Non-incremental Algorithm Research Articles

Incremental NFA minimization

We tackle the (classic) problem of minimizing (non)deterministic finite automata. The algorithm we put forward has the peculiarity of being incremental, i.e., the minimization proceeds by successive iterations, each producing a partially minimized automaton language-equivalent to the input one.Our algorithm builds upon Almeida et al. from 2014, fixing a minor mistake and generalizing it to the nondeterministic case. It relies on a colouring procedure of a graph associated to the automaton, keeping track of partial information. After dealing with the deterministic case, we extend this idea to the bisimulation-minimization of nondeterministic automata.The algorithms for both the deterministic and the nondeterministic cases run in time O(nm) for an automaton with n states and m transitions. The complexity for the deterministic case matches the complexity claimed by Almeida et al.. The nondeterministic case improves the fastest known incremental algorithm for this problem.We conclude introducing and using a notion of signature of a state, whose aim is to exploit pre-computed information potentially available, to speed-up the process. A signature is used to produce an initial partition of the automaton's states and can be easily integrated in both the incremental and the non-incremental algorithm.

Information granularity-based incremental feature selection for partially labeled hybrid data

Feature selection can reduce the dimensionality of data effectively. Most of the existing feature selection approaches using rough sets focus on the static single type data. However, in many real-world applications, data sets are the hybrid data including symbolic, numerical and missing features. Meanwhile, an object set in the hybrid data often changes dynamically with time. For the hybrid data, since acquiring all the decision labels of them is expensive and time-consuming, only small portion of the decision labels for the hybrid data is obtained. Therefore, in this paper, incremental feature selection algorithms based on information granularity are developed for dynamic partially labeled hybrid data with the variation of an object set. At first, the information granularity is given to measure the feature significance for partially labeled hybrid data. Then, incremental mechanisms of information granularity are proposed with the variation of an object set. On this basis, incremental feature selection algorithms with the variation of a single object and group of objects are proposed, respectively. Finally, extensive experimental results on different UCI data sets demonstrate that compared with the non-incremental feature selection algorithms, incremental feature selection algorithms can select a subset of features in shorter time without losing the classification accuracy, especially when the group of objects changes dynamically, the group incremental feature selection algorithm is more efficient.

A dynamic knowledge base and its data compression with homomorphism

In reality there are always a large number of complex massive databases. The notion of homomorphism may be a mathematical tool for studying data compression in knowledge bases. This paper investigates a knowledge base in dynamic environments and its data compression with homomorphism, where “dynamic” refers to the fact that the involved information systems need to be updated with time due to the inflow of new information. First, the relationships among knowledge bases, information systems and relation information systems are illustrated. Next, the idea of non-incremental algorithm for data compression with homomorphism and the concept of dynamic knowledge base are introduced. Two incremental algorithms for data compression with homomorphism in dynamic knowledge bases are presented. Finally, an experimental analysis is employed to demonstrate the applications of the non-incremental algorithm and the incremental algorithms for data compression when calculating the knowledge reduction of dynamic knowledge bases.

Incremental construction of three-way concept lattice for knowledge discovery in social networks

Three-way concept analysis (3WCA), a combination of three-way decision and formal concept analysis, is widely used in the field of knowledge discovery. Generally, constructing three-way concept lattices requires the original formal context and its complement context simultaneously. Additionally, the existing three-way concept lattice construction algorithms focus on the static formal context, and cannot cope with the dynamic formal context that is an essential representation in social networks. Toward this end, this paper pioneers a novel problem and method for the incremental construction of three-way concept lattice for knowledge discovery in social networks. Aiming to facilitate the construction efficiency, this paper firstly investigates the three-way concept lattice construction for attribute-incremental/object-incremental formal contexts, respectively. Then, the dynamic formal context of a social network can be viewed as a special formal context with both attribute-increment and object-increment. Further, we develop the AE/OE concept lattice incremental construction algorithms, called SNS-AE and SNS-OE. Extensive experiments are conducted on various formal contexts to evaluate the effectiveness of our incremental algorithms. The experimental results demonstrate that our proposed incremental algorithms can significantly decrease the construction time of three-way concept lattice compared to the non-incremental algorithm.

