Dynamic dictionary matching with failure functions

AbstractAmir and Farach (1991) and Amir et al. (to appear) recently initiated the study of the dynamic dictionary pattern matching problem. The dictionary D contains a set of patterns that can change over time by insertion and deletion of individual patterns. The user may also present a text string and ask to search for all occurrences of any patterns in the text. For the static dictionary problem, Aho and Corasick (1975) gave a strategy based on a failure function automaton that takes O(|D|log|Σ|) time to build a dictionary of size |D| and searches a text T in time O(|T|log|Σ|+tocc), where tocc, is the total number of pattern occurrences in the text.Amir et al. (to appear) used an automaton based on suffix trees to solve the dynamic problem. Their method can insert or delete a pattern P in time O(|P|log|D|) and can search a text in time O((|T|+tocc)log|D|).We show that the same bounds can be achieved using a framework based on failure functions. We then show that our approach also allows us to achieve faster search times at the expense of the update times; for constant k, we can achieve linear O(|T|(k+log|Σ|)+k tocc) search time with an update time of O(k|P∥D|1k). This is advantageous if the search texts are much larger than the dictionary or searches are more frequent than updates.Finally, we show how to build the initial dictionary in O(|D|log|Σ|) time, regardless of what combination of search and update times is used

A* Orthogonal Matching Pursuit: Best-First Search for Compressed Sensing Signal Recovery

Compressed sensing is a developing field aiming at reconstruction of sparse signals acquired in reduced dimensions, which make the recovery process under-determined. The required solution is the one with minimum $\ell_0$ norm due to sparsity, however it is not practical to solve the $\ell_0$ minimization problem. Commonly used techniques include $\ell_1$ minimization, such as Basis Pursuit (BP) and greedy pursuit algorithms such as Orthogonal Matching Pursuit (OMP) and Subspace Pursuit (SP). This manuscript proposes a novel semi-greedy recovery approach, namely A* Orthogonal Matching Pursuit (A*OMP). A*OMP performs A* search to look for the sparsest solution on a tree whose paths grow similar to the Orthogonal Matching Pursuit (OMP) algorithm. Paths on the tree are evaluated according to a cost function, which should compensate for different path lengths. For this purpose, three different auxiliary structures are defined, including novel dynamic ones. A*OMP also incorporates pruning techniques which enable practical applications of the algorithm. Moreover, the adjustable search parameters provide means for a complexity-accuracy trade-off. We demonstrate the reconstruction ability of the proposed scheme on both synthetically generated data and images using Gaussian and Bernoulli observation matrices, where A*OMP yields less reconstruction error and higher exact recovery frequency than BP, OMP and SP. Results also indicate that novel dynamic cost functions provide improved results as compared to a conventional choice.Comment: accepted for publication in Digital Signal Processin

Adaptive service discovery on service-oriented and spontaneous sensor systems

Service-oriented architecture, Spontaneous networks, Self-organisation, Self-configuration, Sensor systems, Social patternsNatural and man-made disasters can significantly impact both people and environments. Enhanced effect can be achieved through dynamic networking of people, systems and procedures and seamless integration of them to fulfil mission objectives with service-oriented sensor systems. However, the benefits of integration of services will not be realised unless we have a dependable method to discover all required services in dynamic environments. In this paper, we propose an Adaptive and Efficient Peer-to-peer Search (AEPS) approach for dependable service integration on service-oriented architecture based on a number of social behaviour patterns. In the AEPS network, the networked nodes can autonomously support and co-operate with each other in a peer-to-peer (P2P) manner to quickly discover and self-configure any services available on the disaster area and deliver a real-time capability by self-organising themselves in spontaneous groups to provide higher flexibility and adaptability for disaster monitoring and relief

c-trie++: A Dynamic Trie Tailored for Fast Prefix Searches

Given a dynamic set $K$ of $k$ strings of total length $n$ whose characters are drawn from an alphabet of size $\sigma$, a keyword dictionary is a data structure built on $K$ that provides locate, prefix search, and update operations on $K$. Under the assumption that $\alpha = w / \lg \sigma$ characters fit into a single machine word $w$, we propose a keyword dictionary that represents $K$ in $n \lg \sigma + \Theta(k \lg n)$ bits of space, supporting all operations in $O(m / \alpha + \lg \alpha)$ expected time on an input string of length $m$ in the word RAM model. This data structure is underlined with an exhaustive practical evaluation, highlighting the practical usefulness of the proposed data structure, especially for prefix searches - one of the most elementary keyword dictionary operations

パターン照合問題に対する高速なアルゴリズム

Tohoku University篠原歩課