We propose the design and an implementation of a bulk-parallel external memory priority queue to take advantage of both shared-memory parallelism and high external memory transfer speeds to parallel disks. To achieve higher performance by decoupling item insertions and extractions, we offer two parallelization interfaces: one using "bulk" sequences, the other by defining "limit" items. In the design, we discuss how to parallelize insertions using multiple heaps, and how to calculate a dynamic prediction sequence to prefetch blocks and apply parallel multiway merge for extraction. Our experimental results show that in the selected benchmarks the priority queue reaches 75% of the full parallel I/O bandwidth of rotational disks and and 65% of SSDs, or the speed of sorting in external memory when bounded by computation.
A number of concurrent, relaxed priority queues have recently been proposed and implemented. Results are commonly reported for a throughput benchmark that uses a uniform distribution of keys drawn from a large integer range, and mostly for single systems. We have conducted more extensive benchmarking of three recent, relaxed priority queues on four different types of systems with different key ranges and distributions. While we can show superior throughput and scalability for our own k-LSM priority queue for the uniform key distribution, the picture changes drastically for other distributions,…
Priority queues with parallel access are an attractive data structure for applications like prioritized online scheduling, discrete event simulation, or greedy algorithms. However, a classical priority queue constitutes a severe bottleneck in this context, leading to very small throughput. Hence, there has been significant interest in concurrent priority queues with relaxed semantics. We investigate the complementary quality criteria rank error (how close are deleted elements to the global minimum) and delay (for each element x, how many elements with lower priority are deleted before x). In t…
Priority queues are container data structures essential to many high performance computing (HPC) applications. In this paper, we introduce multiresolution priority queues, a data structure that improves the performance of the standard heap based implementations by trading off a controllable amount of resolution in the space of priorities. The new data structure can reduce the worst case performance of inserting an element from O(log(n)) to O(log(r)), where n is the number of elements in the queue and r is the number of resolution groups in the priority space. The worst case cost of removing th…
We address the single source shortest path planning problem (SSSP) in the case of floating point edge weights. We show how any integer based Dijkstra solution that relies on a monotone integer priority queue to create a full ordering over path lengths in order to solve integer SSSP can be used as an oracle to solve floating point SSSP with positive edge weights (floating point P-SSSP). Floating point P-SSSP is of particular interest to the robotics community. This immediately yields a handful of faster runtimes for floating point P-SSSP; for example, ${O({m + n\log \log \frac{C}δ})}$, where $C…
A priority queue is a fundamental data structure that maintains a dynamic set of (key, priority)-pairs and supports Insert, Delete, ExtractMin and DecreaseKey operations. In the external memory model, the current best priority queue supports each operation in amortized $O(\frac{1}{B}\log \frac{N}{B})$ I/Os. If the DecreaseKey operation does not need to be supported, one can design a more efficient data structure that supports the Insert, Delete and ExtractMin operations in $O(\frac{1}{B}\log \frac{N}{B}/ \log \frac{M}{B})$ I/Os. A recent result shows that a degradation in performance is inevit…
One of the biggest open problems in external memory data structures is the priority queue problem with DecreaseKey operations. If only Insert and ExtractMin operations need to be supported, one can design a comparison-based priority queue performing $O((N/B)\lg_{M/B} N)$ I/Os over a sequence of $N$ operations, where $B$ is the disk block size in number of words and $M$ is the main memory size in number of words. This matches the lower bound for comparison-based sorting and is hence optimal for comparison-based priority queues. However, if we also need to support DecreaseKeys, the performance o…
Designing and implementing efficient parallel priority schedulers is an active research area. An intriguing proposed design is the Multi-Queue: given $n$ threads and $m\ge n$ distinct priority queues, task insertions are performed uniformly at random, while, to delete, a thread picks two queues uniformly at random, and removes the observed task of higher priority. This approach scales well, and has probabilistic rank guarantees: roughly, the rank of each task removed, relative to remaining tasks in all other queues, is $O(m)$ in expectation. Yet, the performance of this pattern is below that o…
We present a deterministic oblivious LIFO (Stack), FIFO, double-ended and double-ended priority queue as well as an oblivious mergesort and quicksort algorithm. Our techniques and ideas include concatenating queues end-to-end, size balancing of multiple arrays, several multi-level partitionings of an array. Our queues are the first to enable executions of pop and push operations without any change of the data structure (controlled by a parameter). This enables interesting applications in computing on encrypted data such as hiding confidential expressions. Mergesort becomes practical using our …
We present priority queues in the cache-oblivious external memory model with block size $B$ and main memory size $M$ that support on $N$ elements, operation \textsc{UPDATE} (combination of \textsc{INSERT} and \textsc{DECREASEKEY}) in $O \left(\frac{1}{B}\log_{\fracλ{B}} \frac{N}{B}\right)$ amortized I/Os and operations \textsc{EXTRACT-MIN} and \textsc{DELETE} in $O \left(\lceil \frac{λ^{\varepsilon}}{B} \log_{\fracλ{B}} \frac{N}{B} \rceil \log_{\fracλ{B}} \frac{N}{B}\right)$ amortized I/Os, using $O \left(\frac{N}{B}\log_{\fracλ{B}} \frac{N}{B}\right)$ blocks, for a user-defined parameter $λ\i…
Consider the following random process: we are given $n$ queues, into which elements of increasing labels are inserted uniformly at random. To remove an element, we pick two queues at random, and remove the element of lower label (higher priority) among the two. The cost of a removal is the rank of the label removed, among labels still present in any of the queues, that is, the distance from the optimal choice at each step. Variants of this strategy are prevalent in state-of-the-art concurrent priority queue implementations. Nonetheless, it is not known whether such implementations provide any …
We show the $O(\log n)$ time extract minimum function of efficient priority queues can be generalized to the extraction of the $k$ smallest elements in $O(k \log(n/k))$ time (we define $\log(x)$ as $\max(\log_2(x), 1)$.), which we prove optimal for comparison-based priority queues with $o(\log n)$ time insertion. We show heap-ordered tree selection (Kaplan et al., SOSA '19) can be applied on the heap-ordered trees of the classic Fibonacci heap and Brodal queue, in $O(k \log(n/k))$ amortized and worst-case time, respectively. We additionally show the deletion of $k$ elements or selection withou…
A Grouped Sorting Queue Supporting Dynamic Updates for Timer Management in High-Speed Network Interface Cards
School of Microelectronics, Xidian University（西安电子科技大学微电子学院）；State Key Laboratory of Integrated Service Networks, Xidian University（西安电子科技大学综合业务网理论及关键技术国家重点实验室）
