Searching graphs with A*: applications to job sequencing

The best-first search algorithm A* allows search graphs that are trees, directed acyclic graphs or directed graphs with cycles. In real life applications of A* the search graph is generally implemented as a tree. It is shown here that for certain well known one-machine job sequencing problems that arise in job shops, graph search is much faster than best-first tree search when problem instances are of small and medium size. Moreover, graph search uses less memory and so is able to solve larger problems. Depth-first search needs little memory, and is therefore capable in principle of solving problems of arbitrary size, but is slower than graph search by orders of magnitude for the examples that were studied     

SPLZ: An efficient algorithm for single source shortest path problem using compression method

Efficient solution of the single source shortest path (SSSP) problem on road networks is an important requirement for numerous real-world applications. This paper introduces an algorithm for the SSSP problem using compression method. Owning to precomputing and storing all-pairs shortest path (APSP), the process of solving SSSP problem is a simple lookup of a little data from precomputed APSP and decompression. APSP without compression needs at least 1TB memory for a road network with one million vertices. Our algorithm can compress such an APSP into several GB, and ensure a good performance of decompression. In our experiment on a dataset about Northwest USA (with 1.2 millions vertices), our method can achieve about three orders of magnitude faster than Dijkstra algorithm based on binary heap.     

Scalable model-based clustering for large databases based on data summarization

The scalability problem in data mining involves the development of methods for handling large databases with limited computational resources such as memory and computation time. In this paper, two scalable clustering algorithms, bEMADS and gEMADS, are presented based on the Gaussian mixture model. Both summarize data into subclusters and then generate Gaussian mixtures from their data summaries. Their core algorithm, EMADS, is defined on data summaries and approximates the aggregate behavior of each subcluster of data under the Gaussian mixture model. EMADS is provably convergent. Experimental results substantiate that both algorithms can run several orders of magnitude faster than expectation-maximization with little loss of accuracy.     

A generalized method of moments for closed queueing networks

We introduce a new solution technique for closed product-form queueing networks that generalizes the Method of Moments (MoM), a recently proposed exact algorithm that is several orders of magnitude faster and memory efficient than the established Mean Value Analysis (MVA) algorithm. Compared to MVA, MoM recursively computes higher-order moments of queue lengths instead of mean values, an approach that remarkably reduces the computational costs of exact solutions, especially on models with large numbers of jobs.In this paper, we show that the MoM recursion can be generalized to include multiple recursive branches that evaluate models with different numbers of queues, a solution approach inspired by the Convolution algorithm. Combining the approaches of MoM and Convolution simplifies the evaluation of normalizing constants and leads to large computational savings with respect to the recursive structure originally proposed for MoM.     

Efficient algorithms for mining closed itemsets and their lattice structure

The set of frequent closed itemsets uniquely determines the exact frequency of all itemsets, yet it can be orders of magnitude smaller than the set of all frequent itemsets. In this paper, we present CHARM, an efficient algorithm for mining all frequent closed itemsets. It enumerates closed sets using a dual itemset-tidset search tree, using an efficient hybrid search that skips many levels. It also uses a technique called diffsets to reduce the memory footprint of intermediate computations. Finally, it uses a fast hash-based approach to remove any "nonclosed" sets found during computation. We also present CHARM-L, an algorithm that outputs the closed itemset lattice, which is very useful for rule generation and visualization. An extensive experimental evaluation on a number of real and synthetic databases shows that CHARM is a state-of-the-art algorithm that outperforms previous methods. Further, CHARM-L explicitly generates the frequent closed itemset lattice.     

基于反向PageRank的影响力最大化算法

针对社会网络上的影响力最大化算法在大规模网络上难以同时满足传播范围、时间效率和空间效率要求的问题,提出一种混合PageRank和度中心性的启发式算法（MPRD）。首先,基于PageRank,引入一种反向PageRank思想来评估节点影响力;然后,结合局部指标度中心性,设计一种混合的指标来评估节点的最终影响力;最后,通过相似性方法去掉影响力重合严重的节点,选出种子节点集。在6个数据集和两种传播模型上进行实验,实验结果表明,所提的MPRD在传播范围上优于现有的启发式算法,在时间效率上比贪心算法快四、五个数量级,在空间效率上优于基于反向抽样的IMM算法。所提的MPRD在处理大规模网络上的影响力最大化问题时能够取得传播范围、时间效率和空间效率的平衡。     