Object-First Incremental Algorithms for Updating Approximations in Multi-Granulation Fuzzy Probabilistic Rough Sets Over Two Universes

Multi-granulation fuzzy probabilistic rough set (MFPRS) model over two universes has various applications in recent years. However, data are typically changing with time in real-life applications. When data changes, people have to spend a lot of unnecessary time to recalculate the approximations in MFPRS over two universes. To address this problem, we design incremental algorithms based on the object-first approach for updating approximations in MFPRS over two universes while the objects are added into or removed from the two universes. Firstly, considering a case where the equivalence class of the object with respect to the fuzzy relation could be empty, we introduce a model of type-empty MFPRS over two universes. Then, based on the matrix, a traditional algorithm is introduced to calculate approximations in MFPRS over two universes. In addition, by optimizing the traditional algorithm, we design the object-first algorithm which could calculate approximations more efficient in MFPRS over two universes. After that, based on the object-first algorithm, four object-first incremental algorithms are designed for updating approximations in MFPRS over two universes while the objects are added into or removed from two universes. Finally, experimental results show that the proposed object-first incremental algorithms for updating approximations in MFPRS over two universes are more efficient in comparison with the non-incremental algorithms and the traditional incremental algorithms.

An efficient pipeline processing scheme for programming Protocol-independent Packet Processors

OpenFlow is unable to provide customized flow tables, resulting in memory explosions and high switch retirement rates. This is the bottleneck for the development of SDN. Recently, P4 (Programming Protocol-independent Packet Processors) attracts much attentions from both academia and industry. It provides customized networking services by offering flow-level control. P4 can “produce” various forwarding tables according to packets. P4 increases the speed of custom ASICs. However, with the prevalence of P4, the multiple forwarding tables could explode when used in large scale networks. The explosion problem can slow down the lookup speed, which causes congestions and packet losses. In addition, the pipelined structure of forwarding tables brings additional processing delay. In this study, we will improve the lookup performance by optimizing the forwarding tables of P4. Intuitively, we will install the rules according to their popularity, i.e., the popular rules will appear earlier than others. Thus, the packets can hit the matched rule sooner. In this paper, we formalize the optimization problem, and prove that the problem is NP-hard. To solve the problem, we propose a heuristic algorithm called EPSP (Efficient Pipeline Processing Scheme for P4), which can largely reduce the lookup time while keeping the forwarding actions the same. Because running the optimization algorithm frequently brings additional processing burdens, wedesign an incremental update algorithm to alleviate this problem. To evaluate the proposed algorithms, we set up the simulation environments based on ns-3. The simulation results show that the algorithm greatly reduces both the lookup time and the number of memory accesses. The incremental algorithm largely reduces the processing burdens while the lookup time remains almost the same with the non-incremental algorithm. We also implemented a prototype using floodlight and mininet. The results show that our algorithm brings acceptable burder, and performs better than traditional algorithm.

An incremental algorithm for the role mining problem

The role mining process, i.e., computing minimal set of roles from a user-permission assignment relation, is rather incremental task. In a usual situation the set of roles is already established, and the existing permissions are evolved according to current needs. Computation of roles from scratch after each small change in the data is inefficient. Surprisingly, no incremental algorithm for role mining problem exists. The paper proposes a first attempt to an incremental algorithm for role mining problem. The algorithm is tested with several real-world datasets. The results show that the proposed algorithm is significantly faster than non-incremental algorithms, and in many cases, produces a smaller number of roles than the non-incremental version of the algorithm.

Incremental updating probabilistic neighborhood three-way regions with time-evolving attributes

