Multiresolution Priority Queues

Priority queues are container data structures essential to many high performance computing applications. In this paper, we introduce multiresolution priority queues , a data structure that achieves greater performance than the standard heap based implementation 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 to (log(n)) O , where is the number of elements in the queue (log(r)) O n and is the number of resolution groups in the priority space. r The worst case cost of extracting the top element is . (1) O When the number of elements in the table is high, the amortized cost to insert an element becomes . (1) O 1. Iɴᴛʀᴏᴅᴜᴄᴛɪᴏɴ Priority queues are a type of container data structures designed to guarantee that the element at the front of the queue is the greatest of all the elements it contains, according to some total ordering defined by their priority . This allows for elements of higher priority to be extracted first, independently of the order in which they are inserted into the queue. Fast implementations of priority queues are important to many high performance computing (HPC) applications and hence optimizing their performance has been the subject of intense research. In graph searching, the algorithmic complexity of essential algorithms such as finding the shortest path between two nodes in a graph rely entirely on the performance of a priority queue (see for instance Dijkstra’s algorithm [1] , [2] ). Other essential applications are found in the field of bandwidth management. For instance, in the Internet, routers often have insufficient capacity to transmit all packets at line rate and so they use priority queues in order to assign higher preference to those packets that are most critical in preserving the quality of experience (QoE) of the network (e.g., packets carrying delay sensitive data such as voice). Priority queues are also important in other areas of research including Huffman compression codes, operating systems, Bayesian spam filtering, discrete optimization, simulation of colliding particles, or artificial intelligence to name some examples. The work we present stems from research on improving the performance of a priority queue by introducing a trade-off to exploit an existing gap between the applications’ requirements and the set of priorities supported by a priority queue. With this objective, we introduce the concept of multiresolution priority queue , a new container data structure that can flexibly trade off a controllable amount of resolution in the space of priorities in exchange for achieving greater performance. A simple example works as follows. Suppose that we use a priority queue to hold jobs that need job , , ..., job } { 1 job2 n to be scheduled using a “shortest job first” policy. Each job takes a time to process equal to , and the removal jobi pi of an element from the queue returns the job with the smallest processing time . (Hence determines in{p } m i pi the priority of each job.) A common approach is to use a binary heap based implementation of a priority queue, which effectively provides support for all possible range of priorities in the space of real numbers . Assume now pi that the set of possible priority values is discretized into pi subsets and that the application only requires l guaranteeing the ordering between elements belonging to different subsets. A multiresolution priority queue is a data structure that can provide better performance than a standard priority queue by supporting the coarser grained resolution space consisting of subsets rather than the l complete set of priorities. Multiresolution priority queues can also be understood as a generalization of standard priority queues in which the total ordering requirement imposed on the set of priorities is relaxed, allowing for elements in the queue to be only partially ordered. Hence an alternative name to refer to this type of container data structures would be partial order priority queues. This paper is organized as follows. In Section 2, we summarize some of the main historical results in the research area of high performance priority queues. Section 3 presents the body of our work, introducing a formal definition of the concept of multiresolution priority queues , providing pseudocode for the main routines to insert and extract elements from the queue, and analyzing the algorithm’s complexity. This section introduces also two variants of the base algorithm to support sliding priority windows for applications such as event-driven simulators and a binary tree based optimization applicable to general graph algorithms such as finding the shortest path between two nodes. Section 4 describes our implementation of a multiresolution priority queue and demonstrates how it can help a real world HPC application achieve greater performance than a traditional binary heap based solution.