Optimal Bounds for the k -cut Problem

In the k -cut problem, we want to find the lowest-weight set of edges whose deletion breaks a given (multi)graph into k connected components. Algorithms of Karger and Stein can solve this in roughly O ( n 2k ) time. However, lower bounds from conjectures about the k -clique problem imply that Ω ( n (1- o (1)) k ) time is likely needed. Recent results of Gupta, Lee, and Li have given new algorithms for general k -cut in n 1.98k + O(1) time, as well as specialized algorithms with better performance for certain classes of graphs (e.g., for small integer edge weights). In this work, we resolve the problem for general graphs. We show that the Contraction Algorithm of Karger outputs any fixed k -cut of weight α λ k with probability Ω k ( n - α k ), where λ k denotes the minimum k -cut weight. This also gives an extremal bound of O k ( n k ) on the number of minimum k -cuts and an algorithm to compute λ k with roughly n k polylog( n ) runtime. Both are tight up to lower-order factors, with the algorithmic lower bound assuming hardness of max-weight k -clique. The first main ingredient in our result is an extremal bound on the number of cuts of weight less than 2 λ k / k , using the Sunflower lemma. The second ingredient is a fine-grained analysis of how the graph shrinks—and how the average degree evolves—in the Karger process.

Flipping food during grilling tasks, a dataset of utensils kinematics and dynamics, food pose and subject gaze

This paper presents a multivariate dataset of 2866 food flipping movements, performed by 4 chefs and 5 home cooks, with different grilled food and two utensils (spatula and tweezers). The 3D trajectories of strategic points in the utensils were tracked using optoelectronic motion capture. The pinching force of the tweezers, the bending force and torsion torque of the spatula were also recorded, as well as videos and the subject gaze. These data were collected using a custom experimental setup that allowed the execution of flipping movements with freshly cooked food, without having the sensors near the dangerous cooking area. Complementary, the 2D position of food was computed from the videos. The action of flipping food is, indeed, gaining the attention of both researchers and manufacturers of foodservice technology. The reported dataset contains valuable measurements (1) to characterize and model flipping movements as performed by humans, (2) to develop bio-inspired methods to control a cooking robot, or (3) to study new algorithms for human actions recognition.

PARALLEL OPTIMIZATION TECHNOLOGY FOR ATOMIC-MOLECULAR MORSE CLUSTERS

В статье рассматриваются специализированные вычислительные технологии и алгоритмы, используемые для поиска низкопотенциальных атомно-молекулярных кластеров. Проведенные вычислительные эксперименты продемонстрировали достаточно высокую конкурентоспособность новых алгоритмов по сравнению с классическими для функций рассматриваемого типа. С использованием разработанного программного комплекса получены рекордные результаты оптимизации атомно-молекулярных кластеров Морса рекордных размерностей. The paper deals with specialized computing technology and algorithms used for finding low-potential atomic-molecular clusters. The performed computational experiments demonstrated a rather high competitiveness of the new algorithms in comparison with the classical methods for the considerable functions. Using the developed software, the applied problem of molecular docking was solved. Using the developed software package, record results for optimization of atomic-molecular Morse clusters of large dimensions have been obtained.

Identifying Multiple Influential Spreaders in Complex Networks by Considering the Dispersion of Nodes

Identifying multiple influential spreaders, which relates to finding k (k > 1) nodes with the most significant influence, is of great importance both in theoretical and practical applications. It is usually formulated as a node-ranking problem and addressed by sorting spreaders’ influence as measured based on the topological structure of interactions or propagation process of spreaders. However, ranking-based algorithms may not guarantee that the selected spreaders have the maximum influence, as these nodes may be adjacent, and thus play redundant roles in the propagation process. We propose three new algorithms to select multiple spreaders by taking into account the dispersion of nodes in the following ways: (1) improving a well-performed local index rank (LIR) algorithm by extending its key concept of the local index (an index measures how many of a node’s neighbors have a higher degree) from first-to second-order neighbors; (2) combining the LIR and independent set (IS) methods, which is a generalization of the coloring problem for complex networks and can ensure the selected nodes are non-adjacent if they have the same color; (3) combining the improved second-order LIR method and IS method so as to make the selected spreaders more disperse. We evaluate the proposed methods against six baseline methods on 10 synthetic networks and five real networks based on the classic susceptible-infected-recovered (SIR) model. The experimental results show that our proposed methods can identify nodes that are more influential. This suggests that taking into account the distances between nodes may aid in the identification of multiple influential spreaders.

