arXiv subjects
Publications and source records attributed to Dekel Tsur.
We study the problem of storing the minimum number of bits required to answer next/previous larger/smaller value queries on an array $A$ of $n$ numbers, without storing $A$. We show that these queries can be answered by storing at most $3.701 n$ bits. Our result improves the result of Jo and Satti [TCS 2016] that gives an upper bound of $4.088n$ bits for this problem.
The degree distribution of an ordered tree $T$ with $n$ nodes is $\vec{n} = (n_0,\ldots,n_{n-1})$, where $n_i$ is the number of nodes in $T$ with $i$ children. Let $\mathcal{N}(\vec{n})$ be the number of trees with degree distribution $\vec{n}$. We give a data structure that stores an ordered tree $T$ with $n$ nodes and degree distribution $\vec{n}$ using $\log \mathcal{N}(\vec{n})+O(n/\log^t n)$ bits for every constant $t$. The data structure answers tree queries in constant time. This improves the current data structures with lowest space for ordered trees: The structure of Jansson et al.\ [JCSS 2012] that uses $\log\mathcal{N}(\vec{n})+O(n\log\log n/\log n)$ bits, and the structure of Navarro and Sadakane [TALG 2014] that uses $2n+O(n/\log^t n)$ bits for every constant $t$.
Navarro and Sadakane [TALG 2014] gave a dynamic succinct data structure for storing an ordinal tree. The structure supports tree queries in either $O(\log n/\log\log n)$ or $O(\log n)$ time, and insertion or deletion of a single node in $O(\log n)$ time. In this paper we improve the result of Navarro and Sadakane by reducing the time complexities of some queries (e.g.\ degree and level\_ancestor) from $O(\log n)$ to $O(\log n/\log\log n)$.
We give a succinct data-structure that stores a tree with colors on the nodes. Given a node x and a color alpha, the structure finds the nearest node to x with color alpha. This results improves the $O(n\log n)$-bits structure of Gawrychowski et al.~[CPM 2016].
We study strategies of approximate pattern matching that exploit bidirectional text indexes, extending and generalizing ideas of Lam et al. We introduce a formalism, called search schemes, to specify search strategies of this type, then develop a probabilistic measure for the efficiency of a search scheme, prove several combinatorial results on efficient search schemes, and finally, provide experimental computations supporting the superiority of our strategies.
We give a representation for labeled ordered trees that supports labeled queries such as finding the i-th ancestor of a node with a given label. Our representation is succinct, namely the redundancy is small-o of the optimal space for storing the tree. This improves the representation of He et al. which is succinct unless the entropy of the labels is small.