Related papers: Simpler O(1) Query Algorithm for Level Ancestors

For k>=1, we consider the graph dynamical system known as a k-reversible process. In such process, each vertex in the graph has one of two possible states at each discrete time. Each vertex changes its state between the present time and the…

The use of superposition of states in quantum computation, known as quantum parallelism, has significant advantage in terms of speed over the classical computation. It can be understood from the early invented quantum algorithms such as…

Many search engines such as Google, Bing & Yahoo! show search suggestions when users enter search phrases on their interfaces. These suggestions are meant to assist the user in finding what she wants quickly and also suggesting common…

Min-Cut queries are fundamental: Preprocess an undirected edge-weighted graph, to quickly report a minimum-weight cut that separates a query pair of nodes $s,t$. The best data structure known for this problem simply builds a cut-equivalent…

In this paper we present the first provable approximate nearest-neighbor (ANN) algorithms for Bregman divergences. Our first algorithm processes queries in O(log^d n) time using O(n log^d n) space and only uses general properties of the…

Estimating the average degree of graph is a classic problem in sublinear graph algorithm. Eden, Ron, and Seshadhri (ICALP 2017, SIDMA 2019) gave a simple algorithm for this problem whose running time depended on the graph arboricity, but…

Recently, the predicate detection problem was shown to be in the parallel complexity class NC. In this paper, we give the first work-optimal parallel algorithm to solve the predicate detection problem on a distributed computation with $n$…

Balanced search trees are widely used in computer science to efficiently maintain dynamic ordered data. To support efficient set operations (e.g., union, intersection, difference) using trees, the join-based framework is widely studied.…

Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…

This article introduces a new optimization method to improve mergesort's runtime complexity, when sorting sequences that have equal keys to $O(n log_2 k)$, where $k$ is the number of distinct keys in the sequence. When $k$ is constant, it…

Link-cut trees have been introduced by D.D. Sleator and R.E. Tarjan (Journal of Computer and System Sciences, 1983) with the aim of efficiently maintaining a forest of vertex-disjoint dynamic rooted trees under cut and link operations.…

In recent years, leveraging parallel and distributed computational resources has become essential to solve problems of high computational cost. Bayesian optimization (BO) has shown attractive results in those expensive-to-evaluate problems…

We describe a substring search problem that arises in group presentation simplification processes. We suggest a two-level searching model: skip and match levels. We give two timestamp algorithms which skip searching parts of the text where…

Tree kernels are fundamental tools that have been leveraged in many applications, particularly those based on machine learning for Natural Language Processing tasks. In this paper, we devise a parallel implementation of the sequential…

We design a space-efficient algorithm for performing depth-first search traversal(DFS) of a graph in $O(m+n\log^* n)$ time using $O(n)$ bits of space. While a normal DFS algorithm results in a DFS-tree (in case the graph is connected), our…

Given an $n$-vertex planar embedded digraph $G$ with non-negative edge weights and a face $f$ of $G$, Klein presented a data structure with $O(n\log n)$ space and preprocessing time which can answer any query $(u,v)$ for the shortest path…

Traditional databases commonly support efficient query and update procedures that operate in time which is sublinear in the size of the database. Our goal in this paper is to take a first step toward dynamic reasoning in probabilistic…

We introduce several parallel algorithms operating on a distributed forest of adaptive quadtrees/octrees. They are targeted at large-scale applications relying on data layouts that are more complex than required for standard finite…

An L(2,1)-labeling of a graph $G$ is an assignment $f$ from the vertex set $V(G)$ to the set of nonnegative integers such that $|f(x)-f(y)|\ge 2$ if $x$ and $y$ are adjacent and $|f(x)-f(y)|\ge 1$ if $x$ and $y$ are at distance 2, for all…

Hierarchical clustering studies a recursive partition of a data set into clusters of successively smaller size, and is a fundamental problem in data analysis. In this work we study the cost function for hierarchical clustering introduced by…