination to occur only when robots reach waypoints, and relies on implicit coordination when moving between a given pair of waypoints. At the heart of our algorithm is the use of leader election to efficiently exploit the unique environmental knowledge available to each robot in order to plan paths for the group, which makes it general enough to work with robots that have heterogeneous representations of the environment. We implement our approach both in simulation and on a physical platform, and characterize the performance of the approach under various scenarios. We demonstrate that our approach can successfully be used to combine the planning capabilities of different agents.

Graph-based stochastic control with constraints: A unified approach with perfect and imperfect measurements

Abstract: This paper is concerned with the problem of stochastic optimal control (possibly with imperfect measurements) in the presence of constraints. We propose a computationally tractable framework to address this problem. The method lends itself to sampling-based methods where we construct a graph in the state space of the problem, on which a Dynamic Programming (DP) is solved and a closed-loop feedback policy is computed. The constraints are seamlessly incorporated to the control policy selection by including their effect on the transition probabilities of the graph edges. We present a unified framework that is applicable both in the state space (with perfect measurements) and in the information space (with imperfect measurements).

Improving aggregate behavior in parking lots with appropriate local maneuvers

Abstract: In this paper we study the ingress and egress of pedestrians and vehicles in a parking lot. We show how local maneuvers executed by agents permit them to create trajectories in constrained environments, and to resolve the deadlocks between them in mixed-flow scenarios. We utilize a roadmap-based approach which allows us to map complex environments and generate heuristic local paths that are feasible for both pedestrians and vehicles. Finally, we examine the effect that some agent-behavioral parameters have on parking lot ingress and egress.