DIAGaRa: An Incremental Algorithm for Inferring Implicative Rules from Examples

An approach is proposed for inferring implicative logical rules from examples. The concept of a good diagnostic test for a given set of positive examples lies in the basis of this approach. The process of inferring good diagnostic tests is considered as a process of inductive common sense reasoning. The incremental approach to learning algorithms is implemented in an algorithm DIAGaRa for inferring implicative rules from examples.

Algorithm for incremental compaction of geometrical layouts

In this paper, a new incremental algorithm for layout compaction is proposed. In addition to its linear time performance in terms of the number of rectangles in the layout, we also describe how incremental compaction can form a good feature in the design of a layout editor. The design of such an editor is also described. In the design of the editor, we describe how arrays can be used to implement quadtrees that represent VLSI layouts. Such a representation provides speed of data access and low storage requirements.

The complexity of certain incremental code generation problems

This paper looks at the complexity of four different incremental problems. The following are the problems considered: (1) Interval partitioning of a flow graph (2) Breadth first search (BFS) of a directed graph (3) Lexicographic depth first search (DFS) of a directed graph (4) Constructing the postorder listing of the nodes of a binary tree. The last problem arises out of the need for incrementally computing the Sethi-Ullman (SU) ordering [1] of the subtrees of a tree after it has undergone changes of a given type. These problems are among those that claimed our attention in the process of our designing algorithmic techniques for incremental code generation. BFS and DFS have certainly numerous other applications, but as far as our work is concerned, incremental code generation is the common thread linking these problems. The study of the complexity of these problems is done from two different perspectives. In [2] is given the theory of incremental relative lower bounds (IRLB). We use this theory to derive the IRLBs of the first three problems. Then we use the notion of a bounded incremental algorithm [4] to prove the unboundedness of the fourth problem with respect to the locally persistent model of computation. Possibly, the lower bound result for lexicographic DFS is the most interesting. In [5] the author considers lexicographic DFS to be a problem for which the incremental version may require the recomputation of the entire solution from scratch. In that sense, our IRLB result provides further evidence for this possibility with the proviso that the incremental DFS algorithms considered be ones that do not require too much of preprocessing.

Incremental Verification of Timing Constraints for Real-Time Systems

Testing constraints for real-time systems are usually verified through the satisfiability of propositional formulae. In this paper, we propose an alternative where the verification of timing constraints can be done by counting the number of truth assignments instead of boolean satisfiability. This number can also tell us how “far away” is a given specification from satisfying its safety assertion. Furthermore, specifications and safety assertions are often modified in an incremental fashion, where problematic bugs are fixed one at a time. To support this development, we propose an incremental algorithm for counting satisfiability. Our proposed incremental algorithm is optimal as no unnecessary nodes are created during each counting. This works for the class of path RTL. To illustrate this application, we show how incremental satisfiability counting can be applied to a well-known rail-road crossing example, particularly when its specification is still being refined.

An incremental multilinear system for human face learning and recognition

This dissertation establishes a novel system for human face learning and recognition based on incremental multilinear Principal Component Analysis (PCA). Most of the existing face recognition systems need training data during the learning process. The system as proposed in this dissertation utilizes an unsupervised or weakly supervised learning approach, in which the learning phase requires a minimal amount of training data. It also overcomes the inability of traditional systems to adapt to the testing phase as the decision process for the newly acquired images continues to rely on that same old training data set. Consequently when a new training set is to be used, the traditional approach will require that the entire eigensystem will have to be generated again. However, as a means to speed up this computational process, the proposed method uses the eigensystem generated from the old training set together with the new images to generate more effectively the new eigensystem in a so-called incremental learning process. In the empirical evaluation phase, there are two key factors that are essential in evaluating the performance of the proposed method: (1) recognition accuracy and (2) computational complexity. In order to establish the most suitable algorithm for this research, a comparative analysis of the best performing methods has been carried out first. The results of the comparative analysis advocated for the initial utilization of the multilinear PCA in our research. As for the consideration of the issue of computational complexity for the subspace update procedure, a novel incremental algorithm, which combines the traditional sequential Karhunen-Loeve (SKL) algorithm with the newly developed incremental modified fast PCA algorithm, was established. In order to utilize the multilinear PCA in the incremental process, a new unfolding method was developed to affix the newly added data at the end of the previous data. The results of the incremental process based on these two methods were obtained to bear out these new theoretical improvements. Some object tracking results using video images are also provided as another challenging task to prove the soundness of this incremental multilinear learning method.

Development of a Real-Time Hierarchical 3D Path Planning Algorithm for Unmanned Aerial Vehicles

Unmanned aerial vehicles (UAVs) frequently operate in partially or entirely unknown environments. As the vehicle traverses the environment and detects new obstacles, rapid path replanning is essential to avoid collisions. This thesis presents a new algorithm called Hierarchical D* Lite (HD*), which combines the incremental algorithm D* Lite with a novel hierarchical path planning approach to replan paths sufficiently fast for real-time operation. Unlike current hierarchical planning algorithms, HD* does not require map corrections before planning a new path. Directional cost scale factors, path smoothing, and Catmull-Rom splines are used to ensure the resulting paths are feasible. HD* sacrifices optimality for real-time performance. Its computation time and path quality are dependent on the map size, obstacle density, sensor range, and any restrictions on planning time. For the most complex scenarios tested, HD* found paths within 10% of optimal in under 35 milliseconds.

