Related papers: Towards Tight Lower Bounds for Range Reporting on …
We prove an optimal $\Omega(n)$ lower bound on the randomized communication complexity of the much-studied Gap-Hamming-Distance problem. As a consequence, we obtain essentially optimal multi-pass space lower bounds in the data stream model…
In this paper we investigate the problem of building a static data structure that represents a string s using space close to its compressed size, and allows fast access to individual characters of s. This type of structures was investigated…
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…
Kernel ridge regression, in general, is expensive in memory allocation and computation time. This paper addresses low rank approximations and surrogates for kernel ridge regression, which bridge these difficulties. The fundamental…
We consider the classic Set Cover problem in the data stream model. For $n$ elements and $m$ sets ($m\geq n$) we give a $O(1/\delta)$-pass algorithm with a strongly sub-linear $\tilde{O}(mn^{\delta})$ space and logarithmic approximation…
We describe fully retroactive dynamic data structures for approximate range reporting and approximate nearest neighbor reporting. We show how to maintain, for any positive constant $d$, a set of $n$ points in $\R^d$ indexed by time such…
We show how to represent sets in a linear space data structure such that expressions involving unions and intersections of sets can be computed in a worst-case efficient way. This problem has applications in e.g. information retrieval and…
Content delivery networks often employ caching to reduce transmission rates from the central server to the end users. Recently, the technique of coded caching was introduced whereby coding in the caches and coded transmission signals from…
Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the problem of counting inversions in arrays originated in mathematical…
Range closest-pair (RCP) search is a range-search variant of the classical closest-pair problem, which aims to store a given set $S$ of points into some space-efficient data structure such that when a query range $Q$ is specified, the…
Range-aggregate query is an important type of queries with numerous applications. It aims to obtain some structural information (defined by an aggregate function $F(\cdot)$) of the points (from a point set $P$) inside a given query range…
In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…
The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…
Shallow cuttings are a fundamental tool in computational geometry and spatial databases for solving offline and online range searching problems. For a set $P$ of $N$ points in 3-D, at SODA'14, Afshani and Tsakalidis designed an optimal…
Many problems in computer vision and recommender systems involve low-rank matrices. In this work, we study the problem of finding the maximum entry of a stochastic low-rank matrix from sequential observations. At each step, a learning agent…
Batch codes are a useful notion of locality for error correcting codes, originally introduced in the context of distributed storage and cryptography. Many constructions of batch codes have been given, but few lower bound (limitation)…
We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…
In the Online Machine Covering problem jobs, defined by their sizes, arrive one by one and have to be assigned to $m$ parallel and identical machines, with the goal of maximizing the load of the least-loaded machine. In this work, we study…
We present and discuss general techniques for proving inapproximability results for truthful mechanisms. We make use of these techniques to prove lower bounds on the approximability of several non-utilitarian multi-parameter problems. In…
Large Reasoning Models (LRMs) demonstrate remarkable problem-solving capabilities through extended Chain-of-Thought (CoT) reasoning but often produce excessively verbose and redundant reasoning traces. This inefficiency incurs high…