Related papers: Lower Bounds for Semialgebraic Range Searching and…
This paper presents a distributed O(1)-approximation algorithm, with expected-$O(\log \log n)$ running time, in the $\mathcal{CONGEST}$ model for the metric facility location problem on a size-$n$ clique network. Though metric facility…
We introduce space-efficient plane-sweep algorithms for basic planar geometric problems. It is assumed that the input is in a read-only array of $n$ items and that the available workspace is $\Theta(s)$ bits, where $\lg n \leq s \leq n…
This paper investigates the number of quantum queries made to solve the problem of reconstructing an unknown string from its substrings in a certain query model. More concretely, the goal of the problem is to identify an unknown string $S$…
We study an active cluster recovery problem where, given a set of $n$ points and an oracle answering queries like "are these two points in the same cluster?", the task is to recover exactly all clusters using as few queries as possible. We…
In the range closest pair problem, we want to construct a data structure storing a set $S$ of $n$ points in the plane, such that for any axes-parallel query rectangle $R$, the closest pair in the set $R \cap S$ can be reported. The…
We consider encoding problems for range queries on arrays. In these problems the goal is to store a structure capable of recovering the answer to all queries that occupies the information theoretic minimum space possible, to within lower…
A substring Q of a string S is called a shortest unique substring (SUS) for interval [s,t] in S, if Q occurs exactly once in S, this occurrence of Q contains interval [s,t], and every substring of S which contains interval [s,t] and is…
We prove lower bounds on the error probability of a quantum algorithm for searching through an unordered list of N items, as a function of the number T of queries it makes. In particular, if T=O(sqrt{N}) then the error is lower bounded by a…
We prove that with high probability over the choice of a random graph $G$ from the Erd\H{o}s-R\'enyi distribution $G(n,1/2)$, the $n^{O(d)}$-time degree $d$ Sum-of-Squares semidefinite programming relaxation for the clique problem will give…
We propose a new query application for the well-known Trapezoidal Search DAG (TSD) of a set of $n$~line segments in the plane, where queries are allowed to be {\em vertical line segments}. We show that a simple Depth-First Search reports…
We consider the problem of encoding a string of length $n$ from an integer alphabet of size $\sigma$ so that access and substring equality queries (that is, determining the equality of any two substrings) can be answered efficiently. Any…
Range minimum queries (RMQs) are fundamental operations with widespread applications in database management, text indexing and computational biology. While many space-efficient data structures have been designed for RMQs on arrays with…
In this paper, we present and study the \emph{Hamming distance oracle problem}. In this problem, the task is to preprocess two strings $S$ and $T$ of lengths $n$ and $m$, respectively, to obtain a data-structure that is able to answer…
We present time-space trade-offs for computing the Euclidean minimum spanning tree of a set $S$ of $n$ point-sites in the plane. More precisely, we assume that $S$ resides in a random-access memory that can only be read. The edges of the…
We consider compact representations of collections of similar strings that support random access queries. The collection of strings is given by a rooted tree where edges are labeled by an edit operation (inserting, deleting, or replacing a…
The set equality problem is to tell whether two sets $A$ and $B$ are equal or disjoint under the promise that one of these is the case. This problem is related to the Graph Isomorphism problem. It was an open problem to find any $\omega(1)$…
Given a finite set satisfying condition $\mathcal{A}$, the subset selection problem asks, how large of a subset satisfying condition $\mathcal{B}$ can we find? We make progress on three instances of subset selection problems in planar point…
We study property testing in the subcube conditional model introduced by Bhattacharyya and Chakraborty (2017). We obtain the first equivalence test for $n$-dimensional distributions that is quasi-linear in $n$, improving the previously…
We study a convex resource allocation problem in which lower and upper bounds are imposed on partial sums of allocations. This model is linked to a large range of applications, including production planning, speed optimization, stratified…
Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider…