541 research outputs found

    New Paths from Splay to Dynamic Optimality

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    Consider the task of performing a sequence of searches in a binary search tree. After each search, an algorithm is allowed to arbitrarily restructure the tree, at a cost proportional to the amount of restructuring performed. The cost of an execution is the sum of the time spent searching and the time spent optimizing those searches with restructuring operations. This notion was introduced by Sleator and Tarjan in (JACM, 1985), along with an algorithm and a conjecture. The algorithm, Splay, is an elegant procedure for performing adjustments while moving searched items to the top of the tree. The conjecture, called "dynamic optimality," is that the cost of splaying is always within a constant factor of the optimal algorithm for performing searches. The conjecture stands to this day. In this work, we attempt to lay the foundations for a proof of the dynamic optimality conjecture.Comment: An earlier version of this work appeared in the Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms. arXiv admin note: text overlap with arXiv:1907.0630

    Weighted dynamic finger in binary search trees

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    It is shown that the online binary search tree data structure GreedyASS performs asymptotically as well on a sufficiently long sequence of searches as any static binary search tree where each search begins from the previous search (rather than the root). This bound is known to be equivalent to assigning each item ii in the search tree a positive weight wiw_i and bounding the search cost of an item in the search sequence s1,,sms_1,\ldots,s_m by O(1+logmin(si1,si)xmax(si1,si)wxmin(wsi,wsi1))O\left(1+ \log \frac{\displaystyle \sum_{\min(s_{i-1},s_i) \leq x \leq \max(s_{i-1},s_i)}w_x}{\displaystyle \min(w_{s_i},w_{s_{i-1}})} \right) amortized. This result is the strongest finger-type bound to be proven for binary search trees. By setting the weights to be equal, one observes that our bound implies the dynamic finger bound. Compared to the previous proof of the dynamic finger bound for Splay trees, our result is significantly shorter, stronger, simpler, and has reasonable constants.Comment: An earlier version of this work appeared in the Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithm

    In pursuit of the dynamic optimality conjecture

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    In 1985, Sleator and Tarjan introduced the splay tree, a self-adjusting binary search tree algorithm. Splay trees were conjectured to perform within a constant factor as any offline rotation-based search tree algorithm on every sufficiently long sequence---any binary search tree algorithm that has this property is said to be dynamically optimal. However, currently neither splay trees nor any other tree algorithm is known to be dynamically optimal. Here we survey the progress that has been made in the almost thirty years since the conjecture was first formulated, and present a binary search tree algorithm that is dynamically optimal if any binary search tree algorithm is dynamically optimal.Comment: Preliminary version of paper to appear in the Conference on Space Efficient Data Structures, Streams and Algorithms to be held in August 2013 in honor of Ian Munro's 66th birthda

    Geometric and scale effects on energy absorption of structural composites

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    PhDThe challenge faced by structural designers is becoming increasingly difficult as the imposed design criteria of energy absorbing structures requires weight reduction of structures without compromising cost and crushing performance. The current research is thus aimed at investigating the energy absorption of fibre reinforced composites measured as a function of geometry and scale within weight-critical structures. At the first stage, an innovative structure composed of four intersecting composite plates was tested. It was found that the structural stability played a crucial role in this intersecting structure. In order to avoid generating buckling failure before turning to a progressive crushing regime, Finite Element Method (FEM) was used on composite structures as a technical tool. At the second stage, three geometric structures containing corrugated composite laminates and possessing better structural stability were designed and examined. To increase the interlaminar fracture toughness properties of composite materials, through-thickness stitching methods were introduced. Fracture toughness (Mode-I and Mode-II) and flexure tests were performed on composite materials for comparing the effectiveness of different crushing mechanisms. Fracture toughness results presented a significant improvement of using stitching methods on Mode-I properties, while slight reduction on Mode-II properties was also detected. They also indicated the flexural properties of structural composites can significantly affect their energy absorption capabilities. At the final stage, six different factors including resin type, fibre architecture, crushing speed and stitching parameters were scaled in several levels in a modified geometric structure. An optimization approach based on Taguchi methods was utilised in order to statistically determine the relationship and assist in evaluating the contribution of each factor on crushing properties. It showed that by selecting the combinations of these factors with correct levels, the energy absorbed can be improved remarkably. It found that the crushing performance of this structural composite was mainly dominated by resin and fibre architecture, which contributed 71% capability of energy absorption. The other 29% capability was dominated by trigger, beam web length, edge stitching density and the crushing speed

