Related papers: Predecessor search with distance-sensitive query t…
The fragile complexity of a comparison-based algorithm is $f(n)$ if each input element participates in $O(f(n))$ comparisons. In this paper, we explore the fragile complexity of algorithms adaptive to various restrictions on the input,…
We study the classical approximate string matching problem, that is, given strings $P$ and $Q$ and an error threshold $k$, find all ending positions of substrings of $Q$ whose edit distance to $P$ is at most $k$. Let $P$ and $Q$ have…
We consider the $(1+\epsilon)$-approximate nearest neighbor search problem: given a set $X$ of $n$ points in a $d$-dimensional space, build a data structure that, given any query point $y$, finds a point $x \in X$ whose distance to $y$ is…
We propose a new algorithm for fast approximate nearest neighbor search based on the properties of ordered vectors. Data vectors are classified based on the index and sign of their largest components, thereby partitioning the space in a…
We present a data structure representing a dynamic set S of w-bit integers on a w-bit word RAM. With |S|=n and w > log n and space O(n), we support the following standard operations in O(log n / log w) time: - insert(x) sets S = S + {x}. -…
Temporal distances lie at the heart of many algorithms for planning, control, and reinforcement learning that involve reaching goals, allowing one to estimate the transit time between two states. However, prior attempts to define such…
The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…
We introduce the lazy search tree data structure. The lazy search tree is a comparison-based data structure on the pointer machine that supports order-based operations such as rank, select, membership, predecessor, successor, minimum, and…
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…
We give the first data structure for the problem of maintaining a dynamic set of n elements drawn from a partially ordered universe described by a tree. We define the Line-Leaf Tree, a linear-sized data structure that supports the…
The classic string indexing problem is to preprocess a string $S$ into a compact data structure that supports efficient subsequent pattern matching queries, that is, given a pattern string $P$, report all occurrences of $P$ within $S$. In…
Suppose that we observe a short time series where each time-t-specific data-structure consists of many slightly dependent data indexed by a and that we want to estimate a feature of the law of the experiment that depends neither on t nor on…
The problem of content search through comparisons has recently received considerable attention. In short, a user searching for a target object navigates through a database in the following manner: the user is asked to select the object most…
We present a constraint-based algorithm for learning causal structures from observational time-series data, in the presence of latent confounders. We assume a discrete-time, stationary structural vector autoregressive process, with both…
In the static retrieval problem, a data structure must answer retrieval queries mapping a set of $n$ keys in a universe $[U]$ to $v$-bit values. Information-theoretically, retrieval data structures can use as little as $nv$ bits of space.…
We study the quantum walk search algorithm of Shenvi, Kempe and Whaley [PRA 67 052307 (2003)] on data structures of one to two spatial dimensions, on which the algorithm is thought to be less efficient than in three or more spatial…
Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. Sampled string…
Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…
Space efficient algorithms play a central role in dealing with large amount of data. In such settings, one would like to analyse the large data using small amount of "working space". One of the key steps in many algorithms for analysing…
The equidistant subsequence pattern matching problem is considered. Given a pattern string $P$ and a text string $T$, we say that $P$ is an \emph{equidistant subsequence} of $T$ if $P$ is a subsequence of the text such that consecutive…