Efficient data mining for calling path patterns in GSM networks

In this paper, we explore a new data mining capability that involves mining calling path patterns in global system for mobile communication (GSM) networks. Our proposed method consists of two phases. First, we devise a data structure to convert the original calling paths in the log file into a frequent calling path graph. Second, we design an algorithm to mine the calling path patterns from the frequent calling path graph obtained. By using the frequent calling path graph to mine the calling path patterns, our proposed algorithm does not generate unnecessary candidate patterns and requires less database scans. If the corresponding calling path graph of the GSM network can be fitted in the main memory, our proposed algorithm scans the database only once. Otherwise, the cellular structure of the GSM network is divided into several partitions so that the corresponding calling path sub-graph of each partition can be fitted in the main memory. The number of database scans for this case is equal to the number of partitioned sub-graphs. Therefore, our proposed algorithm is more efficient than the PrefixSpan and a priori-like approaches. The experimental results show that our proposed algorithm outperforms the a priori-like and PrefixSpan approaches by several orders of magnitude.     

CARR: a scalable solution for network packet classification

Modern Internet routers have to handle a large number of packet classification rules, which requires classification schemes to be scalable both in time and space. In this paper, we present a scalable packet classification algorithm that is developed by combining two new concepts to the well‐known bit vector (BV) scheme. We propose a range search method based on a cache‐aware tree (CATree) which makes full use of processor's cache line to reduce the number of dynamic random access memory (DRAM) accesses. Theoretically, the number of DRAM accesses of CATree is about log(m+1) times lower than that of the widely used binary search algorithm, where m is the number of keys in a single cache line. Based on our computational results on a set of 1024 keys, the CATree algorithm is 36% faster than binary search algorithm and the performance is better when applied to a larger set of keys. In addition, we develop a rule re‐arrangement algorithm to reduce the bitmap space of BV. With this re‐arrangement, the rules for the same action may be assigned an identical priority. This reduces the number of priorities as well as the memory space of the bitmap. Furthermore, this also reduces the number of memory accesses and hence, increases the CPU cache utilization. With CATree and rule re‐arrangement, the cache‐aware bit vector with rule re‐arrangement algorithm achieves better performance in comparison with the regular BV scheme, both in space and time. In our experiments, the proposed algorithm reduces the bitmap memory space of a practical set of firewall rules by two orders of magnitude and is 91% faster than the regular BV.     

基于SPB树的公路网络最短路径查询

针对在线地图服务和路程安排等领域中的点对点最短路径查询方法,提出一种新的数据结构——最短路径B+树(SPB树),以有效存储预先计算好的点空间信息和与之对应的最短路径信息.实验结果证明,利用SPB树在公路网络上进行最短路径查询比经典的Dijkstra算法最高快出3个数量级.     

挖掘闭合模式的高性能算法

频繁闭合模式集惟一确定频繁模式完全集并且尺寸小得多,然而挖掘频繁闭合模式仍然是时间与存储开销很大的任务.提出一种高性能算法来解决这一难题.采用复合型频繁模式树来组织频繁模式集,存储开销较小.通过集成深度与宽度优先策略,伺机选择基于数组或基于树的模式支持子集表示形式,启发式运用非过滤虚拟投影或过滤型投影,实现复合型频繁模式树的快速生成.局部和全局剪裁方法有效地缩小了搜索空间.通过树生成与剪裁代价的平衡实现时间效率与可伸缩性最大化.实验表明,该算法时间效率比其他算法高5倍到3个数量级,空间可伸缩性最佳.它可以进一步应用到无冗余关联规则发现、序列分析等许多数据挖掘问题.     

挖掘多支持率分类规则的虚拟投影算法

本文首先提出了一种挖掘频集的高效算法PP。它采用了一种基于树的模式支持集表示，避免了反复扫描数据库和递归建造个数与频繁模式数相同的模式支持集，其效率比Apriori和FPGrowth高1—3个数量级。PP被进一步扩展成发现分类规则的有效算法CRM-PP。CRM-PP将多支持率剪裁集成到频集发现阶段，将二阶段挖掘法改进为单阶段挖掘法。CRM-PP的效率也比基于Apriori和FPGrowth的二阶段算法高1—3个数量级。     

