Related papers: Amortized Dynamic Cell-Probe Lower Bounds from Fou…
In this paper we investigate the problem of building a static data structure that represents a string s using space close to its compressed size, and allows fast access to individual characters of s. This type of structures was investigated…
In this work, we prove a $\tilde{\Omega}(\lg^{3/2} n )$ unconditional lower bound on the maximum of the query time and update time for dynamic data structures supporting reachability queries in $n$-node directed acyclic graphs under edge…
We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $\sum_{i = 1}^N f_i (x)$. This problem arises naturally in…
Many dynamic graph algorithms have an amortized update time, rather than a stronger worst-case guarantee. But amortized data structures are not suitable for real-time systems, where each individual operation has to be executed quickly. For…
We investigate the number of maximal independent set queries required to reconstruct the edges of a hidden graph. We show that randomised adaptive algorithms need at least $\Omega(\Delta^2 \log(n / \Delta) / \log \Delta)$ queries to…
We present a randomized algorithm for dynamic graph connectivity. With failure probability less than $1/n^c$ (for any constant $c$ we choose), our solution has worst case running time $O(\log^3 n)$ per edge insertion, $O(\log^4 n)$ per edge…
Lifting theorems are one of the most powerful tools for proving communication lower bounds, with numerous downstream applications in proof complexity, monotone circuit lower bounds, data structures, and combinatorial optimization. However,…
In this thesis, I study the minimax oracle complexity of distributed stochastic optimization. First, I present the "graph oracle model", an extension of the classic oracle complexity framework that can be applied to study distributed…
This paper addresses safe distributed online optimization over an unknown set of linear safety constraints. A network of agents aims at jointly minimizing a global, time-varying function, which is only partially observable to each…
In this paper we present new data structures for two extensively studied variants of the orthogonal range searching problem. First, we describe a data structure that supports two-dimensional orthogonal range minima queries in $O(n)$ space…
We investigate the limits of one of the fundamental ideas in data structures: fractional cascading. This is an important data structure technique to speed up repeated searches for the same key in multiple lists and it has numerous…
The dynamic set cover problem has been subject to extensive research since the pioneering works of [Bhattacharya et al, 2015] and [Gupta et al, 2017]. The input is a set system $(U, S)$ on a fixed collection $S$ of sets and a dynamic…
We show tight lower bounds for the entire trade-off between space and query time for the Approximate Near Neighbor search problem. Our lower bounds hold in a restricted model of computation, which captures all hashing-based approaches. In…
A recent work (Korten, Pitassi, and Impagliazzo, FOCS 2025) established an insightful connection between static data structure lower bounds, range avoidance of $\text{NC}^0$ circuits, and the refutation of pseudorandom CSP instances,…
We give new deterministic bounds for fully-dynamic graph connectivity. Our data structure supports updates (edge insertions/deletions) in $O(\log^2n/\log\log n)$ amortized time and connectivity queries in $O(\log n/\log\log n)$ worst-case…
We consider the problem of estimating the support size of a distribution $D$. Our investigations are pursued through the lens of distribution testing and seek to understand the power of conditional sampling (denoted as COND), wherein one is…
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…
Today's scientific simulations require a significant reduction of data volume because of extremely large amounts of data they produce and the limited I/O bandwidth and storage space. Error-bounded lossy compression has been considered one…
We present a simple and provably optimal non-adaptive cell probe data structure for the static dictionary problem. Our data structure supports storing a set of n key-value pairs from [u]x[u] using s words of space and answering key lookup…
We give a simplified and improved lower bound for the simplex range reporting problem. We show that given a set $P$ of $n$ points in $\mathbb{R}^d$, any data structure that uses $S(n)$ space to answer such queries must have…