Fully-online Construction of Suffix Trees for Multiple Texts

We consider fully-online construction of indexing data structures for multiple texts. Let T = {T_1, ..., T_K} be a collection of texts. By fully-online, we mean that a new character can be appended to any text in T at any time. This is a natural generalization of semi-online construction of indexing data structures for multiple texts in which, after a new character is appended to the kth text T_k, then its previous texts T_1, ..., T_k-1 will remain static. Our fully-online scenario arises when we maintain dynamic indexes for multi-sensor data. Let N and sigma denote the total length of texts in T and the alphabet size, respectively. We first show that the algorithm by Blumer et al. [Theoretical Computer Science, 40:31-55, 1985] to construct the directed acyclic word graph (DAWG) for T can readily be extended to our fully-online setting, retaining O(N log sigma)-time and O(N)-space complexities. Then, we give a sophisticated fully-online algorithm which constructs the suffix tree for T in O(N log sigma) time and O(N) space. A key idea of this algorithm is synchronized maintenance of the DAWG and the suffix tree

Managing Unbounded-Length Keys in Comparison-Driven Data Structures with Applications to On-Line Indexing

This paper presents a general technique for optimally transforming any dynamic data structure that operates on atomic and indivisible keys by constant-time comparisons, into a data structure that handles unbounded-length keys whose comparison cost is not a constant. Examples of these keys are strings, multi-dimensional points, multiple-precision numbers, multi-key data (e.g.~records), XML paths, URL addresses, etc. The technique is more general than what has been done in previous work as no particular exploitation of the underlying structure of is required. The only requirement is that the insertion of a key must identify its predecessor or its successor. Using the proposed technique, online suffix tree can be constructed in worst case time $O(\log n)$ per input symbol (as opposed to amortized $O(\log n)$ time per symbol, achieved by previously known algorithms). To our knowledge, our algorithm is the first that achieves $O(\log n)$ worst case time per input symbol. Searching for a pattern of length $m$ in the resulting suffix tree takes $O(\min(m\log |\Sigma|, m + \log n) + tocc)$ time, where $tocc$ is the number of occurrences of the pattern. The paper also describes more applications and show how to obtain alternative methods for dealing with suffix sorting, dynamic lowest common ancestors and order maintenance

Computationally Efficient Relational Reinforcement Learning

Relational Reinforcement Learning (RRL) is a technique that enables Reinforcement Learning (RL) agents to generalize from their experience, allowing them to learn over large or potentially infinite state spaces, to learn context sensitive behaviors, and to learn to solve variable goals and to transfer knowledge between similar situations. Prior RRL architectures are not sufficiently computationally efficient to see use outside of small, niche roles within larger Artificial Intelligence (AI) architectures. I present a novel online, incremental RRL architecture and an implementation that is orders of magnitude faster than its predecessors. The first aspect of this architecture that I explore is a computationally efficient implementation of an adaptive Hierarchical Tile Coding (aHTC), a kind of Adaptive Tile Coding (ATC) in which more general tiles which cover larger portions of the state-action space are kept as ones that cover smaller portions of the state-action space are introduced, using k-dimensional tries (k-d tries) to implement the value function for non-relational Temporal Difference (TD) methods. In order to achieve comparable performance for RRL, I implement the Rete algorithm to replace my k-d tries due to its efficient handling of both the variable binding problem and variable numbers of actions. Tying aHTCs and Rete together, I present a rule grammar that both maps aHTCs onto Rete and allows the architecture to automatically extract relational features in order to support adaptation of the value function over time. I experiment with several refinement criteria and additional functionality with which my agents attempt to determine if rerefinement using different features might allow them to better learn a near optimal policy. I present optimal results using a value criterion for several variants of BlocksWorld. I provide transfer results for BlocksWorld and a scalable Taxicab domain. I additionally introduce a Higher Order Grammar (HOG) that grants online, incremental RRL agents additional flexibility to introduce additional variables and corresponding relations as needed in order to learn effective value functions. I evaluate agents that use the HOG on a version of Blocks World and on an Adventure task. In summary, I present a new online, incremental RRL architecture, a grammar to map aHTCs onto the Rete, and an implementation that is orders of magnitude faster than its predecessors.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145859/1/bazald_1.pd

Motion planning for geometric models in data visualization

Interaktivní geometrické modely pro simulaci přírodních jevů (LH11006)Pokročilé grafické a počítačové systémy (SGS-2016-013)A finding of path is an important task in many research areas and it is a common problem solved in a wide range of applications. New problems of finding path appear and complex problems persist, such as a real-time plan- ning of paths for huge crowds in dynamic environments, where the properties according to which the cost of a path is evaluated as well as the topology of paths may change. The task of finding a path can be divided into path planning and motion planning, which implicitly respects the collision with surroundings in the environment. Within the first group this thesis focuses on path planning on graphs for crowds. The main idea is to group members of the crowd by their common initial and target positions and then plan the path for one representative member of each group. These representative members can be navigated by classic approaches and the rest of the group will follow them. If the crowd can be divided into a few groups this way, the proposed approach will save a huge amount of computational and memory demands in dynamic environments. In the second area, motion planning, we are dealing with another problem. The task is to navigate the ligand through the protein or into the protein, which turns out to be a challenging problem because it needs to be solved in 3D with the collision detection