Related papers: Lower Bounds on Retroactive Data Structures
We present a compressed representation of tries based on top tree compression [ICALP 2013] that works on a standard, comparison-based, pointer machine model of computation and supports efficient prefix search queries. Namely, we show how to…
The paper studies the expectation of the inspection time in complex aging systems. Under reasonable assumptions, this problem is reduced to studying the expectation of the length of the shortest path in the directed degradation graph of the…
Given a set of $m$ points and a set of $n$ lines in the plane, we consider the problem of computing the faces of the arrangement of the lines that contain at least one point. In this paper, we present an $O(m^{2/3}n^{2/3}+(n+m)\log n)$ time…
In this paper we present a foundational study on a constrained method that defines learning problems with Neural Networks in the context of the principle of least cognitive action, which very much resembles the principle of least action in…
Recent research demonstrated that training large language models involves memorization of a significant fraction of training data. Such memorization can lead to privacy violations when training on sensitive user data and thus motivates the…
Retrieval data structures are data structures that answer key-value queries without paying the space overhead of explicitly storing keys. The problem can be formulated in four settings (static, value-dynamic, incremental, or dynamic), each…
We address reinforcement learning problems with finite state and action spaces where the underlying MDP has some known structure that could be potentially exploited to minimize the exploration rates of suboptimal (state, action) pairs. For…
In the fillable array problem one must maintain an array A[1..n] of $w$-bit entries subject to random access reads and writes, and also a $\texttt{fill}(\Delta)$ operation which sets every entry of to some $\Delta\in\{0,\ldots,2^w-1\}$. We…
We consider the problem of computing the Maximal Exact Matches (MEMs) of a given pattern $P[1 .. m]$ on a large repetitive text collection $T[1 .. n]$, which is represented as a (hopefully much smaller) run-length context-free grammar of…
This paper shows the weighted matching problem on general graphs can be solved in time $O(n(m + n\log n))$ for $n$ and $m$ the number of vertices and edges, respectively. This was previously known only for bipartite graphs. The crux is a…
We study the fundamental tradeoffs between computational tractability and statistical accuracy for a general family of hypothesis testing problems with combinatorial structures. Based upon an oracle model of computation, which captures the…
For general exact repair regenerating codes, the optimal trade-offs between storage size and repair bandwith remain undetermined. Various outer bounds and partial results have been proposed. Using a simple chain rule argument we identify…
The celebrated result of Kabanets and Impagliazzo (Computational Complexity, 2004) showed that PIT algorithms imply circuit lower bounds, and vice versa. Since then it has been a major challenge to understand the precise connections between…
Integer Linear Programming with $n$ binary variables and $m$ many $0/1$-constraints can be solved in time $2^{\tilde O(m^2)} \text{poly}(n)$ and it is open whether the dependence on $m$ is optimal. Several seemingly unrelated problems,…
We show that any one-counter automaton with $n$ states, if its language is non-empty, accepts some word of length at most $O(n^2)$. This closes the gap between the previously known upper bound of $O(n^3)$ and lower bound of $\Omega(n^2)$.…
Pointer analysis is one of the fundamental problems in static program analysis. Given a set of pointers, the task is to produce a useful over-approximation of the memory locations that each pointer may point-to at runtime. The most common…
Let $S$ be a set of $n$ points in $\mathbb{R}^d$, where $d \geq 2$ is a constant, and let $H_1,H_2,\ldots,H_{m+1}$ be a sequence of vertical hyperplanes that are sorted by their first coordinates, such that exactly $n/m$ points of $S$ are…
A central computational task in database theory, finite model theory, and computer science at large is the evaluation of a first-order sentence on a finite structure. In the context of this task, the \emph{width} of a sentence, defined as…
We study the influence of a graph parameter called modular-width on the time complexity for optimally solving well-known polynomial problems such as Maximum Matching, Triangle Counting, and Maximum $s$-$t$ Vertex-Capacitated Flow. The…
We study time/memory tradeoffs of function inversion: an algorithm, i.e., an inverter, equipped with an s-bit advice on a randomly chosen function $f : [n] -> [n]$ and using $q$ oracle queries to $f$, tries to invert a randomly chosen…