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This paper develops a new technique for proving amortized, randomized cell-probe lower bounds on dynamic data structure problems. We introduce a new randomized nondeterministic four-party communication model that enables "accelerated",…

Data Structures and Algorithms · Computer Science 2016-04-12 Omri Weinstein , Huacheng Yu

We report the first improvement in the space-time trade-off of lower bounds for the orthogonal range searching problem in the semigroup model, since Chazelle's result from 1990. This is one of the very fundamental problems in range…

Data Structures and Algorithms · Computer Science 2019-03-20 Peyman Afshani

Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored the constant factors or not obtained the tightest possible values. Recent work has…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-05-27 Hussam Al Daas , Grey Ballard , Laura Grigori , Suraj Kumar , Kathryn Rouse

We study the fundamental problem of approximate nearest neighbor search in $d$-dimensional Hamming space $\{0,1\}^d$. We study the complexity of the problem in the famous cell-probe model, a classic model for data structures. We consider…

Data Structures and Algorithms · Computer Science 2016-02-16 Mingmou Liu , Xiaoyin Pan , Yitong Yin

We prove essentially optimal fine-grained lower bounds on the gap between a data structure and a partially retroactive version of the same data structure. Precisely, assuming any one of three standard conjectures, we describe a problem that…

Data Structures and Algorithms · Computer Science 2022-11-29 Lily Chung , Erik D. Demaine , Dylan Hendrickson , Jayson Lynch

Since the introduction of retroactive data structures at SODA 2004, a major unsolved problem has been to bound the gap between the best partially retroactive data structure (where changes can be made to the past, but only the present can be…

Data Structures and Algorithms · Computer Science 2018-04-26 Lijie Chen , Erik D. Demaine , Yuzhou Gu , Virginia Vassilevska Williams , Yinzhan Xu , Yuancheng Yu

Given an array of size $n$ from a total order, we consider the problem of constructing a data structure that supports various queries (range minimum/maximum queries with their variants and next/previous larger/smaller queries) efficiently.…

Data Structures and Algorithms · Computer Science 2025-06-05 Seungbum Jo , Geunho Kim

We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…

Information Theory · Computer Science 2018-08-28 Chao Tian

We present space-efficient parallel strategies for two fundamental combinatorial search problems, namely, backtrack search and branch-and-bound, both involving the visit of an $n$-node tree of height $h$ under the assumption that a node can…

Data Structures and Algorithms · Computer Science 2014-03-27 Andrea Pietracaprina , Geppino Pucci , Francesco Silvestri , Fabio Vandin

We consider the problem of performing predecessor searches in a bounded universe while achieving query times that depend on the distribution of queries. We obtain several data structures with various properties: in particular, we give data…

Data Structures and Algorithms · Computer Science 2017-07-06 Prosenjit Bose , Rolf Fagerberg , John Howat , Pat Morin

We develop an extension of recently developed methods for obtaining time-space tradeoff lower bounds for problems of learning from random test samples to handle the situation where the space of tests is signficantly smaller than the space…

Machine Learning · Computer Science 2017-08-10 Paul Beame , Shayan Oveis Gharan , Xin Yang

In a landmark paper, P\v{a}tra\c{s}cu demonstrated how a single lower bound for the static data structure problem of reachability in the butterfly graph, could be used to derive a wealth of new and previous lower bounds via reductions.…

Data Structures and Algorithms · Computer Science 2020-11-03 Kasper Green Larsen , Jonathan Lindegaard Starup , Jesper Steensgaard

In this paper, we investigate space-time tradeoffs for answering Boolean conjunctive queries. The goal is to create a data structure in an initial preprocessing phase and use it for answering (multiple) queries. Previous work has developed…

Data Structures and Algorithms · Computer Science 2023-08-15 Shaleen Deep , Xiao Hu , Paraschos Koutris

Given an integer array $A[1..n]$, the Range Minimum Query problem (RMQ) asks to preprocess $A$ into a data structure, supporting RMQ queries: given $a,b\in [1,n]$, return the index $i\in[a,b]$ that minimizes $A[i]$, i.e.,…

Data Structures and Algorithms · Computer Science 2021-11-05 Mingmou Liu , Huacheng Yu

Read-only memory model is a classical model of computation to study time-space tradeoffs of algorithms. One of the classical results on the ROM model is that any sorting algorithm that uses O(s) words of extra space requires $\Omega…

Data Structures and Algorithms · Computer Science 2017-11-28 Sankardeep Chakraborty , Anish Mukherjee , Venkatesh Raman , Srinivasa Rao Satti

It is widely assumed that $O(m+\lg \sigma)$ is the best one can do for finding a pattern of length $m$ in a compacted trie storing strings over an alphabet of size $\sigma$, if one insists on linear-size data structures and deterministic…

Data Structures and Algorithms · Computer Science 2013-02-15 Johannes Fischer , Pawel Gawrychowski

There are several known data structures that answer distance queries between two arbitrary vertices in a planar graph. The tradeoff is among preprocessing time, storage space and query time. In this paper we present three data structures…

Data Structures and Algorithms · Computer Science 2011-02-23 Yahav Nussbaum

We attempt to determine the best order and search algorithm to store $n$ comparable data items in an array, $A$, of length $n$ so that we can, for any query value, $x$, quickly find the smallest value in $A$ that is greater than or equal to…

Data Structures and Algorithms · Computer Science 2017-03-16 Paul-Virak Khuong , Pat Morin

Under the word RAM model, we design three data structures that can be constructed in $O(n\sqrt{\lg n})$ time over $n$ points in an $n \times n$ grid. The first data structure is an $O(n\lg^{\epsilon} n)$-word structure supporting orthogonal…

Data Structures and Algorithms · Computer Science 2020-06-23 Younan Gao , Meng He , Yakov Nekrich

We investigate the complexity of sorting in the model of sequential quantum circuits. While it is known that in general a quantum algorithm based on comparisons alone cannot outperform classical sorting algorithms by more than a constant…

Quantum Physics · Physics 2007-05-23 Hartmut Klauck