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Text indexing, the problem in which one desires to preprocess a (usually large) text for future (shorter) queries, has been researched ever since the suffix tree was invented in the early 70's. With textual data continuing to increase and…
In this paper, a new and novel data structure is proposed to dynamically insert and delete segments. Unlike the standard segment trees[3], the proposed data structure permits insertion of a segment with interval range beyond the interval…
We introduce K-tree in an information retrieval context. It is an efficient approximation of the k-means clustering algorithm. Unlike k-means it forms a hierarchy of clusters. It has been extended to address issues with sparse…
We define a search problem on trees that closely captures the backtracking behavior of all current practical graph isomorphism algorithms. Given two trees with colored leaves, the goal is to find two leaves of matching color, one in each of…
We propose a new linear-size data structure which provides a fast access to all palindromic substrings of a string or a set of strings. This structure inherits some ideas from the construction of both the suffix trie and suffix tree. Using…
The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…
With the rapid advance of the Internet, search engines (e.g., Google, Bing, Yahoo!) are used by billions of users for each day. The main function of a search engine is to locate the most relevant webpages corresponding to what the user…
The increasing complexity of data requires methods and models that can effectively handle intricate structures, as simplifying them would result in loss of information. While several analytical tools have been developed to work with complex…
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…
Dependency trees help relation extraction models capture long-range relations between words. However, existing dependency-based models either neglect crucial information (e.g., negation) by pruning the dependency trees too aggressively, or…
We describe new results and algorithms for two different, but related, problems which deal with circulant matrices: learning shift-invariant components from training data and calculating the shift (or alignment) between two given signals.…
Tree structures appear in many fields of the life sciences, including phylogenetics, developmental biology and nucleic acid structures. Trees can be used to represent RNA secondary structures, which directly relate to the function of…
Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…
With the rise of social networks, information on the internet is no longer solely organized by web pages. Rather, content is generated and shared among users and organized around their social relations on social networks. This presents new…
We prove a new formula for the generating function of multitype Cayley trees counted according to their degree distribution. Using this formula we recover and extend several enumerative results about trees. In particular, we extend some…
We consider the in-plane motion of elastic strings on tree-like network, observed from the 'leaves'. We investigate the inverse problem of recovering not only the physical properties i.e. the 'optical lengths' of each string, but also the…
In this paper I present several novel, efficient, algorithmic techniques for solving some multidimensional geometric data management and analysis problems. The techniques are based on several data structures from computational geometry…
A data structure, called a biased range tree, is presented that preprocesses a set S of n points in R^2 and a query distribution D for 2-sided orthogonal range counting queries. The expected query time for this data structure, when queries…
Recursive neural models, which use syntactic parse trees to recursively generate representations bottom-up, are a popular architecture. But there have not been rigorous evaluations showing for exactly which tasks this syntax-based method is…
How can we effectively find the best structures in tree models? Tree models have been favored over complex black box models in domains where interpretability is crucial for making irreversible decisions. However, searching for a tree…