اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAn analysis of a random algorithm for estimating all the matchings
200
0
0.0
(
0
)
تأليف
Jinshan Zhang
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Counting the number of all the matchings on a bipartite graph has been transformed into calculating the permanent of a matrix obtained from the extended bipartite graph by Yan Huo, and Rasmussen presents a simple approach (RM) to approximate the permanent, which just yields a critical ratio O($nomega(n)$) for almost all the 0-1 matrices, provided its a simple promising practical way to compute this #P-complete problem. In this paper, the performance of this method will be shown when its applied to compute all the matchings based on that transformation. The critical ratio will be proved to be very large with a certain probability, owning an increasing factor larger than any polynomial of $n$ even in the sense for almost all the 0-1 matrices. Hence, RM fails to work well when counting all the matchings via computing the permanent of the matrix. In other words, we must carefully utilize the known methods of estimating the permanent to count all the matchings through that transformation.
قيم البحث
اقرأ أيضاً
Conformal Geometric Algebra (CGA) is a framework that allows the representation of objects, such as points, planes and spheres, and deformations, such as translations, rotations and dilations as uniform vectors, called multivectors. In this work, we
demonstrate the merits of multivector usage with a novel, integrated rigged character simulation framework based on CGA. In such a framework, and for the first time, one may perform real-time cuts and tears as well as drill holes on a rigged 3D model. These operations can be performed before and/or after model animation, while maintaining deformation topology. Moreover, our framework permits generation of intermediate keyframes on-the-fly based on user input, apart from the frames provided in the model data. We are motivated to use CGA as it is the lowest-dimension extension of dual-quaternion algebra that amends the shortcomings of the majority of existing animation and deformation techniques. Specifically, we no longer need to maintain objects of multiple algebras and constantly transmute between them, such as matrices, quaternions and dual-quaternions, and we can effortlessly apply dilations. Using such an all-in-one geometric framework allows for better maintenance and optimization and enables easier interpolation and application of all native deformations. Furthermore, we present these three novel algorithms in a single CGA representation which enables cutting, tearing and drilling of the input rigged model, where the output model can be further re-deformed in interactive frame rates. These close to real-time cut,tear and drill algorithms can enable a new suite of applications, especially under the scope of a medical VR simulation.
In this work, we present an integrated geometric framework: deep- cut that enables for the first time a user to geometrically and algorithmically cut, tear and drill the surface of a skinned model without prior constraints, layered on top of a custom
soft body mesh deformation algorithm. Both layered algorithms in this frame- work yield real-time results and are amenable for mobile Virtual Reality, in order to be utilized in a variety of interactive application scenarios. Our framework dramatically improves real-time user experience and task performance in VR, without pre-calculated or artificially designed cuts, tears, drills or surface deformations via predefined rigged animations, which is the current state-of-the-art in mobile VR. Thus our framework improves user experience on one hand, on the other hand saves both time and costs from expensive, manual, labour-intensive design pre-calculation stages.
We introduce a large scale benchmark for continuous collision detection (CCD) algorithms, composed of queries manually constructed to highlight challenging degenerate cases and automatically generated using existing simulators to cover common cases.
We use the benchmark to evaluate the accuracy, correctness, and efficiency of state-of-the-art continuous collision detection algorithms, both with and without minimal separation. We discover that, despite the widespread use of CCD algorithms, existing algorithms are either: (1) correct but impractically slow, (2) efficient but incorrect, introducing false negatives which will lead to interpenetration, or (3) correct but over conservative, reporting a large number of false positives which might lead to inaccuracies when integrated in a simulator. By combining the seminal interval root finding algorithm introduced by Snyder in 1992 with modern predicate design techniques, we propose a simple and efficient CCD algorithm. This algorithm is competitive with state of the art methods in terms of runtime while conservatively reporting the time of impact and allowing explicit trade off between runtime efficiency and number of false positives reported.
Toolpath planning is an important task in laser aided additive manufacturing (LAAM) and other direct energy deposition (DED) processes. The deposition toolpaths for complex geometries with slender structures can be further optimized by partitioning t
he sliced 2D layers into sub-regions, and enable the design of appropriate infill toolpaths for different sub-regions. However, reported approaches for 2D layer segmentation generally require manual operations that are tedious and time-consuming. To increase segmentation efficiency, this paper proposes an autonomous approach based on evolutional computation for 2D layer segmentation. The algorithm works in an identify-and-segment manner. Specifically, the largest quasi-quadrilateral is identified and segmented from the target layer iteratively. Results from case studies have validated the effectiveness and efficacy of the developed algorithm. To further improve its performance, a roughing-finishing strategy is proposed. Via multi-processing, the strategy can remarkably increase the solution variety without affecting solution quality and search time, thus providing great application potential in LAAM toolpath planning. To the best of the authors knowledge, this work is the first to address automatic 2D layer segmentation problem in LAAM process. Therefore, it may be a valuable supplement to the state of the art in this area.
We are given a stable matching instance $A$ and a set $S$ of errors that can be introduced into $A$. Each error consists of applying a specific permutation to the preference list of a chosen boy or a chosen girl. Assume that $A$ is being transmitted
over a channel which introduces one error from set $S$; as a result, the channel outputs this new instance. We wish to find a matching that is stable for $A$ and for each of the $|S|$ possible new instances. If $S$ is picked from a special class of errors, we give an $O(|S| p(n))$ time algorithm for this problem. We call the obtained matching a fully robust stable matching w.r.t. $S$. In particular, if $S$ is polynomial sized, then our algorithm runs in polynomial time. Our algorithm is based on new, non-trivial structural properties of the lattice of stable matchings; these properties pertain to certain join semi-sublattices of the lattice. Birkhoffs Representation Theorem for finite distributive lattices plays a special role in our algorithms.
الأسئلة المقترحة
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
