Related papers: Dynamic data structures for parameterized string p…
In the dynamic minimum set cover problem, a challenge is to minimize the update time while guaranteeing close to the optimal $\min(O(\log n), f)$ approximation factor. (Throughout, $m$, $n$, $f$, and $C$ are parameters denoting the maximum…
We present new results on a number of fundamental problems about dynamic geometric data structures: 1. We describe the first fully dynamic data structures with sublinear amortized update time for maintaining (i) the number of vertices or…
In this work, we tackle a natural variation of the String Matching Problem on the case of a dynamic pattern, that is, given a static text $T$ and a pattern $P$, we want to support character additions and deletions to the pattern, and after…
String Edit Distance is a more-than-classical problem whose behavior in the dynamic setting, where the strings are updated over time, is well studied. A single-character substitution, insertion, or deletion can be processed in time…
Motivated by the imminent growth of massive, highly redundant genomic databases, we study the problem of compressing a string database while simultaneously supporting fast random access, substring extraction and pattern matching to the…
Dynamic Complexity studies the maintainability of queries with logical formulas in a setting where the underlying structure or database changes over time. Most often, these formulas are from first-order logic, giving rise to the dynamic…
We consider the problem of maintaining a collection of strings while efficiently supporting splits and concatenations on them, as well as comparing two substrings, and computing the longest common prefix between two suffixes. This problem…
We design a randomized data structure that, for a fully dynamic graph $G$ updated by edge insertions and deletions and integers $k, d$ fixed upon initialization, maintains the answer to the Split Completion problem: whether one can add $k$…
Two strings are considered to have parameterized matching when there exists a bijection of the parameterized alphabet onto itself such that it transforms one string to another. Parameterized matching has application in software duplication…
We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…
In this paper, we construct a data structure to efficiently compute the longest increasing subsequence of a sequence subject to dynamic updates. Our data structure supports a query for the longest increasing subsequence in $O(r+\log n)$…
We present the first dynamic algorithms for Dyck and tree edit distances with subpolynomial update times. Dyck edit distance measures how far a parenthesis string is from a well-parenthesized expression, while tree edit distance quantifies…
We present deterministic algorithms for maintaining a $(3/2 + \epsilon)$ and $(2 + \epsilon)$-approximate maximum matching in a fully dynamic graph with worst-case update times $\hat{O}(\sqrt{n})$ and $\tilde{O}(1)$ respectively. The…
We present two deterministic dynamic algorithms for the maximum matching problem. (1) An algorithm that maintains a $(2+\epsilon)$-approximate maximum matching in general graphs with $O(\text{poly}(\log n, 1/\epsilon))$ update time. (2) An…
We revisit the complexity of approximate pattern matching in an elastic-degenerate string. Such a string is a sequence of $n$ finite sets of strings of total length $N$, and compactly describes a collection of strings obtained by first…
Let $\mathcal{D}$ be a collection of $D$ documents, which are strings over an alphabet of size $\sigma$, of total length $n$. We describe a data structure that uses linear space and and reports $k$ most relevant documents that contain a…
We study dynamic algorithms for the longest increasing subsequence (\textsf{LIS}) problem. A dynamic \textsf{LIS} algorithm maintains a sequence subject to operations of the following form arriving one by one: (i) insert an element, (ii)…
The edit distance is a fundamental measure of sequence similarity, defined as the minimum number of character insertions, deletions, and substitutions needed to transform one string into the other. Given two strings of length at most $n$,…
We give new upper and lower bounds for the {\em dynamic} set cover problem. First, we give a $(1+\epsilon) f$-approximation for fully dynamic set cover in $O(f^2\log n /\epsilon^5)$ (amortized) update time, for any $\epsilon > 0$, where $f$…
Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There…