相关论文: One (more) line on the most Ancient Algorithm in H…

The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…

Finding the length of the longest increasing subsequence (LIS) is a classic algorithmic problem. Let $n$ denote the size of the array. Simple $O(n\log n)$ algorithms are known for this problem. We develop a polylogarithmic time randomized…

We give a near-optimal quantum algorithm for the longest common substring (LCS) problem between two run-length encoded (RLE) strings, with the assumption that the prefix-sums of the run-lengths are given. Our algorithm costs…

We investigate the approximation for computing the sum $a_1+...+a_n$ with an input of a list of nonnegative elements $a_1,..., a_n$. If all elements are in the range $[0,1]$, there is a randomized algorithm that can compute an…

We describe an algorithm that takes as input a complex sequence $(u_n)$ given by a linear recurrence relation with polynomial coefficients along with initial values, and outputs a simple explicit upper bound $(v_n)$ such that $|u_n| \leq…

We give an iterative algorithm for finding the maximum flow between a set of sources and sinks that lie on the boundary of a planar graph. Our algorithm uses only O(n) queries to simple data structures, achieving an O(n log n) running time…

We propose a novel randomized linear programming algorithm for approximating the optimal policy of the discounted Markov decision problem. By leveraging the value-policy duality and binary-tree data structures, the algorithm adaptively…

Our main result is a new proof of correctness of Euclid's algorithm. The proof is conducted in algorithmic theory of natural numbers Th3. A formula H is constructed that expresses the halting property of the algorithm. Next, the proof of H…

We introduce a just-in-time runtime program transformation strategy based on repeated recursion unfolding. Our online program optimization generates several versions of a recursion differentiated by the minimal number of recursive steps…

For online matching with the line metric, we present a lower bound of $\Omega(\log n)$ on the approximation ratio of any online (possibly randomized) algorithm. This beats the previous best lower bound of $\Omega(\sqrt{\log n})$ and matches…

One of the greatest algorithms of all time is Quicksort. Its average running time is famously O(nlog(n)), and its variance, less famously, is O(n^2) (hence its standard deviation is O(n)). But what about higher moments? Here we find…

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…

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 note gives a lower bound of $\Omega(n^{\lceil 2d/3\rceil})$ on the maximal complexity of the Euclidean Voronoi diagram of $n$ non-intersecting lines in $\mathbb{R}^d$ for $d>2$.

Longest common extension queries (LCE queries) and runs are ubiquitous in algorithmic stringology. Linear-time algorithms computing runs and preprocessing for constant-time LCE queries have been known for over a decade. However, these…

We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given $n$ $d$-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training…

Gomory-Hu tree [Gomory and Hu, 1961] is a succinct representation of pairwise minimum cuts in an undirected graph. When the input graph has general edge weights, classic algorithms need at least cubic running time to compute a Gomory-Hu…

We revisit Min-Mean-Cycle, the classical problem of finding a cycle in a weighted directed graph with minimum mean weight. Despite an extensive algorithmic literature, previous work falls short of a near-linear runtime in the number of…

We present an algorithm to find an {\it Euclidean Shortest Path} from a source vertex $s$ to a sink vertex $t$ in the presence of obstacles in $\Re^2$. Our algorithm takes $O(T+m(\lg{m})(\lg{n}))$ time and $O(n)$ space. Here, $O(T)$ is the…

Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empirical performance,…