Modern robotic exploratory strategies assume multi-agent cooperation that raises a need for an effective exchange of acquired scans of the environment with the absence of a reliable global positioning system. In such situations, agents compare the scans of the outside world to determine if they overlap in some region, and if they do so, they determine the right matching between them. The process of matching multiple point-cloud scans is called point-cloud registration. Using the existing point-cloud registration approaches, a good match between any two-point-clouds is achieved if and only if there exists a large overlap between them, however, this limits the advantage of using multiple robots, for instance, for time-effective 3D mapping. Hence, a point-cloud registration approach is highly desirable if it can work with low overlapping scans. This work proposes a novel solution for the point-cloud registration problem with a very low overlapping area between the two scans. In doing so, no initial relative positions of the point-clouds are assumed. Most of the state-of-the-art point-cloud registration approaches iteratively match keypoints in the scans, which is computationally expensive. In contrast to the traditional approaches, a more efficient line-features-based point-cloud registration approach is proposed in this work. This approach, besides reducing the computational cost, avoids the problem of high false-positive rate of existing keypoint detection algorithms, which becomes especially significant in low overlapping point-cloud registration. The effectiveness of the proposed approach is demonstrated with the help of experiments.

A fundamental computational problem is to find a shortest non-zero vector in Euclidean lattices, a problem known as the Shortest Vector Problem (SVP). This problem is believed to be hard even on quantum computers and thus plays a pivotal role in post-quantum cryptography. In this work we explore how (efficiently) Noisy Intermediate Scale Quantum (NISQ) devices may be used to solve SVP. Specifically, we map the problem to that of finding the ground state of a suitable Hamiltonian. In particular, (i) we establish new bounds for lattice enumeration, this allows us to obtain new bounds (resp. estimates) for the number of qubits required per dimension for any lattices (resp. random q-ary lattices) to solve SVP; (ii) we exclude the zero vector from the optimization space by proposing (a) a different classical optimisation loop or alternatively (b) a new mapping to the Hamiltonian. These improvements allow us to solve SVP in dimension up to 28 in a quantum emulation, significantly more than what was previously achieved, even for special cases. Finally, we extrapolate the size of NISQ devices that is required to be able to solve instances of lattices that are hard even for the best classical algorithms and find that with approximately 103 noisy qubits such instances can be tackled.

One of the most important factors in the success of a business is its location, therefore the problem of identifying an optimal site for a new commercial opening has remained the focus of the research community. The ideal business site depends on many criteria including competitors, ease of access, traffic condition, etc. Precisely, optimal business site selection is a Multi Criteria Decision Making (MCDM) problem, which deals with the selection of the best alternative from several potential candidates based on several criteria. In this work we present an AHP/TOPSIS hybrid approach to identify an optimal site for a commercial opening, given a set a candidate sites. Both the AHP and TOPSIS are MCDM methods, however the hybrid approach is chosen as it results in the reduction of the computational complexity, and the reduction in the manual effort required in the construction of the AHP pairwise comparison matrices. The proposed approach ranks all the candidate sites based on their performance scores and the candidate with the highest score is identified as the optimal site. A nexus of complex factors such as competition in the area, traffic conditions, and area popularity are considered for ranking the candidates, where the factor values are computed with the assistance of real GeoSpatial data. The proposed approach is flexible and can effectively incorporate any number of factors to rank the candidates. The effectiveness of the proposed approach is proved with the help of a case study to identify an optimal location for a new gas station in the New York City.

Findingmmx 00tqe00-prokop-3501683_header.xml the shortest vector in a lattice is a problem that is believed to be hard both for classical and quantum computers. Many major post-quantum secure cryptosystems base their security on the hardness of the Shortest Vector Problem (SVP) [1]. Finding the best classical, quantum or hybrid classical-quantum algorithms for SVP is necessary to select cryptosystem parameters that offer sufficient level of security. Grover's search quantum algorithm provides a generic quadratic speed-up, given access to an oracle implementing some function which describes when a solution is found. In this paper we provide concrete implementation of such an oracle for the SVP. We define the circuit, and evaluate costs in terms of number of qubits, number of gates, depth and T-quantum cost. We then analyze how to combine Grover's quantum search for small SVP instances with state-of-the-art classical solvers that use well known algorithms, such as the BKZ [2], where the former is used as a subroutine. This could enable solving larger instances of SVP with higher probability than classical state-of-the-art records, but still very far from posing any threat to cryptosystems being considered for standardization. Depending on the technology available, there is a spectrum of trade-offs in creating this combination.