Related papers: Towards Tight Lower Bounds for Range Reporting on …

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…

A classic data structure problem is to preprocess a string T of length $n$ so that, given a query $q$, we can quickly find all substrings of T with Hamming distance at most $k$ from the query string. Variants of this problem have seen…

The goal of this work is to fill a gap in [Yang, SIAM J. Matrix Anal. Appl, 41 (2020), 1797--1825]. In that work, an approximation procedure was proposed for orthogonal low-rank tensor approximation; however, the approximation lower bound…

Data dissemination is a fundamental task in distributed computing. This paper studies broadcast problems in various innovative models where the communication network connecting $n$ processes is dynamic (e.g., due to mobility or failures)…

Memory-augmented neural networks consisting of a neural controller and an external memory have shown potentials in long-term sequential learning. Current RAM-like memory models maintain memory accessing every timesteps, thus they do not…

As DNA data storage moves closer to practical deployment, minimizing sequencing coverage depth is essential to reduce both operational costs and retrieval latency. This paper addresses the recently studied Random Access Problem, which…

This paper proves the first super-logarithmic lower bounds on the cell probe complexity of dynamic boolean (a.k.a. decision) data structure problems, a long-standing milestone in data structure lower bounds. We introduce a new method for…

We present a structure in external memory for "top-k range reporting", which uses linear space, answers a query in O(lg_B n + k/B) I/Os, and supports an update in O(lg_B n) amortized I/Os, where n is the input size, and B is the block size.…

The rank problem in succinct data structures asks to preprocess an array A[1..n] of bits into a data structure using as close to n bits as possible, and answer queries of the form rank(k) = Sum_{i=1}^k A[i]. The problem has been intensely…

We develop a new technique for proving cell-probe lower bounds on dynamic data structures. This technique enables us to prove an amortized randomized Omega(lg n) lower bound per operation for several data structural problems on n elements,…

Inference-time computation offers a powerful axis for scaling the performance of language models. However, naively increasing computation in techniques like Best-of-N sampling can lead to performance degradation due to reward hacking.…

Let ${\cal{D}}$ = $\{d_1, d_2, d_3, ..., d_D\}$ be a given set of $D$ (string) documents of total length $n$. The top-$k$ document retrieval problem is to index $\cal{D}$ such that when a pattern $P$ of length $p$, and a parameter $k$ come…

In this paper we consider a variant of the orthogonal range reporting problem when all points should be reported in the sorted order of their $x$-coordinates. We show that reporting two-dimensional points with this additional condition can…

We seek to perform efficient queries for the predecessor among $n$ values stored in $k$ sorted arrays. Evading the $\Omega(n \log k)$ lower bound from merging $k$ arrays, we support predecessor queries in $O(\log n)$ time after $O(n…

First order methods endowed with global convergence guarantees operate using global lower bounds on the objective. The tightening of the bounds has been shown to increase both the theoretical guarantees and the practical performance. In…

Given a conjunctive query and a database instance, we aim to develop an index that can efficiently answer spatial queries on the results of a conjunctive query. We are interested in some commonly used spatial queries, such as range…

In this paper we study lower bounds for the fundamental problem of text indexing with mismatches and differences. In this problem we are given a long string of length $n$, the "text", and the task is to preprocess it into a data structure…

We consider the dictionary problem in external memory and improve the update time of the well-known buffer tree by roughly a logarithmic factor. For any \lambda >= max {lg lg n, log_{M/B} (n/B)}, we can support updates in time O(\lambda /…

We study a sequential resource allocation problem between a fixed number of arms. On each iteration the algorithm distributes a resource among the arms in order to maximize the expected success rate. Allocating more of the resource to a…

In the planar range skyline reporting problem, we store a set P of n 2D points in a structure such that, given a query rectangle Q = [a_1, a_2] x [b_1, b_2], the maxima (a.k.a. skyline) of P \cap Q can be reported efficiently. The query is…