Neighborhood decision systems (NDSs) are commonly-used systems in real-world applications such as credit scoring. Probabilistic neighborhood rough sets (PNRSs) model, which is a generalized rough set model by combining neighborhood rough sets (NRSs) with probabilistic theory, can efficiently handle numerical data with noise values and allow tolerance of errors. Approximations of a target concept are fundamental and vital notions of the PNRSs, which can induce the certain and uncertain decision rules. Nevertheless, data evolves over time due to dynamic characteristics, especially, the addition of new attributes and the deletion of redundant or irrelevant attributes. Therefore, the potential meaningful knowledge may alter over time accordingly. To improve the efficiency of acquiring decision rules, the three-way regions (i.e., the positive, negative, and boundary regions) of the PNRSs need to be updated in an incremental fashion. To address this issue, two incremental algorithms for updating the three-way regions of each decision class of the PNRSs are investigated from the matrix perspective with time-evolving attributes (namely, adding attributes and deleting attributes). First, a matrix-based characterization of the three-way regions of each decision class of the PNRSs is constructed. Subsequently, considering the variation of the attributes, matrix-based updating mechanisms for relevant matrices are developed by means of the previously calculated information. Furthermore, the incremental algorithms are developed by taking advantage of the matrix-based updating mechanisms. Comprehensive experiments are performed on benchmark UCI data sets, and comparative results demonstrate our proposed algorithms consistently outperform the non-incremental algorithm in terms of computational efficiency.

Incremental feature selection for dynamic hybrid data using neighborhood rough set

Feature selection with rough sets aims to delete redundant conditional features from static data by considering single type features. However, traditional feature selection methods generally ignore real-world scenarios: hybrid conditional feature set including missing, categorical and numerical ones coexists in the data, and the object set may change dynamically in one by one over time. To deal with dynamic hybrid data with mixed-type features, we propose a neighborhood entropy-based incremental feature selection framework by neighborhood rough set model. In this paper, the dynamics of an object set involves the change of a single object and multiple objects. Therefore, two incremental feature selection algorithms are developed for hybrid data with the dynamic change of a single object and multiple objects, respectively. At first, an incremental manner is utilized to compute the neighborhood entropy as feature criterion. On this basis, the incremental computations of feature significance are used to select candidate features in a descending order. Meanwhile, a deletion strategy is employed to filter out redundant features from the selection results. Finally, experimental results on different real-life data sets demonstrate the proposed incremental algorithms can outperform the non-incremental algorithm for feature selection in speed within comparable classification accuracy. Especially for multiple objects adding into and deleting from the hybrid data, the incremental algorithm is more efficient to select a subset of features than the algorithm for handling the dynamic change of a single object.

Incremental approaches to update multigranulation approximations for dynamic information systems

Multigranulation rough set (MGRS) theory provides an effective manner for the problem solving by making use of multiple equivalence relations. As the information systems always dynamically change over time due to the addition or deletion of multiple objects, how to efficiently update the approximations in multigranulation spaces by making fully utilize the previous results becomes a crucial challenge. Incremental learning provides an efficient manner because of the incorporation of both the current information and previously obtained knowledge. In spite of the success of incremental learning, well-studied findings performed to update approximations in multigranulation spaces have relatively been scarce. To address this issue, in this paper, we propose matrix-based incremental approaches for updating approximations from the perspective of multigranulation when multiple objects vary over time. Based on the matrix characterization of multigranulation approximations, the incremental mechanisms for relevant matrices are systematically investigated while adding or deleting multiple objects. Subsequently, in accordance with the incremental mechanisms, the corresponding incremental algorithms for maintaining multigranulation approximations are developed to reduce the redundant computations. Finally, extensive experiments on eight datasets available from the University of California at Irvine (UCI) are conducted to verify the effectiveness and efficiency of the proposed incremental algorithms in comparison with the existing non-incremental algorithm.

Testing and Diagnosis of Delay Faults in Finfet VLSI Circuits using Non-Incremental Genetic Algorithm

FinFet transistors are used in major semiconductor organizations which play a significant role in the development of the silicon industries. Due to few embedded memories and other circuit issues the transistors have specific faults in manufacturing, designing of the circuit etc. This paper presents an advanced test algorithm to diagnose those faults. The circuit with different gates is designed to identify the places having faults. In addition, algorithms such as non-incremental algorithms is used to find critical path, path delay and PDF of Critical path delay and Genetic Algorithm for optimisation of Critical path delay for sensitive test vector and no of iterations. The transfer characteristics curve is plotted along with the delay curve which helps in finding out the simulation parameters such as noise margin, propagation delay. The results in the methodology calculate the probability density function of the critical path by estimating mean, standard deviation and variance. The advantages of the integration of the two algorithms in this paper help in analyzing the specific faults in the circuits and the error correction of the broken link in the path analysis and has enhanced performance. Furthermore, more complicated circuits are analyzed for fault detection with different approach. In this paper the research work on testing, diagnosis, estimation of Critical path and PDF of Critical path delay faults for FinFET based Combinational Circuits for 20nm and 32 nm Technologies are presented for the first time using latest Non Incremental Genetic algorithm.

