Related papers: Logarithmic-Time Updates and Queries in Probabilis…
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…
I present a parallel algorithm for exact probabilistic inference in Bayesian networks. For polytree networks with n variables, the worst-case time complexity is O(log n) on a CREW PRAM (concurrent-read, exclusive-write parallel…
In this paper we present novel algorithmic techniques with a O(H(N)+N/H(N)) time complexity for performing several types of queries and updates on general rooted trees, binary search trees and lists of size N. For rooted trees we introduce…
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…
Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
Updating and querying on a range is a classical algorithmic problem with a multitude of applications. The Segment Tree data structure is particularly notable in handling the range query and update operations. A Segment Tree divides the…
Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…
Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…
We describe a framework for maintaining forest algebra representations that are of logarithmic height for unranked trees. Such representations can be computed in O(n) time and updated in O(log(n)) time. The framework is of potential…
Navarro and Sadakane [TALG 2014] gave a dynamic succinct data structure for storing an ordinal tree. The structure supports tree queries in either $O(\log n/\log\log n)$ or $O(\log n)$ time, and insertion or deletion of a single node in…
Bayesian online algorithms for Sum-Product Networks (SPNs) need to update their posterior distribution after seeing one single additional instance. To do so, they must compute moments of the model parameters under this distribution. The…
Efficient stochastic simulation algorithms are of paramount importance to the study of spreading phenomena on complex networks. Using insights and analytical results from network science, we discuss how the structure of contacts affects the…
This paper considers fully dynamic graph algorithms with both faster worst case update time and sublinear space. The fully dynamic graph connectivity problem is the following: given a graph on a fixed set of n nodes, process an online…
Gaussian processes (GPs) produce good probabilistic models of functions, but most GP kernels require $O((n+m)n^2)$ time, where $n$ is the number of data points and $m$ the number of predictive locations. We present a new kernel that allows…
A fundamental problem in data management is to find the elements in an array that match a query. Recently, learned indexes are being extensively used to solve this problem, where they learn a model to predict the location of the items in…
We present the first sub-quadratic time algorithm that with high probability correctly reconstructs phylogenetic trees for short sequences generated by a Markov model of evolution. Due to rapid expansion in sequence databases, such very…
A Bayesian network is a directed acyclic graph that represents statistical dependencies between variables of a joint probability distribution. A fundamental task in data science is to learn a Bayesian network from observed data.…
We suggest a new non-recursive algorithm for constructing a binary search tree given an array of numbers. The algorithm has $O(N)$ time and $O(1)$ memory complexity if the given array of $N$ numbers is sorted. The resulting tree is of…
In this paper we show that two-dimensional nearest neighbor queries can be answered in optimal $O(\log n)$ time while supporting insertions in $O(\log^{1+\varepsilon}n)$ time. No previous data structure was known that supports $O(\log…
We give an algorithm to enumerate the results on trees of monadic second-order (MSO) queries represented by nondeterministic tree automata. After linear time preprocessing (in the input tree), we can enumerate answers with linear delay (in…