Related papers: Dynamic data structures for twin-ordered matrices
In the setting of DynFO, dynamic programs update the stored result of a query whenever the underlying data changes. This update is expressed in terms of first-order logic. We introduce a strategy for constructing dynamic programs that…
In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure. In this paper, we consider a class of binary matrices, arising in many…
We study geometric set cover problems in dynamic settings, allowing insertions and deletions of points and objects. We present the first dynamic data structure that can maintain an $O(1)$-approximation in sublinear update time for set cover…
We investigate dynamic algorithms for the interval scheduling problem. Our algorithm runs in amortised time $O(\log n)$ for query operation and $O(d\log^2 n)$ for insertion and removal operations, where $n$ and $d$ are the maximal numbers…
In this paper, we study the $d$-dimensional update-query problem. We provide lower bounds on update and query running times, assuming a long-standing conjecture on min-plus matrix multiplication, as well as algorithms that are close to the…
We develop a dynamic version of the primal-dual method for optimization problems, and apply it to obtain the following results. (1) For the dynamic set-cover problem, we maintain an $O(f^2)$-approximately optimal solution in $O(f \cdot \log…
We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every…
Given a set $P$ of coloured points on the real line, we study the problem of answering range $\alpha$-majority (or "heavy hitter") queries on $P$. More specifically, for a query range $Q$, we want to return each colour that is assigned to…
In this paper, we consider maintaining strongly connected components (SCCs) of a directed planar graph subject to edge insertions and deletions. We show a data structure maintaining an implicit representation of the SCCs within…
This paper presents a general technique for optimally transforming any dynamic data structure that operates on atomic and indivisible keys by constant-time comparisons, into a data structure that handles unbounded-length keys whose…
In this paper we present a new data structure for double ended priority queue, called min-max fine heap, which combines the techniques used in fine heap and traditional min-max heap. The standard operations on this proposed structure are…
Dynamic connectivity is one of the most fundamental problems in dynamic graph algorithms. We present a randomized Las Vegas dynamic connectivity data structure with $O(\log n(\log\log n)^2)$ amortized expected update time and $O(\log…
We present here new mechanisms for hashing data via binary embeddings. Contrary to most of the techniques presented before, the embedding matrix of our mechanism is highly structured. That enables us to perform hashing more efficiently and…
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 provide a compact data structure for representing polyominoes that supports neighborhood and visibility queries. Neighborhood queries concern reporting adjacent cells to a given cell, and visibility queries determine whether a straight…
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…
The binary indexed tree, or Fenwick tree, is a data structure that can efficiently update values and calculate prefix sums in an array. It allows both of these operations to be performed in $O(\log_2 N)$ time. Here we present a novel data…
Purpose: Simulation-based digital twins represent an effort to provide high-accuracy real-time insights into operational physical processes. However, the computation time of many multi-physical simulation models is far from real-time. It…
Many different classification tasks need to manage structured data, which are usually modeled as graphs. Moreover, these graphs can be dynamic, meaning that the vertices/edges of each graph may change during time. Our goal is to jointly…
In this paper, we introduce zip-tries, which are simple, dynamic, memory-efficient data structures for strings. Zip-tries support search and update operations for $k$-length strings in $\mathcal{O}(k+\log n)$ time in the standard RAM model…