Related papers: Space-Efficient Data Structures for Lattices
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…
Let $\mathcal{D}$ be a set of $n$ pairwise disjoint unit disks in the plane. We describe how to build a data structure for $\mathcal{D}$ so that for any point set $P$ containing exactly one point from each disk, we can quickly find the…
In the last decades, the necessity to process massive amounts of textual data fueled the development of compressed text indexes: data structures efficiently answering queries on a given text while occupying space proportional to the…
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…
Motivated by lattice mixture identification and grain boundary detection, we present a framework for lattice pattern representation and comparison, and propose an efficient algorithm for lattice separation. We define new scale and shape…
We present a data structure that stores a sequence $s[1..n]$ over alphabet $[1..\sigma]$ in $n\Ho(s) + o(n)(\Ho(s){+}1)$ bits, where $\Ho(s)$ is the zero-order entropy of $s$. This structure supports the queries \access, \rank\ and \select,…
Order-preserving pattern matching was introduced recently but it has already attracted much attention. Given a reference sequence and a pattern, we want to locate all substrings of the reference sequence whose elements have the same…
This paper addresses the overwhelming computational resources needed with standard numerical approaches to simulate architected materials. Those multiscale heterogeneous lattice structures gain intensive interest in conjunction with the…
Palindromes are strings that read the same forward and backward. The computation of palindromic structures within strings is a fundamental problem in string algorithms, being motivated by potential applications in formal language theory and…
Lattice-type structures can provide a combination of stiffness with light weight that is desirable in a variety of applications. Design optimization of these structures must rely on approximations of the governing physics to render solution…
An arrangement of $n$ curves in the plane is given. The query is a point $q$ and the goal is to find the face of the arrangement that contains $q$. A data-structure for point-location, preprocesses the curves into a data structure of…
Let $S$ be a string of length $n$ over an alphabet $\Sigma$ and let $Q$ be a subset of $\Sigma$ of size $q \geq 2$. The 'co-occurrence problem' is to construct a compact data structure that supports the following query: given an integer $w$…
Lattice-based planning techniques simplify the motion planning problem for autonomous vehicles by limiting available motions to a pre-computed set of primitives. These primitives are then combined online to generate more complex maneuvers.…
The nearest lattice point problem in $\mathbb{R}^n$ is formulated in a distributed network with $n$ nodes. The objective is to minimize the probability that an incorrect lattice point is found, subject to a constraint on inter-node…
Most of the attention in statistical compression is given to the space used by the compressed sequence, a problem completely solved with optimal prefix codes. However, in many applications, the storage space used to represent the prefix…
We present a highly optimized implementation of tiered vectors, a data structure for maintaining a sequence of $n$ elements supporting access in time $O(1)$ and insertion and deletion in time $O(n^\epsilon)$ for $\epsilon > 0$ while using…
We revisit the range minimum query problem and present a new O(n)-space data structure that supports queries in O(1) time. Although previous data structures exist whose asymptotic bounds match ours, our goal is to introduce a new solution…
We study map lattices coupled by collision and show how perturbations of transfer operators associated with the spatially periodic approximation of the model can be used to extract information about collisions per lattice unit. More…
This paper studies the lattice agreement problem and the generalized lattice agreement problem in distributed message passing systems. In the lattice agreement problem, given input values from a lattice, processes have to non-trivially…
We introduce a lattice model of protein conformations which is able to reproduce second structures of proteins (alpha--helices and beta--sheets). This model is based on the following two main ideas. First, we model backbone parts of amino…