Emerging memory technologies have a significant gap between the cost, both in
time and in energy, of writing to memory versus reading from memory. In this
paper we present models and algorithms that account for this difference, with a
focus on write-efficient sorting algorithms. First, we consider the PRAM model
with asymmetric write cost, and show that sorting can be performed in
$O\left(n\right)$ writes, $O\left(n \log n\right)$ reads, and logarithmic depth
(parallel time). Next, we consider a variant of the External Memory (EM) model
that charges $\omega > 1$ for writing a block of size $B$ to the secondary
memory, and present variants of three EM sorting algorithms (multi-way
mergesort, sample sort, and heapsort using buffer trees) that asymptotically
reduce the number of writes over the original algorithms, and perform roughly
$\omega$ block reads for every block write. Finally, we define a variant of the
Ideal-Cache model with asymmetric write costs, and present write-efficient,
cache-oblivious parallel algorithms for sorting, FFTs, and matrix
multiplication. Adapting prior bounds for work-stealing and
parallel-depth-first schedulers to the asymmetric setting, these yield parallel
cache complexity bounds for machines with private caches or with a shared
cache, respectively
In this paper, we study the problem of moving n sensors on a line to form a barrier coverage of a specified segment of the line such that the maximum moving distance of the sensors is minimized. Previously, it was an open question whether this problem on sensors with arbitrary sensing ranges is solvable in polynomial time. We settle this open question positively by giving an O(n 2 log n) time algorithm. For the special case when all sensors have the same-size sensing range, the previously best solution takes O(n 2 ) time. We present an O(n log n) time algorithm for this case; further, if all sensors are initially located on the coverage segment, our algorithm takes O(n) time. Also, we extend our techniques to the cycle version of the problem where the barrier coverage is for a simple cycle and the sensors are allowed to move only along the cycle. For sensors with the same-size sensing range, we solve the cycle version in O(n) time, improving the previously best O(n 2 ) time solution.
We introduce Approximate Agglomerative Clustering (AAC), an efficient, easily parallelizable algorithm for generating high-quality bounding volume hierarchies using agglomerative clustering. The main idea of AAC is to compute an approximation to the true greedy agglomerative clustering solution by restricting the set of candidates inspected when identifying neighboring geometry in the scene. The result is a simple algorithm that often produces higher quality hierarchies (in terms of subsequent ray tracing cost) than a full sweep SAH build yet executes in less time than the widely used top-down, approximate SAH build algorithm based on binning.
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