Data structures for retrieval on integer grids

A family of data structures is presented for retrieval of the sum of values of points within a half-plane or polygon, given that the points are on integer coordinates in the plane. Fredman has shown that the problem has a lower bound of Ω(N^2/3) for intermixed updates and retrievals. Willard has shown an upper bound of O(N^2log6^4) for the case where the points are not restricted to integer coordinates.We have developed families of related data structures for retrievals of half-planes or polygons. One of the data structures permits intermixed updates and half-plane retrievals in O(N^2/3log N) time, where N is the size of the grid.We use a technique we call "Rotation" to permit a better match of a portion of the data structure to the particular problem. Rotations appear to be an effective method for trading-off storage redundancy against retrieval time for certain classes of problems

Jigsaw: Scalable software-defined caches

Shared last-level caches, widely used in chip-multi-processors (CMPs), face two fundamental limitations. First, the latency and energy of shared caches degrade as the system scales up. Second, when multiple workloads share the CMP, they suffer from interference in shared cache accesses. Unfortunately, prior research addressing one issue either ignores or worsens the other: NUCA techniques reduce access latency but are prone to hotspots and interference, and cache partitioning techniques only provide isolation but do not reduce access latency.United States. Defense Advanced Research Projects Agency (DARPA PERFECT contract HR0011-13-2-0005)Quanta Computer (Firm

A survey of outlier detection methodologies

Outlier detection has been used for centuries to detect and, where appropriate, remove anomalous observations from data. Outliers arise due to mechanical faults, changes in system behaviour, fraudulent behaviour, human error, instrument error or simply through natural deviations in populations. Their detection can identify system faults and fraud before they escalate with potentially catastrophic consequences. It can identify errors and remove their contaminating effect on the data set and as such to purify the data for processing. The original outlier detection methods were arbitrary but now, principled and systematic techniques are used, drawn from the full gamut of Computer Science and Statistics. In this paper, we introduce a survey of contemporary techniques for outlier detection. We identify their respective motivations and distinguish their advantages and disadvantages in a comparative review

Jigsaw: Scalable Software-Defined Caches (Extended Version)

Shared last-level caches, widely used in chip-multiprocessors (CMPs), face two fundamental limitations. First, the latency and energy of shared caches degrade as the system scales up. Second, when multiple workloads share the CMP, they suffer from interference in shared cache accesses. Unfortunately, prior research addressing one issue either ignores or worsens the other: NUCA techniques reduce access latency but are prone to hotspots and interference, and cache partitioning techniques only provide isolation but do not reduce access latency. We present Jigsaw, a technique that jointly addresses the scalability and interference problems of shared caches. Hardware lets software define shares, collections of cache bank partitions that act as virtual caches, and map data to shares. Shares give software full control over both data placement and capacity allocation. Jigsaw implements efficient hardware support for share management, monitoring, and adaptation. We propose novel resource-management algorithms and use them to develop a system-level runtime that leverages Jigsaw to both maximize cache utilization and place data close to where it is used. We evaluate Jigsaw using extensive simulations of 16- and 64-core tiled CMPs. Jigsaw improves performance by up to 2.2x (18% avg) over a conventional shared cache, and significantly outperforms state-of-the-art NUCA and partitioning techniques.This work was supported in part by DARPA PERFECT contract HR0011-13-2-0005 and Quanta Computer

Improving Strategies via SMT Solving

We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number of iterations (ii) the use of merge operations (often, convex hulls) at the merge points of the control flow graph. It instead computes the least inductive invariant expressible in the domain at a restricted set of program points, and analyzes the rest of the code en bloc. We emphasize that we compute this inductive invariant precisely. For that we extend the strategy improvement algorithm of [Gawlitza and Seidl, 2007]. If we applied their method directly, we would have to solve an exponentially sized system of abstract semantic equations, resulting in memory exhaustion. Instead, we keep the system implicit and discover strategy improvements using SAT modulo real linear arithmetic (SMT). For evaluating strategies we use linear programming. Our algorithm has low polynomial space complexity and performs for contrived examples in the worst case exponentially many strategy improvement steps; this is unsurprising, since we show that the associated abstract reachability problem is Pi-p-2-complete

Distributed Multi-Robot Formation Control among Obstacles: A Geometric and Optimization Approach with Consensus

This paper presents a distributed method for navigating a team of robots in formation in 2D and 3D environments with static and dynamic obstacles. The robots are assumed to have a reduced communication and visibility radius and share information with their neighbors. Via distributed consensus the robots compute (a) the convex hull of the robot positions and (b) the largest convex region within free space. The robots then compute, via sequential convex programming, the locally optimal parameters for the formation within this convex neighborhood of the robots. Reconfiguration is allowed, when required, by considering a set of target formations. The robots navigate towards the target collision-free formation with individual local planners that account for their dynamics. The approach is efficient and scalable with the number of robots and performs well in simulations with up to sixteen quadrotors.United States. Office of Naval Research (pDOT N00014-12-1-1000)United States. Army Research Laboratory (Grant W911NF-08-2-0004)Boeing CompanySingapore-MIT Alliance for Research and Technology Center (Future of Urban Mobility Project)Spanish Government (Project DPI2012-32100)Spanish Government (Project DPI2015-69376-R)Spanish Government (Project CUD2013-05)Spanish Government (Grant CAS14/00205