Given a grid terrain T and a viewpoint v, the viewshed of v is the set of grid points of T that are visible from v. To decide whether a point p is visible one needs to interpolate the elevation of the terrain along the line-of-sight vp. Existing viewshed algorithms differ widely in what points they chose to interpolate and how they interpolate the terrain. These choices crucially affect the running time and accuracy of the algorithms. This paper describes I O-efficient algorithms for computing visibility maps in a couple of different models. First, we describe two algorithms that sweep the terrain by rotating a ray around the viewpoint while maintaining the terrain profile along the ray. Second, we describe an algorithm which sweeps the terrain centrifugally, growing a star-shaped region around the viewpoint while maintaining the approximate visible horizon of the terrain within the swept region. Our last two algorithms are based on computing and merging horizons. All algorithms are I O-efficient in the I O-model of Aggarwal and Vitter. We present an experimental analysis on large terrains obtained from NASA SRTM data. All our algorithms are scalable to volumes of data that are over 50 times larger than main memory. Our main finding is that, in practice, horizons are significantly smaller than their theoretical worst case bound, which makes horizon-based approaches very fast. Our last two algorithms, which compute the most accurate viewshed, turn out to be very fast in practice, although their worst-case bound is inferior.
Haverkort, Toma and Zhuang @cite_12 presented the first IO-efficient viewshed algorithm using Van Kreveld's model. Using a technique called they turned Van Kreveld's algorithm into an algorithm running in @math time and @math , cache-obliviously. The authors also presented practical results showing that their algorithm scales well to large data and outperforms Van Kreveld's algorithm running in (virtual) memory.
@cite_12
2473549844 2145588009 2042852020 2029463952
We consider the adversarial convex bandit problem and we build the first @math -time algorithm with @math -regret for this problem. To do so we introduce three new ideas in the derivative-free optimization literature: (i) kernel methods, (ii) a generalization of Bernoulli convolutions, and (iii) a new annealing schedule for exponential weights (with increasing learning rate). The basic version of our algorithm achieves @math -regret, and we show that a simple variant of this algorithm can be run in @math -time per step at the cost of an additional @math factor in the regret. These results improve upon the @math -regret and @math -time result of the first two authors, and the @math -regret and @math -time result of Hazan and Li. Furthermore we conjecture that another variant of the algorithm could achieve @math -regret, and moreover that this regret is unimprovable (the current best lower bound being @math and it is achieved with linear functions). For the simpler situation of zeroth order stochastic convex optimization this corresponds to the conjecture that the optimal query complexity is of order @math . Given an arbitrary viewpoint v and a terrain, the visibility map or viewshed of v is the set of points in the terrain that are visible from v. In this article we consider the problem of computing the viewshed of a point on a very large grid terrain in external memory. We describe algorithms for this problem in the cache-aware and cache-oblivious models, together with an implementation and an experimental evaluation. Our algorithms are a novel application of the distribution sweeping technique and use O(sort(n)) I Os, where sort(n) is the complexity of sorting n items of data in the I O-model. The experimental results demonstrate that our algorithm scales up and performs significantly better than the traditional internal-memory plane sweep algorithm and can compute visibility for terrains of 1.1 billion points in less than 4 hours on a low-cost machine compared to more than 32 hours with the internal-memory algorithm. In this paper, we present an efficient implementation of theO(mn + n2 logn) time algorithm originally proposed by Nagamochi and Ibaraki (1992) for computing the minimum capacity cut of an undirected network. To enhance computation, various ideas are added so that it can contract as many edges as possible in each iteration. To evaluate the performance of the resulting implementation, we conducted extensive computational experiments, and compared the results with that of Padberg and Rinaldi's algorithm (1990), which is currently known as one of the practically fastest programs for this problem. The results indicate that our program is considerably faster than Padberg and Rinaldi's program, and its running time is not significantly affected by the types of the networks being solved. The efficient, distributed factorization of large matrices on clusters of commodity machines is crucial to applying latent factor models in industrial-scale recommender systems. We propose an efficient, data-parallel low-rank matrix factorization with Alternating Least Squares which uses a series of broadcast-joins that can be efficiently executed with MapReduce. We empirically show that the performance of our solution is suitable for real-world use cases. We present experiments on two publicly available datasets and on a synthetic dataset termed Bigflix, generated from the Netflix dataset. Bigflix contains 25 million users and more than 5 billion ratings, mimicking data sizes recently reported as Netflix' production workload. We demonstrate that our approach is able to run an iteration of Alternating Least Squares in six minutes on this dataset. Our implementation has been contributed to the open source machine learning library Apache Mahout.