Constant Computation Time Research Articles

SMCEWS: Binary Robust Multicentre Features

The Oriented FAST and Rotated BRIEF (ORB) algorithms have been improved, and a new method for calculating descriptors based on symmetrical multicentric weighted binary encoding is proposed, which enhances the robustness of feature points. This method employs a string of binary descriptors to encode the features and uses the multiple descriptor centre strategy to sample descriptors at the feature point and on the symmetrical circumference around it. Furthermore, a weighted summation is introduced in the descriptor calculation process to address the noise in the image during the sampling process. Specifically, the pixel values around the sampled point and the sampled point itself are combined using a certain weight to produce the final pixel value of the sampled point. The reliability of the descriptor is enhanced by introducing the pixel information around the sample point while solving the noise problem. Our method makes full use of the pixel information in the various parts of the descriptor sampling region to improve the distinguishability of the descriptors. We compare it with the ORB algorithm and experimentally show that the feature extraction method achieves better matching results with almost constant computation time.

Number-Theoretic Transform with Constant Time Computation for Embedded Post-Quantum Cryptography

Abstract In this article, we describe the principles and advantages of using the Number-Theoretic Transform (NTT) in post-quantum cryptography. We deal with usages of NTT in post-quantum algorithms included in the competition announced by the National Institute of Standards and Technology. Attention is paid to the fast multiplication of polynomials using NTT and negacyclic convolution. We also focus on the existing implementation of NTT and its modifications to analyze the effectiveness of individual modifications. Separate attention is paid to the Constant Time implementation of NTT because the constant computation time of the transformation decreases a possibility of side channel attack. We describe measurements performed on OS Linux Ubuntu 20.04 LTS environment in Linux kernel mode, with the highest attention to the measurement executed on a microcontroller with an ARM 32-bit core. Measurements performed on microcontroller units are done using 32-bit and 16-bit arithmetic to demonstrate how to achieve constant computation time of the transformation. We present the results and analysis of measurements performed using modified implementations.

A New Constructive Heuristic Driven by Machine Learning for the Traveling Salesman Problem

Recent systems applying Machine Learning (ML) to solve the Traveling Salesman Problem (TSP) exhibit issues when they try to scale up to real case scenarios with several hundred vertices. The use of Candidate Lists (CLs) has been brought up to cope with the issues. A CL is defined as a subset of all the edges linked to a given vertex such that it contains mainly edges that are believed to be found in the optimal tour. The initialization procedure that identifies a CL for each vertex in the TSP aids the solver by restricting the search space during solution creation. It results in a reduction of the computational burden as well, which is highly recommended when solving large TSPs. So far, ML was engaged to create CLs and values on the elements of these CLs by expressing ML preferences at solution insertion. Although promising, these systems do not restrict what the ML learns and does to create solutions, bringing with them some generalization issues. Therefore, motivated by exploratory and statistical studies of the CL behavior in multiple TSP solutions, in this work, we rethink the usage of ML by purposely employing this system just on a task that avoids well-known ML weaknesses, such as training in presence of frequent outliers and the detection of under-represented events. The task is to confirm inclusion in a solution just for edges that are most likely optimal. The CLs of the edge considered for inclusion are employed as an input of the neural network, and the ML is in charge of distinguishing when such edge is in the optimal solution from when it is not. The proposed approach enables a reasonable generalization and unveils an efficient balance between ML and optimization techniques. Our ML-Constructive heuristic is trained on small instances. Then, it is able to produce solutions—without losing quality—for large problems as well. We compare our method against classic constructive heuristics, showing that the new approach performs well for TSPLIB instances up to 1748 cities. Although ML-Constructive exhibits an expensive constant computation time due to training, we proved that the computational complexity in the worst-case scenario—for the solution construction after training—is O(n2logn2), n being the number of vertices in the TSP instance.

Transfer matrix based layered materials rendering

A statistical multi-lobe approach was recently introduced in order to efficiently handle layered materials rendering as an alternative to expensive general-purpose approaches. However, this approach poorly supports scattering volumes as the method does not account for back-scattering and resorts to single scattering approximations. In this paper, we address these limitations with an efficient solution based upon a transfer matrix approach which leverages the properties of the Henyey-Greenstein phase function. Under this formalism, each scattering component of the stack is described through a lightweight matrix, layering operations are reduced to simple matrix products and the statistics of each BSDF lobe accounting for multiple scattering effects are obtained through matrix operators. Based on this representation, we leverage the versatility of the transfer matrix approach to efficiently handle forward and backward scattering which occurs in arbitrary layered materials. The resulting model enables the reproduction of a wide range of layered structures embedding scattering volumes of arbitrary depth, in constant computation time and with low variance.

