Important Data Structures and Operations. The next step after profiling for the designer is to locate the important data structures and operations at the computationally intensive part of the algorithm. Data structures are important as using the proper ones the computations can be in parallel. As most appropriate Data Structures for mapping at reconfigurable hardware are considered static structures, with 1 and 2 dimensions tables as the most suitable. Dynamic structures using pointers, as trees, are considered as inappropriate structures for mapping in reconfigurable hardware If for example there is a comparison of an input against many comparators working in parallel will boost design performance, but even a DFS in a binary tree is challenging to map it in hardware efficiently. Operations are also important in order to identify how system arithmetic will be implemented. If the application uses integers, and in which range, vs. single- or double-precision floating point numbers the required hardware resources may change substantially. Identifying the arithmetic, the designer will assign the available resources in order to achieve the maximum performance.
Important Data Structures and Operations. This section describes all the important data structures and operations, which are implemented by the Count-Min algorithm, as described above, and they will be presented in our hardware-based proposed architecture. As described in Section 4.1, the Count–Min algorithm implements a data structure that summarizes the information from streaming data and it can serve various types of queries on streaming data. This core data structure is a 2-dimensional array, i.e. count[w, d], which stores the synopses of the input streaming data. The size of the 2-dimensional array is defined by the w and d parameters, which are defined by two factors: ε and δ, where the error in answering the query is within a factor of ε with probability δ. Thus, the factors ε and δ, which as described in Section 4.1 are selected with the formulas d=⌈ln(1/δ)⌉and w =⌈e/ε⌉, can tune the size of the implemented 2-dimensional array based on the space that is available and the accuracy of the results that the data structure can offer. The Count-Min algorithm uses hashing techniques to process the updates and report queries using sub linear space. Thus, the hash functions are pair wise independent to ensure lower number of collisions in the hash implementation. These hash functions can be precomputed and placed in local lookup tables, i.e. internal BRAMs of the FPGA device. Another important issue of the Count-Min algorithm is the data input during the update process. The data streams are modeled as vectors, where each element consists of two values, i.e. the id and the incrementing value. When an new update transaction, i.e. (id, value), arrives, the algorithm hashes through each of the hash functions h1...hd and increment the corresponding w entries. At any time, the approximate value of an element can get be computed from the minimum value in each of the d cells of count table, where the element hashes to. This is typically called the Point Query that returns an approximation of an input element. Similarly a Count-Min sketch can get the approximation query for ranges, which is typically a summation over multiple point queries.
Important Data Structures and Operations. This section describes all the important data structures and operations of the Exponential Histogram algorithm, which are implemented by our hardware-based architecture. As described above, the EH algorithm maintains the number of the elements with 1 values over a stream. The EH data structure is a list of buckets in a row, which are connected with each other. The number of buckets depends on the processing window size while the number of the size of each bucket is defined by the acceptable error rate ε, as described in 2.4. During the insert function there are three different processes that need to take place. First, the EH data structure is examined, if it contains expired data, i.e. data that do not belong anymore to the processing window. Second, the new timestamp of the element with 1 value inserts to the first bucket. Third, all the buckets of the data structure are examined in order to merge buckets that reach to their maximum size. Moreover, the EH data structure can estimate the number of the 1‟s that have appeared either in a complete window of time or from a specific timestamp up to the most recent current timestamp. The estimation of the 1s values over a window size is an easy procedure as the EH keeps at each time the total number of the 1s that have appeared and the number of the 1s at the last bucket level. Thus, the calculation of the total number of the 1‟s values takes places using these two counters. On the other hand, the calculation of the 1‟s values from a specific timestamp till recent timestamp needs the traversing of the EH data structure till to the specific timestamp by adding the estimation values from the previous buckets.
Important Data Structures and Operations. This section describes the basic data structures that were used for the computation of the HY estimator. As described above, we implemented a variation of the official algorithm that calculates the Xxxxxxx-Xxxxxxx estimator. Our proposed solution offers lower time complexity and takes advantage of the algorithm‟s streaming nature. First, we implemented a data structure that keeps the stocks‟ transaction values at the beginning and at the end of the overlapping time intervals for each pair of the input stocks. This data structure is a 2-dimensionalarray that stores at each timestamp the new transactions of the stocks (if they exist). Next, these values are used for the computation of the HY covariance, as presented from equation of Figure 11. Next, we used another 2-dimensional array that keeps just the transactions of the stocks. This table is, also, updated by the transaction values that arrive at each timestamp. The values of this array are used for the calculation of the denominator values of the HY estimator.
Important Data Structures and Operations. Data Structures As mentioned in the beginning of the SVM Modeling section, the LIBSVM software receives as input a file that follows a specific format. The information contained in this file is copied to a data structure so as to be able to utilize the given information. Prior to describing this important structure we need to provide further information about the input file. More specifically, although the number of features a data instance can have equals the maximum number of features of the dataset, this does not imply that all data instances will feature equal to the maximum number of features. For example, in a dataset where the maximum number of instances is equal to 6, data instance 1 could have features 1, 2 and 3 and data instance 2 could have features 4 and 5. Not having a specific feature implies that the value of this feature is 0. Thus data instance 1 has value 0 in columns 4 and 5, since these columns correspond to features 4 and 5. Similarly data instance 2 has value 0 in columns 1, 2 and 3. The data structure that contains the above information is essential to the algorithm, as all the important functions of the implementation need it to produce outcomes. In order to understand its elements we describe the following two structures. structsvm_node { int index; double value; }; structsvm_problem { int l; double *y; structsvm_node **x; };
Important Data Structures and Operations. Variational Inference and standard Xxxxx sampling are mentioned as these are the basic algorithms for LDA. Sparse LDA achieves performance improvement up to 20x over these algorithms, using a new algorithmic approach. For that reason it is not worthy to analyze further the Variational Inference and standard Xxxxx sampling, and so we focus only on SparseLDA.