Discernibility matrix based incremental feature selection on fused decision tables

In rough set philosophy, each set of data can be seen as a fuzzy decision table. Since a decision table dynamically increases with time and space, these decision tables are integrated into a new one called fused decision table. In this paper, we focus on designing an incremental feature selection method on fused decision table by optimizing the space constraint of storing discernibility matrix. Here discernibility matrix is a known way of discernibility information measure in rough set theory. This paper applies the quasi/pseudo value of discernibility matrix rather than the true value of discernibility matrix to design an incremental mechanism. Unlike those discernibility matrix based non-incremental algorithms, the improved algorithm needs not save the whole discernibility matrix in main memory, which is desirable for the large data sets. More importantly, with the increment of decision tables, the discernibility matrix-based feature selection algorithm could constrain the computational cost by applying efficient information updating techniques—quasi/pseudo approximation operators. Finally, our experiments reveal that the proposed algorithm needs less computational cost, especially less occupied space, on the condition that the accuracy is limitedly lost.

Analysis of 3D linear elastic masonry-like structures through the API of a finite element software

A new numerical procedure is presented to perform the analysis of three-dimensional linear elastic no-tension structures exploiting the application programming interface of a general purpose finite element analysis software. Masonry is replaced by an equivalent orthotropic material with spatially varying elastic properties and negligible stiffness in the case of cracking strain. A non-incremental algorithm is implemented to define the distribution of the equivalent material, minimizing the strain energy so as to achieve a compression-only state of stress for any given compatible load. Applications are shown for masonry-like solids of general shape visualizing load paths in walls subject to dead loads and out-of-plane live loads, circular domes under self-weight and a groin vault acted upon by both vertical and horizontal seismic loading.

Related families-based attribute reduction of dynamic covering decision information systems

Many efforts have focused on studying techniques for selecting most informative features from data sets. Especially, the related family-based approaches have been provided for attribute reduction of covering information systems. However, the existing related family-based methods have to recompute reducts for dynamic covering decision information systems. In this paper, firstly, we investigate the mechanisms of updating the related families and attribute reducts by the utilization of previously learned results in dynamic covering decision information systems with variations of attributes. Then, we design incremental algorithms for attribute reduction of dynamic covering decision information systems in terms of attribute arriving and leaving using the related families and employ examples to demonstrate that how to update attribute reducts with the proposed algorithms. Finally, experimental comparisons with the non-incremental algorithms on UCI data sets illustrate that the proposed incremental algorithms are feasible and efficient to conduct attribute reduction of dynamic covering decision information systems with immigration and emigration of attributes.

A unified framework of dynamic three-way probabilistic rough sets

The incremental learning technology has been widely applied in efficient and effective data mining with big data based on granular computing, rough sets and three-way approaches. In real-life applications, the information systems will evolve over time with four levels of variational situations, which can be described by the combination of the variations of attributes, objects, condition attributes values and decision attributes values. Considering updating knowledge with multilevel variations of data, this paper proposes a unified dynamic framework of decision-theoretic rough sets for incrementally updating three-way probabilistic regions, namely, positive region, boundary region and negative region. Through improving the representation of three-way regions based on the well-established Bayesian decision procedure, a novel matrix approach is introduced by the construction of Boolean matrix and specific definition of matrix operation. Subsequently, at the variations of level-1, the fundamental updating propositions, which can induce the corresponding propositions with the variations of level-2, level-3, level-4, respectively, are presented by the matrix updating strategies. Finally, experiments with four incremental algorithms developed for the verification of feasibility and efficiency under multilevel variations of data are conducted by comparison with non-incremental algorithm.

Incremental approaches for updating reducts in dynamic covering information systems

In various real-world situations, there are actually a large number of dynamic covering information systems, and non-incremental learning technique is time consuming for updating approximations of sets in dynamic covering information systems. In this paper, we investigate incremental mechanisms of updating the second and sixth lower and upper approximations of sets in dynamic covering information systems with variations of attributes. Especially, we design effective algorithms for calculating the second and sixth lower and upper approximations of sets in dynamic covering information systems. The experimental results indicate that incremental algorithms outperform non-incremental algorithms in the presence of dynamic variation of attributes. Finally, we explore several examples to illustrate that the proposed approaches are feasible to perform knowledge reduction of dynamic covering information systems.

