Related papers: A Near-Linear Pseudopolynomial Time Algorithm for …

Longest common substring (LCS), longest palindrome substring (LPS), and Ulam distance (UL) are three fundamental string problems that can be classically solved in near linear time. In this work, we present sublinear time quantum algorithms…

We devise a polynomial-time approximation scheme for the classical geometric problem of finding an approximate short path amid weighted regions. In this problem, a triangulated region P comprising of n vertices, a positive weight associated…

In this work, we study the problem of finding the maximum value of a non-negative submodular function subject to a limit on the number of items selected, a ubiquitous problem that appears in many applications, such as data summarization and…

Arising from structural graph theory, treewidth has become a focus of study in fixed-parameter tractable algorithms in various communities including combinatorics, integer-linear programming, and numerical analysis. Many NP-hard problems…

We investigate the question whether Subset Sum can be solved by a polynomial-time algorithm with access to a certificate of length poly(k) where k is the maximal number of bits in an input number. In other words, can it be solved using only…

We consider the classic 3SUM problem: given sets of integers $A, B, C $, determine whether there is a tuple $(a, b, c) \in A \times B \times C$ satisfying $a + b + c = 0$. The 3SUM Hypothesis, central in fine-grained complexity, states that…

We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…

We study partial and budgeted versions of the well studied connected dominating set problem. In the partial connected dominating set problem, we are given an undirected graph G = (V,E) and an integer n', and the goal is to find a minimum…

The authors recently gave an $n^{O(\log\log n)}$ time membership query algorithm for properly learning decision trees under the uniform distribution (Blanc et al., 2021). The previous fastest algorithm for this problem ran in $n^{O(\log…

Let $X$ be a set of points in $\mathbb{R}^2$ and $\mathcal{O}$ be a set of geometric objects in $\mathbb{R}^2$, where $|X| + |\mathcal{O}| = n$. We study the problem of computing a minimum subset $\mathcal{O}^* \subseteq \mathcal{O}$ that…

A classical algorithm by Bellman and Ford from the 1950's computes shortest paths in weighted graphs on $n$ vertices and $m$ edges with possibly negative weights in $O(mn)$ time. Indeed, this algorithm is taught regularly in undergraduate…

Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in $O(n \log n)$ time and space. Our goal in this paper is to reduce the space consumption while…

We revisit the 3SUM problem in the \emph{preprocessed universes} setting. We present an algorithm that, given three sets $A$, $B$, $C$ of $n$ integers, preprocesses them in quadratic time, so that given any subsets $A' \subseteq A$, $B'…

In this paper we provide faster algorithms for solving the geometric median problem: given $n$ points in $\mathbb{R}^{d}$ compute a point that minimizes the sum of Euclidean distances to the points. This is one of the oldest non-trivial…

This paper addresses the single-item lot sizing problem with a 1-breakpoint all-units quantity discount in a monotonic setting where the purchase prices are non-increasing over the planning horizon. For this case, we establish several novel…

We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…

We present an $\mathcal{O}^\star(2^{0.5n})$ time and $\mathcal{O}^\star(2^{0.249999n})$ space randomized algorithm for solving worst-case Subset Sum instances with $n$ integers. This is the first improvement over the long-standing…

We consider the approximate pattern matching problem under the edit distance. Given a text $T$ of length $n$, a pattern $P$ of length $m$, and a threshold $k$, the task is to find the starting positions of all substrings of $T$ that can be…

The Subset Sum problem, which asks whether a set of $n$ integers has a subset summing to a target $t$, is a fundamental NP-complete problem in cryptography and combinatorial optimization. The classical meet-in-the-middle (MIM) algorithm of…

We present a sublinear randomized algorithm to compute a sparse Fourier transform for nonequispaced data. Suppose a signal S is known to consist of N equispaced samples, of which only L<N are available. If the ratio p=L/N is not close to 1,…