Search results for " Complexity theory"
showing 10 items of 131 documents
Forrelation
2014
We achieve essentially the largest possible separation between quantum and classical query complexities. We do so using a property-testing problem called Forrelation, where one needs to decide whether one Boolean function is highly correlated with the Fourier transform of a second function. This problem can be solved using 1 quantum query, yet we show that any randomized algorithm needs Ω(√(N)log(N)) queries (improving an Ω(N[superscript 1/4]) lower bound of Aaronson). Conversely, we show that this 1 versus Ω(√(N)) separation is optimal: indeed, any t-query quantum algorithm whatsoever can be simulated by an O(N[superscript 1-1/2t])-query randomized algorithm. Thus, resolving an open questi…
A two-armed bandit collective for hierarchical examplar based mining of frequent itemsets with applications to intrusion detection
2014
Published version of a chapter in the book: Transactions on Computational Collective Intelligence XIV. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-662-44509-9_1 In this paper we address the above problem by posing frequent item-set mining as a collection of interrelated two-armed bandit problems. We seek to find itemsets that frequently appear as subsets in a stream of itemsets, with the frequency being constrained to support granularity requirements. Starting from a randomly or manually selected examplar itemset, a collective of Tsetlin automata based two-armed bandit players - one automaton for each item in the examplar - learns which items should be included in …
Quantum search of spatial regions
2003
Can Grover's algorithm speed up search of a physical region - for example a 2-D grid of size sqrt(n) by sqrt(n)? The problem is that sqrt(n) time seems to be needed for each query, just to move amplitude across the grid. Here we show that this problem can be surmounted, refuting a claim to the contrary by Benioff. In particular, we show how to search a d-dimensional hypercube in time O(sqrt n) for d at least 3, or O((sqrt n)(log n)^(3/2)) for d=2. More generally, we introduce a model of quantum query complexity on graphs, motivated by fundamental physical limits on information storage, particularly the holographic principle from black hole thermodynamics. Our results in this model include a…
Cooperative Inventory control
2005
In multi-retailer inventory control the possibility of sharing setup costs motivates communication and coordination among the retailers. We solve the problem of finding suboptimal distributed reordering policies that minimize setup, ordering, storage, and shortage costs incurred by the retailers over a finite horizon. Neuro-dynamic programming (NDP) reduces the computational complexity of the solution algorithm from exponential to polynomial on the number of retailers.
Image boundaries detection: from thresholding to implicit curve evolution
2014
The development of high dimensional large-scale imaging devices increases the need of fast, robust and accurate image segmentation methods. Due to its intrinsic advantages such as the ability to extract complex boundaries, while handling topological changes automatically, the level set method (LSM) has been widely used in boundaries detection. Nevertheless, their computational complexity limits their use for real time systems. Furthermore, most of the LSMs share the limit of leading very often to a local minimum, while the effectiveness of many computer vision applications depends on the whole image boundaries. In this paper, using the image thresholding and the implicit curve evolution fra…
The PLVC display color characterization model revisited
2008
This work proposes a study of the Piecewise Linear assuming Variation in Chromaticity (PLVC) dis- play color characterization model. This model has not been widely used as the improved accuracy compared with the more common PLCC (Piecewise Linear assuming Chromaticity Constancy) model is not significant for CRT (Cathode Ray Tube) display technology, and it requires more computing power than this model. With today's computers, computational complexity is less of a problem, and today's display technologies show a different colori- metric behavior than CRTs. The main contribution of this work is to generalize the PLVC model to multiprimary displays and to provide extensive experimental results…
Real Time Stereo Matching Using Two Step Zero-Mean SAD and Dynamic Programing
2018
Dense depth map extraction is a dynamic research field in a computer vision that tries to recover three-dimensional information from a stereo image pair. A large variety of algorithms has been developed. The local methods based on block matching that are prevalent due to the linear computational complexity and easy implementation. This local cost is used on global methods as graph cut and dynamic programming in order to reduce sensitivity to local to occlusion and uniform texture. This paper proposes a new method for matching images based on a two-stage of block matching as local cost function and dynamic programming as energy optimization approach. In our work introduce the two stage of th…
The guarded fragment with transitive guards
2004
The guarded fragment with transitive guards, (GF+TG), is an extension of the guarded frag- ment of 9rst-order logic, GF, in which certain predicates are required to be transitive, transitive predicate letters appear only in guards of the quanti9ers and the equality symbol may appear everywhere. We prove that the decision problem for (GF+TG) is decidable. Moreover, we show that the problem is in 2EXPTIME. This result is optimal since the satis9ability problem for GF is 2EXPTIME-complete (J. Symbolic Logic 64 (1999) 1719-1742). We also show that the satis- 9ability problem for two-variable (GF+TG) is NEXPTIME-hard in contrast to GF with bounded number of variables for which the satis9ability …
Resource allocation for OFDMA systems with multi-cell joint transmission
2012
This paper considers the downlink resource allocation of a coordinated multi-cell cluster in OFDMA systems with universal frequency reuse. Multi-cell joint transmission is considered via zero-forcing precoding. Furthermore, joint optimization of the user selection and power allocation across multiple subchannels and multiple cells is studied. The objective is to maximize the weighted sum rate under per-base-station power constraints. Based on general duality theory, two iterative resource allocation algorithms are proposed and compared with the optimal solution, which requires an exhaustive search of all possible combinations of users over all subchannels. Simulation results show that the t…
Data-Driven Pump Scheduling for Cost Minimization in Water Networks
2021
Pumps consume a significant amount of energy in a water distribution network (WDN). With the emergence of dynamic energy cost, the pump scheduling as per user demand is a computationally challenging task. Computing the decision variables of pump scheduling relies over mixed integer optimization (MIO) formulations. However, MIO formulations are NP-hard in general and solving such problems is inefficient in terms of computation time and memory. Moreover, the computational complexity of solving such MIO formulations increases exponentially with the size of the WDN. As an alternative, we propose a data-driven approach to estimate the decision variables of pump scheduling using deep neural netwo…