Dynamic probabilistic rough sets with incomplete data

Data in real-world applications are typically changing with time and are often incomplete. To address the challenge of processing such dynamic and incomplete data, we propose a model of dynamic probabilistic rough sets with incomplete data. We introduce incremental methods for estimating the conditional probability and present principles for updating probabilistic approximations when adding and removing objects, respectively. Based on the proposed updating strategies, algorithms are designed for dynamically updating probabilistic approximations with incomplete data. We report experimental evaluations of the efficiency and effectiveness of the proposed incremental algorithms for constructing probabilistic rough set approximations in terms of the size of data and updating ratio by comparing with a non-incremental algorithm. The results show that the new algorithms can effectively utilize the previously acquired knowledge, leading to significantly improved performance over a non-incremental algorithm.

Communication Lower Bounds for Distributed Convex Optimization: Partition Data on Features

Recently, there has been an increasing interest in designing distributed convex optimization algorithms under the setting where the data matrix is partitioned on features. Algorithms under this setting sometimes have many advantages over those under the setting where data is partitioned on samples, especially when the number of features is huge. Therefore, it is important to understand the inherent limitations of these optimization problems. In this paper, with certain restrictions on the communication allowed in the procedures, we develop tight lower bounds on communication rounds for a broad class of non-incremental algorithms under this setting. We also provide a lower bound on communication rounds for a class of (randomized) incremental algorithms.

Fuzzy rough set based incremental attribute reduction from dynamic data with sample arriving

Attribute reduction with fuzzy rough set is an effective technique for selecting most informative attributes from a given real-valued dataset. However, existing algorithms for attribute reduction with fuzzy rough set have to re-compute a reduct from dynamic data with sample arriving where one sample or multiple samples arrive successively. This is clearly uneconomical from a computational point of view. In order to efficiently find a reduct from such datasets, this paper studies incremental attribute reduction with fuzzy rough sets. At the arrival of one sample or multiple samples, the relative discernibility relation is updated for each attribute. On the basis of the updated relation, an insight into the incremental process of attribute reduction with fuzzy rough sets is gained to reveal how to add new attributes into the current reduct and delete existing attributes from the current reduct. Applying the incremental process, two incremental algorithms for attribute reduction with fuzzy rough sets are presented for one incoming sample and multiple incoming samples, respectively. Experimental comparisons with several non-incremental algorithms and the proposed incremental algorithm for one incoming sample show that our proposed incremental algorithm for multiple incoming samples can efficiently find one reduct with a comparable classification accuracy.

Efficient updating rough approximations with multi-dimensional variation of ordered data

Ordered data widely exists in practical problems. Dominance-based Rough Set Approach (DRSA) is an effective mathematical tool to obtain approximations of concepts and discovery knowledge from ordered data. In this paper, we focus on the dynamic DRSA for the multi-dimensional variation of an ordered information system, and propose a novel incremental simplified algorithm which can efficiently update approximations of DRSA when objects and attributes increase simultaneously. Most of existing algorithms can efficiently deal with the single-dimensional variation of an information system. However, multi-dimensional variations often occur in real dynamic data. That is, the object set, the attribute set or attribute values of an information system often vary simultaneously. Although we can directly use the definitions of approximations, or integrate some single-dimensional incremental algorithms to cope with multi-dimensional variations, this always results in complex algorithm architectures and a large amount of inefficient computation. In our works, by simplifying traditional definitions of DRSA and employing the incremental learning strategy, we develop an algorithm to neglect unnecessary parameters and avoid much redundant computation. Then, we present two different storage schemes for our proposed algorithm to solve the problem of memory consumption. Finally, a series of experiments are conducted to evaluate its efficiency. Experimental results clearly show that for the two-dimensional variation of objects and attributes in an ordered information system, our proposed algorithm is much faster not only than the non-incremental algorithm based on traditional definitions, but also than the integration of two single-dimensional incremental algorithms.