The lazy sweep ray casting algorithm for rendering irregular grids

Lazy sweep ray casting is a fast algorithm for rendering general irregular grids. It is based on the sweep-plane paradigm, and it is able to accelerate ray casting for rendering irregular grids, including disconnected and nonconvex unstructured irregular grids (even with holes) with a rendering cost that decreases as the “disconnectedness” decreases. The algorithm is carefully tailored to exploit spatial coherence even if the image resolution differs substantially from the object space resolution. Lazy sweep ray casting has several desirable properties, including its generality, (depth-sorting) accuracy, low memory consumption, speed, simplicity of implementation and portability (e.g. no hardware dependencies). We establish the practicality of our method through experimental results based on our implementation, which is shown to be substantially faster (by up to two orders of magnitude) than other algorithms implemented in software. We also provide theoretical results, both lower and upper bounds, on the complexity of ray casting of irregular grids     

Memory bandwidth analysis of hierarchical multiprocessors usingmodel decomposition and steady-state flow analysis

For memory bandwidth analysis, researchers generally discard requests that are not accepted during a memory cycle. This assumption simplifies the analysis and produces negligible discrepancies with actual results for a system with a non-hierarchical interconnection network. However, the assumption, “the requests that are not occupied during a memory cycle are discarded,” cannot be used for a multiprocessor system with a hierarchical interconnection network (HIN), because the error introduced assumption can be several orders of magnitude higher than the actual bandwidth. An improved analytical model to determine the bandwidth of a HIN-based system is presented     

A distributed self-scheduler for partially ordered tasks

Large scale scientific applications such as weather modelling and continuous simulation require the orders of magnitude performance improvement available with the new generation of parallel vector supercomputers such as the Floating Point Systems T Series. Many of these applications exhibit a high degree of parallelism, much of which can be expressed as computational tasks which are of varying size and degrees of dependence on one another, and can be partially ordered for execution. DeSPOT (A Distributed Self-Scheduler for Partially Ordered Tasks) is an algorithm for the dynamic distribution of such non-uniform tasks to achieve automatic load balancing on a distributed memory hypercube multiprocessor. This paper describes the DeSPOt algorithm and presents its performance characteristics of various test cases using result timings on the FPS T 20.     

The Hypercube Separation algorithm: A fast and efficient algorithm for on-line handwritten character recognition

This paper introduces a new neural network training algorithm, Hypercube Separation (HCS) algorithm which is very fast and guaranteed to learn. HCS is a simple algorithm suitable for hardware implementation which classifies different input patterns presented to it through the formation of multiple hyperplanes. The performance of the HCS algorithm is compared to that of the Binary Synaptic Weights (BSW) algorithm and to the Backpropagation (BP) algorithm in solving the two spiral problem, which is an almost pathological problem for pattern separation. The HCS algorithm was able to successfully separate the input patterns, requiring three orders of magnitude less training time than the BP algorithm and one order of magnitude less hidden layer nodes than the BSW algorithm. We also present the application of HCS to on-line handwritten character recognition with good results, especially when the simple nature of the algorithm is taken into consideration.     

Efficient evaluation of generalized tree-pattern queries on XML streams

The streaming evaluation is a popular way of evaluating queries on XML documents. Besides its many advantages, it is also the only option for a number of important XML applications. Unfortunately, existing algorithms focus almost exclusively on tree-pattern queries (TPQs). Requirements for flexible querying of XML data have motivated recently the introduction of query languages that are more general and flexible than TPQs. These languages are not supported by existing algorithms. In this paper, we consider a partial tree-pattern query (PTPQ) language which generalizes and strictly contains TPQs. PTPQs can express a fragment of XPath which comprises reverse axes and the node identity equality (is) operator, in addition to forward axes, wildcards and predicates. They constitute an important subclass of XPath, which is very useful in practice. Unfortunately, previous streaming algorithms for TPQs cannot be applied to PTPQs. PTPQs can be represented as dags enhanced with constraints. We explore this representation to design an original polynomial time streaming algorithm for PTPQs. Our algorithm aggressively filters incoming data that is irrelevant to the query and wisely avoids processing redundant query matches (i.e., matches of the query dag that do not contribute to new solutions). Our algorithm is the first one to support the streaming evaluation of such a broad fragment of XPath. We provide an analysis of it, and conduct an extensive experimental evaluation of its performance and scalability. Compared to the only known streaming algorithm that supports TPQs extended with reverse axes, our algorithm performs better by orders of magnitude while consuming a much smaller fraction of memory space. Current streaming applications have stringent requirements on query response time and memory consumption because of the large (possibly unbounded) size of data they handle. In order to keep memory usage and CPU consumption low for the PTPQ streaming evaluation, we design another streaming algorithm called Eager PSX for PTPQs. Its key feature is that it applies an eager evaluation strategy to quickly determine when node matches should be returned as solutions to the user and also to proactively detect redundant matches. We theoretically analyze Eager PSX, and experimentally test its time and space performance and scalability. We compare it with PSX. Our results show that Eager PSX not only achieves better space performance without compromising time performance, but it also greatly improves query response time for both simple and complex queries, in many cases, by orders of magnitude.     

