ND-Tree-based update: a Fast Algorithm for the Dynamic Non-Dominance Problem

In this paper we propose a new method called ND-Tree-based update (or shortly ND-Tree) for the dynamic non-dominance problem, i.e. the problem of online update of a Pareto archive composed of mutually non-dominated points. It uses a new ND-Tree data structure in which each node represents a subset of points contained in a hyperrectangle defined by its local approximate ideal and nadir points. By building subsets containing points located close in the objective space and using basic properties of the local ideal and nadir points we can efficiently avoid searching many branches in the tree. ND-Tree may be used in multiobjective evolutionary algorithms and other multiobjective metaheuristics to update an archive of potentially non-dominated points. We prove that the proposed algorithm has sub-linear time complexity under mild assumptions. We experimentally compare ND-Tree to the simple list, Quad-tree, and M-Front methods using artificial and realistic benchmarks with up to 10 objectives and show that with this new method substantial reduction of the number of point comparisons and computational time can be obtained. Furthermore, we apply the method to the non-dominated sorting problem showing that it is highly competitive to some recently proposed algorithms dedicated to this problem.Comment: 15 pages, 21 figures, 3 table

ROSIA: Rotation-Search-Based Star Identification Algorithm

This paper presents a rotation-search-based approach for addressing the star identification (Star-ID) problem. The proposed algorithm, ROSIA, is a heuristics-free algorithm that seeks the optimal rotation that maximally aligns the input and catalog stars in their respective coordinates. ROSIA searches the rotation space systematically with the Branch-and-Bound (BnB) method. Crucially affecting the runtime feasibility of ROSIA is the upper bound function that prioritizes the search space. In this paper, we make a theoretical contribution by proposing a tight (provable) upper bound function that enables a 400x speed-up compared to an existing formulation. Coupling the bounding function with an efficient evaluation scheme that leverages stereographic projection and the R-tree data structure, ROSIA achieves feasible operational speed on embedded processors with state-of-the-art performances under different sources of noise. The source code of ROSIA is available at https://github.com/ckchng/ROSIA.Comment: 21 pages, 16 figures, Accepted to IEEE Transactions on Aerospace and Electronic System

Quantum magic rectangles: Characterization and application to certified randomness expansion

We study a generalization of the Mermin-Peres magic square game to arbitrary rectangular dimensions. After exhibiting some general properties, these rectangular games are fully characterized in terms of their optimal win probabilities for quantum strategies. We find that for $m \times n$ rectangular games of dimensions $m,n \geq 3$ there are quantum strategies that win with certainty, while for dimensions $1 \times n$ quantum strategies do not outperform classical strategies. The final case of dimensions $2 \times n$ is richer, and we give upper and lower bounds that both outperform the classical strategies. Finally, we apply our findings to quantum certified randomness expansion to find the noise tolerance and rates for all magic rectangle games. To do this, we use our previous results to obtain the winning probability of games with a distinguished input for which the devices give a deterministic outcome, and follow the analysis of C. A. Miller and Y. Shi [SIAM J. Comput. 46, 1304 (2017)].Comment: 23 pages, 3 figures; published version with minor correction

Surveillance Planning against Smart Insurgents in Complex Terrain

This study is concerned with finding a way to solve a surveillance system allocation problem based on the need to consider intelligent insurgency that takes place in a complex geographical environment. Although this effort can be generalized to other situations, it is particularly geared towards protecting military outposts in foreign lands. The technological assets that are assumed available include stare-devices, such as tower-cameras and aerostats, as well as manned and unmanned aerial systems. Since acquiring these assets depends on the ability to control and monitor them on the target terrain, their operations on the geo-location of interest ought to be evaluated. Such an assessment has to also consider the risks associated with the environmental advantages that are accessible to a smart adversary. Failure to consider these aspects might render the forces vulnerable to surprise attacks. The problem of this study is formulated as follows: given a complex terrain and a smart adversary, what types of surveillance systems, and how many entities of each kind, does a military outpost need to adequately monitor its surrounding environment? To answer this question, an analytical framework is developed and structured as a series of problems that are solved in a comprehensive and realistic fashion. This includes digitizing the terrain into a grid of cell objects, identifying high-risk spots, generating flight tours, and assigning the appropriate surveillance system to the right route or area. Optimization tools are employed to empower the framework in enforcing constraints--such as fuel/battery endurance, flying assets at adequate altitudes, and respecting the climbing/diving rate limits of the aerial vehicles--and optimizing certain mission objectives--e.g. revisiting critical regions in a timely manner, minimizing manning requirements, and maximizing sensor-captured image quality. The framework is embedded in a software application that supports a friendly user interface, which includes the visualization of maps, tours, and related statistics. The final product is expected to support designing surveillance plans for remote military outposts and making critical decisions in a more reliable manner