Related papers: Independent Range Sampling on Interval Data (Longe…
Linear causal analysis is central to a wide range of important application spanning finance, the physical sciences, and engineering. Much of the existing literature in linear causal analysis operates in the time domain. Unfortunately, the…
The problem of recovering (count and sum) range queries over multidimensional data only on the basis of aggregate information on such data is addressed. This problem can be formalized as follows. Suppose that a transformation T producing a…
The string indexing problem is a fundamental computational problem with numerous applications, including information retrieval and bioinformatics. It aims to efficiently solve the pattern matching problem: given a text T of length n for…
We consider the problem of estimating the number of distinct elements in a large data set (or, equivalently, the support size of the distribution induced by the data set) from a random sample of its elements. The problem occurs in many…
Traditional orthogonal range problems allow queries over a static set of points, each with some value. Dynamic variants allow points to be added or removed, one at a time. To support more powerful updates, we introduce the Grid Range class…
Sampling is a fundamental problem in computer science and statistics. However, for a given task and stream, it is often not possible to choose good sampling probabilities in advance. We derive a general framework for adaptively changing the…
Sampling is a fundamental technique, and sampling without replacement is often desirable when duplicate samples are not beneficial. Within machine learning, sampling is useful for generating diverse outputs from a trained model. We present…
Probabilistic distributions over spanning trees in directed graphs are a fundamental model of dependency structure in natural language processing, syntactic dependency trees. In NLP, dependency trees often have an additional root…
Interval scheduling is a basic problem in the theory of algorithms and a classical task in combinatorial optimization. We develop a set of techniques for partitioning and grouping jobs based on their starting and ending times, that enable…
Indexing intervals is a fundamental problem, finding a wide range of applications. Recent work on managing large collections of intervals in main memory focused on overlap joins and temporal aggregation problems. In this paper, we propose…
We consider an interval coverage problem. Given $n$ intervals of the same length on a line $L$ and a line segment $B$ on $L$, we want to move the intervals along $L$ such that every point of $B$ is covered by at least one interval and the…
We propose a variant of the Rapidly Exploring Random Tree Star (RRT$^{\star}$) algorithm to synthesize trajectories satisfying a given spatio-temporal specification expressed in a fragment of Signal Temporal Logic (STL) for linear systems.…
The range, segment and rectangle query problems are fundamental problems in computational geometry, and have extensive applications in many domains. Despite the significant theoretical work on these problems, efficient implementations can…
This paper studies a multi-armed bandit (MAB) version of the range-searching problem. In its basic form, range searching considers as input a set of points (on the real line) and a collection of (real) intervals. Here, with each specified…
Modern tracking technology has made the collection of large numbers of densely sampled trajectories of moving objects widely available. We consider a fundamental problem encountered when analysing such data: Given $n$ polygonal curves $S$…
For any $\epsilon \in (0,1)$, a $(1+\epsilon)$-approximate range mode query asks for the position of an element whose frequency in the query range is at most a factor $(1+\epsilon)$ smaller than the true mode. For this problem, we design an…
We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in…
Recent advancements in large language models (LLMs) have highlighted their potential across a variety of tasks, but their performance still heavily relies on the design of effective prompts. Existing methods for automatic prompt…
We consider the classical makespan minimization scheduling problem where $n$ jobs must be scheduled on $m$ identical machines. Using weighted random sampling, we developed two sublinear time approximation schemes: one for the case where $n$…
Independent set is a fundamental problem in combinatorial optimization. While in general graphs the problem is essentially inapproximable, for many important graph classes there are approximation algorithms known in the offline setting.…