Substantiation of the influence of changes in the coefficient of axle distribution of braking force on the handling of a passenger car

The article considers the change of the radius of the instantaneous center of rotation of a car moving along a curved trajectory during braking, taking into account the lateral input of the wheels of both axles of cars, both equipped with electronic tracking systems and not equipped with such. A criterion for assessing the controllability of cars moving on a curved trajectory in a braked state, by comparing the ratio of the current speed of the car to the longitudinal base with the ratio of the coefficients of lateral tire input to the product of the longitudinal base of the car, mass and cosines. It is established that the radius of instantaneous rotation of the longitudinal axis of the car moving along a curved trajectory during braking depends on the speed of the center of mass of the car, the coefficient of axle distribution of braking force, physical characteristics of applied tires, steering wheel angle and design and weight parameters. As a result, it allows you to set controllability. The authors obtained dependences that will create new algorithms for the operation of modern electronic control systems for stabilizing the longitudinal axis of a braked car, taking into account the speed of the car, its design and weight characteristics, the main characteristics of its braking system (coefficient of axle braking force distribution), physical characteristics used tires on wheels and connect them to the angles of the steered wheels, controlling the deviation of the longitudinal axis, which allows the driver to maintain the possibility of quite sharp maneuvers directly in the braking process, moving along a curved trajectory.

Fast Sampling and Counting k -SAT Solutions in the Local Lemma Regime

We give new algorithms based on Markov chains to sample and approximately count satisfying assignments to k -uniform CNF formulas where each variable appears at most d times. For any k and d satisfying kd < n o(1) and k ≥ 20 log k + 20 log d + 60, the new sampling algorithm runs in close to linear time, and the counting algorithm runs in close to quadratic time. Our approach is inspired by Moitra (JACM, 2019), which remarkably utilizes the Lovász local lemma in approximate counting. Our main technical contribution is to use the local lemma to bypass the connectivity barrier in traditional Markov chain approaches, which makes the well-developed MCMC method applicable on disconnected state spaces such as SAT solutions. The benefit of our approach is to avoid the enumeration of local structures and obtain fixed polynomial running times, even if k = ω (1) or d = ω (1).

ALGORITHMS FOR OBJECT POSITION MONITORING ON THE SEA SURFACE USING MONOCULAR VIDEO CAMERA

The article proposes new algorithms for estimating the coordinates of objects (both linear and angular) relative to the coordinate system related to the video camera. A two-step algorithm is proposed. At the first stage, the processing of images coming from the camera is performed – the selection of an area be-longing to the sea surface in the image, the detection and video tracking of objects, the determination of azimuth and elevation angles from the obtained images. Our approach is based on the representation of elevation and azimuth angles in the form of non-stationary autoregression models, recurrent estimation of their parameters and subsequent estimation of the object coordinates.

Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions

We study the efficient computation of power indices for weighted voting games with precoalitions amongst subsets of players (reflecting, e.g., ideological proximity) using the paradigm of dynamic programming. Starting from the state-of-the-art algorithms for computing the Banzhaf and Shapley–Shubik indices for weighted voting games, we present a framework for fast algorithms for the three most common power indices with precoalitions, i.e., the Owen index, the Banzhaf–Owen index and the symmetric coalitional Banzhaf index, and point out why our new algorithms are applicable for large numbers of players. We discuss implementations of our algorithms for the three power indices with precoalitions in C++ and review computing times, as well as storage requirements.