A GPU‐based Streaming Algorithm for High‐Resolution Cloth Simulation

We present a GPU‐based streaming algorithm to perform high‐resolution and accurate cloth simulation. We map all the components of cloth simulation pipeline, including time integration, collision detection, collision response, and velocity updating to GPU‐based kernels and data structures. Our algorithm perform intra‐object and inter‐object collisions, handles contacts and friction, and is able to accurately simulate folds and wrinkles. We describe the streaming pipeline and address many issues in terms of obtaining high throughput on many‐core GPUs. In practice, our algorithm can perform high‐fidelity simulation on a cloth mesh with 2M triangles using 3GB of GPU memory. We highlight the parallel performance of our algorithm on three different generations of GPUs. On a high‐end NVIDIA Tesla K20c, we observe up to two orders of magnitude performance improvement as compared to a single‐threaded CPU‐based algorithm, and about one order of magnitude improvement over a 16‐core CPU‐based parallel implementation.     

Dynamic Load Balancing Computation of Pulses Propagating in a Nonlinear Medium

Loop tiling is an effective optimizing transformation to boost the memory performance of a program, especially for dense matrix scientific computations. The magnitude and stability of the achieved performance improvements are heavily dependent on the appropriate selection of tile sizes. Many existing tile selection algorithms try to find tile sizes which eliminate self-interference cache conflict misses, maximize cache utilization, and minimize cross-interference cache conflict misses. These techniques depend heavily on the actual layout of the arrays in memory. Array padding, an effective data layout optimization technique, is therefore incorporated by many algorithms to help loop tiling stabilize its effectiveness by avoiding pathological array sizes.In this paper, we examine several such combined algorithms in terms of cost-benefit trade-offs, and introduce a new algorithm. The preliminary experimental results show that more precise and costly tile selection and array padding algorithms may not be justified by the resulting performance improvements since such improvements may also be achieved by much simpler and therefore less expensive strategies. The key issues in finding a good tiling algorithm are (1) to identify critical performance factors and (2) to develop corresponding performance models that allow predictions at a sufficient level of accuracy. Following this insight, we have developed a new tiling algorithm that performs better than previous algorithms in terms of execution time and stability, and generates code with a performance comparable to the best measured algorithm. Experimental results on two standard benchmark kernels for matrix multiply and LU factorization show that the new algorithm is orders of magnitude faster than the best previous algorithm without sacrificing stability and execution speed of the generated code.     

Estimating graph distance and centrality on shared nothing architectures

We present a parallel toolkit for pairwise distance computation in massive networks. Computing the exact shortest paths between a large number of vertices is a costly operation, and serial algorithms are not practical for billion‐scale graphs. We first describe an efficient parallel method to solve the single source shortest path problem on commodity hardware with no shared memory. Using it as a building block, we introduce a new parallel algorithm to estimate the shortest paths between arbitrary pairs of vertices. Our method exploits data locality, produces highly accurate results, and allows batch computation of shortest paths with 7% average error in graphs that contain billions of edges. The proposed algorithm is up to two orders of magnitude faster than previously suggested algorithms and does not require large amounts of memory or expensive high‐end servers. We further leverage this method to estimate the closeness and betweenness centrality metrics, which involve systems challenges dealing with indexing, joining, and comparing large datasets efficiently. In one experiment, we mined a real‐world Web graph with 700 million nodes and 12 billion edges to identify the most central vertices and calculated more than 63 billion shortest paths in 6 h on a 20‐node commodity cluster. Copyright © 2014 John Wiley & Sons, Ltd.     

B样条曲线曲面的节点消去算法研究

在分析了Tiller给出的B样条曲线节点消去算法的基础上,提出了改进算法。改进算法充分地利用了B样条曲线的局部性质,无需考虑节点消去的顺序,一次消去多个节点。实验表明,与Tiller的算法相比较,改进后的算法效率有较大提高。