Linear Programming Model and Online Algorithm for Customer-Centric Train Calendar Generation

An important objective for train operating companies is to let users, especially commuters, directly query the ICT system about trains’ availability calendar, based on an online approach, and give them clear and brief information, expressed through “intelligent” phrases instead of bit maps. This paper provides a linear programming model of this problem and a fast and flexible heuristic algorithm to create descriptive sentences from train calendars. The algorithmic method, based on the “Divide and Conquer” approach, takes the calendar period queried in its whole and divides it into subsets, which are successively processed one by one. The dominant limitation of previous methods is their strong dependence on the size and complexity of instances. On the contrary, our computational findings show that the proposed online algorithm has a very limited and constant computation time, even when increasing the problem complexity, keeping its processing time between 0 and 16 ms, while producing good quality solutions that differ by an average surplus of 0.13 subsentences compared to benchmark state-of-art solutions.

An efficient hypercube labeling schema for dynamic Peer-to-Peer networks

This paper addresses the general problem of reducing unnecessary message transmission thereby lowering overall bandwidth utilization in a Peer-to-Peer (P2P) network. In particular, we exploit the characteristics of a P2P network engineered to resemble a hypercube. The reason for doing this is to achieve constant computation time for inter-node distances that are needed in the process of query optimization. To realize such a hypercube-like engineered structure, we develop a new labeling scheme which assigns identifiers (labels) to each node and then uses these labels to determine inter-node distances as is done in a hypercube, thus eliminating the need to send out queries to find the distance from one node to another. The labels allow for creating a virtual overlay which resembles a hypercube. We prove that the labeling scheme does in fact allow for reducing bandwidth utilization in the network. To confirm our theoretical findings we conduct various experiments with randomly selected P2P networks of various sizes. Detailed statistics on the outcome of these experiments are provided which show clearly the practical utility of the labeling approach.

A computationally efficient safety assessment for collaborative robotics applications

Safety during interaction with unstructured and dynamic environments is now a well established requirement for complex robotic systems. A wide variety of approaches focus on the introduction of safety evaluation methods in order to shape a consequent safety-oriented control strategy, able to reactively prevent collisions between the robot and potential obstacles, including a human being. This paper presents a new safety assessment, named kinetostatic safety field, that captures the risk in the vicinity of an arbitrary rigid body “source of danger” (e.g. an obstacle, a human body part or a robot link) moving in R3. The safety field depends on the position and velocity of the body but it is also influenced by its real shape and size, exploiting its triangular mesh. The introduction of a body-fixed reference frame in the definition of the field provides closed form computability and an effective computation time reduction, that allows for real-time applications. In particular, intensive computations, connected to the specific body geometry, can be performed only once and off-line, ensuring a fast and constant on-line computation time, independently of the number of mesh elements. Furthermore, we combine the safety field concept with a safety-oriented reactive control strategy for redundant manipulators. Our approach allows to enhance safety in several real-time collision avoidance scenarios, including collision avoidance with potential obstacles, self-collision avoidance and safe human–robot coexistence. The proposed control strategy is validated through experiments performed on an ABB FRIDA dual arm robot.

Repetitions detection on a linear array with reconfigurable pipelined bus system

The optical bus based arrays have recently shown many applications. In this paper we use the pipelining ability of the LARPBS to solve the repetitions detection problem. We propose an algorithm that finds all kind of repetitions in a string including k-power repetitions, overlapping repetitions and non-contiguous repetitions. For a given distance, this operation is performed in O(1) communication cycle with a constant computation time processors on a O(n) processors LARPBS for a string of length n. For all the periods, it is O(n) bus cycle. No previous algorithms were known for this problem on the LARPBS.

Arbitrary Throughput Versus Complexity Tradeoffs in Wireless Networks Using Graph Partitioning

Several policies have recently been proposed for attaining the maximum throughput region, or a guaranteed fraction thereof, through dynamic link scheduling. Among these policies, the ones that attain the maximum throughput region require a computation time which is linear in the network size, and the ones that require constant or logarithmic computation time attain only certain fractions of the maximum throughput region. In contrast, in this paper we propose policies that can attain any desirable fraction of the maximum throughput region using a computation time that is largely independent of the network size. First, using a combination of graph partitioning techniques and Lyapunov arguments, we propose a simple policy for tree topologies under the primary interference model that requires each link to exchange only 1 bit information with its adjacent links and approximates the maximum throughput region using a computation time that depends only on the maximum degree of nodes and the approximation factor. Then we develop a framework for attaining arbitrary close approximations for the maximum throughput region in arbitrary networks, and use this framework to obtain any desired tradeoff between throughput guarantees and computation times for a large class of networks and interference models. Specifically, given any epsiv > 0, the maximum throughput region can be approximated in these networks within a factor of 1-epsiv using a computation time that depends only on the maximum node degree and epsiv .