Prototype Selection on Large and Streaming Data

Since streaming data keeps coming continuously as an ordered sequence, massive amounts of data is created. A big challenge in handling data streams is the limitation of time and space. Prototype selection on streaming data requires the prototypes to be updated in an incremental manner as new data comes in. We propose an incremental algorithm for prototype selection. This algorithm can also be used to handle very large datasets. Results have been presented on a number of large datasets and our method is compared to an existing algorithm for streaming data. Our algorithm saves time and the prototypes selected gives good classification accuracy.

Social optimum in social groups with give-and-take criterion

We consider a Social Group' of networked nodes, seeking a universe' of segments. Each node has a subset of the universe and access to an expensive resource for downloading data. Nodes can also acquire the universe by exchanging copies of segments among themselves, at low cost, using inter-node links. While exchanges over inter-node links ensure minimum cost, some nodes in the group try to exploit the system. We term such nodes as non-reciprocating nodes' and prohibit such behavior by proposing the give-and-take' criterion, where exchange is allowed if each node has segments unavailable with the other. Under this criterion, we consider the problem of maximizing the number of nodes with the universe at the end of local exchanges. First, we present a randomized algorithm that is shown to be optimal in the asymptotic regime. Then, we present greedy links algorithm, which performs well for most of the scenarios and yields an optimal result when the number of nodes is four. The polygon algorithm is proposed, which yields an optimal result when each of the nodes has a unique segment. After presenting some intuitive algorithms (e.g., greedy incremental algorithm and rarest first algorithm), we compare the performances of all proposed algorithms with the optimal. Copyright (c) 2015 John Wiley & Sons, Ltd.

Regrouping metric-space search index for search engine size adaptation

This work contributes to the development of search engines that self-adapt their size in response to fluctuations in workload. Deploying a search engine in an Infrastructure as a Service (IaaS) cloud facilitates allocating or deallocating computational resources to or from the engine. In this paper, we focus on the problem of regrouping the metric-space search index when the number of virtual machines used to run the search engine is modified to reflect changes in workload. We propose an algorithm for incrementally adjusting the index to fit the varying number of virtual machines. We tested its performance using a custom-build prototype search engine deployed in the Amazon EC2 cloud, while calibrating the results to compensate for the performance fluctuations of the platform. Our experiments show that, when compared with computing the index from scratch, the incremental algorithm speeds up the index computation 2–10 times while maintaining a similar search performance.

Self-adapting parallel metric-space search engine for variable query loads

This research focuses on automatically adapting a search engine size in response to fluctuations in query workload. Deploying a search engine in an Infrastructure as a Service (IaaS) cloud facilitates allocating or deallocating computer resources to or from the engine. Our solution is to contribute an adaptive search engine that will repeatedly re-evaluate its load and, when appropriate, switch over to a dierent number of active processors. We focus on three aspects and break them out into three sub-problems as follows: Continually determining the Number of Processors (CNP), New Grouping Problem (NGP) and Regrouping Order Problem (ROP). CNP means that (in the light of the changes in the query workload in the search engine) there is a problem of determining the ideal number of processors p active at any given time to use in the search engine and we call this problem CNP. NGP happens when changes in the number of processors are determined and it must also be determined which groups of search data will be distributed across the processors. ROP is how to redistribute this data onto processors while keeping the engine responsive and while also minimising the switchover time and the incurred network load. We propose solutions for these sub-problems. For NGP we propose an algorithm for incrementally adjusting the index to t the varying number of virtual machines. For ROP we present an ecient method for redistributing data among processors while keeping the search engine responsive. Regarding the solution for CNP, we propose an algorithm determining the new size of the search engine by re-evaluating its load. We tested the solution performance using a custom-build prototype search engine deployed in the Amazon EC2 cloud. Our experiments show that when we compare our NGP solution with computing the index from scratch, the incremental algorithm speeds up the index computation 2{10 times while maintaining a similar search performance. The chosen redistribution method is 25% to 50% faster than other methods and reduces the network load around by 30%. For CNP we present a deterministic algorithm that shows a good ability to determine a new size of search engine. When combined, these algorithms give an adapting algorithm that is able to adjust the search engine size with a variable workload.

Algebraic theory of minimal nondeterministic finite automata with applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA’s behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

Algebraic Theory of Minimal Nondeterministic Finite Automata with Applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA's behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

Enhancing an Incremental Clustering Algorithm for Web Page Collections

With the size and state of the Internet today, a good quality approach to organizing this mass of information is of great importance. Clustering web pages into groups of similar documents is one approach, but relies heavily on good feature extraction and document representation as well as a good clustering approach and algorithm. Due to the changing nature of the Internet, resulting in a dynamic dataset, an incremental approach is preferred. In this work we propose an enhanced incremental clustering approach to develop a better clustering algorithm that can help to better organize the information available on the Internet in an incremental fashion. Experiments show that the enhanced algorithm outperforms the original histogram based algorithm by up to 7.5%.