    Test Methods for Composites Crashworthiness: A Review

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    Crashworthiness is a material\u27s ability to absorb energy during a vehicle crash. Modern automobiles, aircraft, rail vehicles, and marine vessels incorporate crashworthy structures. The use of composite materials, with their high specific strength and stiffness, can result in efficient and safe vehicles. Mechanical testing is essential for obtaining a deeper understanding of the crash-worthiness capabilities of composite materials. This review highlights the many aspects involved in crashworthiness testing of composites, including a brief overview of the field of crashworthiness, general crushing behavior, typical testing methodologies, and the effect of the loading rate and friction on test results

    Investigation of normal growth faulting in the Columbus Basin, Trinidad, using fault displacement back-stripping

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    The Columbus Basin offshore Trinidad is a thin-skinned detached basin characterised by large-scale, syn-depositional gravitational extensions faulting and rapid creation of accommodation filled by thick sedimentary sequences since the Late Miocene. The investigation of extensional growth faults using fault displacement back-stripping is based on faults and horizons mapped on a high-quality 3D seismic survey. The study area contains three major block-bounding normal faults, with maximum throws of 1400-2500 m. Smaller fault systems show various evolutionary patterns, including (1) fault linkage after breaching of a relay ramp, and (2) upward splaying into several fault segments from a continuous fault at depth. This suggests that geometric linkage and kinematic linkage are not necessarily simply related. Most faults have higher throw rates during their early stages that decrease until their deaths. The largest faults have throw rates of up to 2.5-3.5 mm/a, whilst the smaller ones are generally below 1 mm/a. Variations from this general trend are attributed to fault Interaction, non-uniform basin extension and the migration of the deltaic depocentre, which governs the location of primary sediment deposition and, therefore, gravitational collapse. Fault activity was reconstructed for successive time intervals from 2.78 Ma to the present- day. The data show pronounced seaward migration of fault activity for progressively younger horizons which is attributed to the progradation of the shelf-edge delta. Initiation of a major block-bounding fault results in numerous smaller faults in its hanging wall, whose activity rapidly decreases as soon as the next major basinward fault becomes active. The total throw rate across the study area varies over the investigated time span. This may reflect broader regional variations of fault activity that might be controlled by the rate of sediment supply and the location and migration of the centre of gravitational collapse. A series of vertically persistent, small-scale hanging wall anticlines that are located at kinks in the fault plane and associated with the largest faults in the study area are interpreted as remnants of fault linkage. In this study, the fault interaction and evolution of several extensional faults in the Columbus Basin were investigated and the throw rates at which these faults moved were determined. Within the study area, the temporal and spatial migration of active faulting in a detached gravitational basin was quantified.Open acces

    Progressive Crushing of Polymer Matrix Composite Tubular Structures: Review

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    The present paper reviews crushing process of fibre-reinforced polymer (FRPs) composites tubular structures. Working with anisotropic material requires consideration of specific parameter definition in order to tailor a well-engineered composite structure. These parameters include geometry design, strain rate sensitivity, material properties, laminate design, interlaminar fracture toughness and off-axis loading conditions which are reviewed in this paper to create a comprehensive data base for researchers, engineers and scientists in the field. Each of these parameters influences the structural integrity and progressive crushing behaviour. In this extensive review each of these parameters is introduced, explained and evaluated. Construction of a well-engineered composite structure and triggering mechanism to strain rate sensitivity and testing conditions followed by failure mechanisms are extensively reviewed. Furthermore, this paper has mainly focused on experimental analysis that has been carried out on different types of FRP composites in the past two decades
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