Fast and robust computation of colon centerline in CT colonography

Although several methods for generating the centerline of a colon from CT colonographic scans have been proposed, in general they are time-consuming and do not take into account that the images of the colon may be of nonoptimal quality, with collapsed regions, and stool within the colon. Furthermore, the colonic lumen or wall, which is often used as a basis for computation of a centerline, is not always precisely segmented. In this study, we have developed an algorithm for computation of a colon centerline that is fast compared to the centerline algorithms presented in the reviewed literature, and that relies little on a complete colon segments identification. The proposed algorithm first extracts local maxima in a distance map of a segmented colonic lumen. The maxima are considered to be nodes in a set of graphs, and are iteratively linked together, based on a set of connection criteria, giving a minimum distance spanning tree. The connection criteria are computed from the distance from object boundary, the Euclidean distance between nodes and the voxel values on the pathway between pairs of nodes. After the last iteration, redundant branches are removed and end segments are recovered for each remaining graph. A subset of the initial maxima is used for distinguishing between the colon and noncolonic centerline segments among the set of graphs, giving the final centerline representation. A phantom study showed that, with respect to phantom variations, the algorithm achieved nearly constant computation time (2.3-2.9 s) except for the most extreme setting (20.2 s). The algorithm successfully found all, or most of, the centerline (93% - 100%). Displacement from optimum varied with colon diameter (1.2-6.6 mm). By use of 40 CT colonographic scans, the computer-generated centerlines were compared with the centerlines generated by three radiologists. The similarity was measured based on percent coverage and average displacement. The computer-generated centerlines, when compared with human-generated centerlines, had approximately the same displacement as when the human-generated centerlines were compared among each other (3.8 mm versus 4.0 mm). The coverage of the computer-generated centerlines was slightly less than that of the human-generated centerlines (92% versus 94%). The 40 centerlines were, on average, computed in 10.5 seconds, including computation time for the distance transform, with an Intel Pentium-based 800 MHz computer, as compared with 12-17 seconds or more (excluding computation time for the distance transform needed) per centerline as reported in other studies.

An Energy‐Based Approach for Contact Force Computation

AbstractA new approach for computing resting contact forces between solids is presented, which handles both static and sliding friction, while avoiding the problems arising from previous approaches. Each iteration provides values for all unknowns and needs a constant computation time. The first iteration is a global dynamic solution involving inertia and external forces. The subsequent iterations consist of global redistributions of energy through the solids in order to restrict the values within correct bounds, leading to a progressive refinement of the solution. This allows the termination of the computation when a user‐defined level of precision is reached. Convergence is proven in the frictionless case.The method is concise and is easily usable in a motion control system. It was implemented and tested on some examples involving simultaneously static and sliding friction along with motion control.

Simulation of neural network digital adder and multiplier

AbstractA novel adder and multiplier using Hopfield‐type neural networks for which a technique is introduced to avoid the false operations is proposed, and the simulation results for these operations are illustrated. The main feature of these circuits is high‐speed operation which is achieved at the almost constant computation time due to their parallel calculation ability even if the number of bits in digital circuits increases.The previously proposed adder has a problem in that some false operations occur in the special cases of addition. The error between the correct and false values in the operations is always only a binary value of ±1 once the false operation occurs.This paper describes in detail the technique to avoid the false operations. It is important to determine the ratio of weight of the object function to constraint function, taking into consideration the energy function that should be chosen. Computer simulations for the adder verify that the correct operation can be achieved by choosing the special ratio of the weight for these functions.On the other hand, a novel multiplier is described using a Hopfield‐type network which is composed of the proposed adder and a neural network to perform a logical product. The simulation results for the multiplier show that the correct operations of a multiplication can be achieved with high‐speed performance. It is clear from these results that a high‐performance digital adder and multiplier can be constructed by using the Hopfield‐type neural network model.

Optimal infinite impulse response zero crossing based edge detectors

We present formal optimality criteria and a complete design methodology for a family of zero crossing based, infinite impulse response (recursive) edge detection filters. In particular, we adapt the optimality criteria proposed by Canny ( IEEE Trans. Pattern Anal. Mach. Intelligence PAMI-8, 1986 , 679–714) to filters designed to respond with a zero crossing in the output at an edge location and additionally to impulse responses which are (allowed to be) infinite in extent. The spurious response criterion is captured directly by an appropriate measure of filter spatial extent for infinite responses. Infinite duration impulse responses may be implemented efficiently with recursive filtering techniques and so require constant computation time with respect to scale. As we will show, we can achieve both superior performance and increased speed by designing directly for an infinite impulse response than by any of the proposed finite duration approaches. We also show that the optimal filter which responds with a zero crossing in its output may not be implemented by designing the optimal peak responding filter (similar to Canny) and taking an additional derivative. It is necessary to formulate the criteria and design for a zero crossing response from the outset, else optimality is sacrificed. Filter parameters and performance criteria are presented for several designs, and experimental results are presented on a variety of images which demonstrate the behavior in the presence of very adverse noise, with respect to scale, and as compared to other “optimal” IIR filters which have been reported.