Related papers: Near-Optimality for Single-Source Personalized Pag…

We study the Stochastic Shortest Path (SSP) problem with a linear mixture transition kernel, where an agent repeatedly interacts with a stochastic environment and seeks to reach certain goal state while minimizing the cumulative cost.…

Utilizing graph algorithms is a common activity in computer science. Algorithms that perform computations on large graphs are not always efficient. This work investigates the Single-Source Shortest Path (SSSP) problem, which is considered…

For a set $A$ of $n$ people and a set $B$ of $m$ items, with each person having a preference list that ranks all items from most wanted to least wanted, we consider the problem of matching every person with a unique item. A matching $M$ is…

We propose an efficient $\epsilon$-differentially private algorithm, that given a simple {\em weighted} $n$-vertex, $m$-edge graph $G$ with a \emph{maximum unweighted} degree $\Delta(G) \leq n-1$, outputs a synthetic graph which…

In this paper, we propose a novel stochastic gradient estimator -- ProbAbilistic Gradient Estimator (PAGE) -- for nonconvex optimization. PAGE is easy to implement as it is designed via a small adjustment to vanilla SGD: in each iteration,…

In this paper, we present near-optimal space bounds for Lp-samplers. Given a stream of updates (additions and subtraction) to the coordinates of an underlying vector x \in R^n, a perfect Lp sampler outputs the i-th coordinate with…

We study the problem of supporting queries on a string $S$ of length $n$ within a space bounded by the size $\gamma$ of a string attractor for $S$. Recent works showed that random access on $S$ can be supported in optimal…

Stochastic saddle point (SSP) problems are, in general, less studied compared to stochastic minimization problems. However, SSP problems emerge from machine learning (adversarial training, e.g., GAN, AUC maximization), statistics (robust…

We establish nearly optimal upper and lower bounds for approximating decision tree splits in data streams. For regression with labels in the range $\{0,1,\ldots,M\}$, we give a one-pass algorithm using $\tilde{O}(M^2/\epsilon)$ space that…

We bound the smoothed running time of the FLIP algorithm for local Max-Cut as a function of $\alpha$, the arboricity of the input graph. We show that, with high probability and in expectation, the following holds (where $n$ is the number of…

Consider the problem of maximizing the probability of stopping with one of the two highest values in a Bernoulli random walk with arbitrary parameter $p$ and finite time horizon $n$. Allaart \cite{Allaart} proved that the optimal strategy…

The step-reinforced random walk (SRRW), where each step may replicate a randomly chosen past step, exhibits complex dependencies on the history. This paper introduces a generalized SRRW on groups, incorporating arbitrary transformations of…

Large data applications rely on storing data in massive, sparse graphs with millions to trillions of nodes. Graph-based methods, such as node prediction, aim for computational efficiency regardless of graph size. Techniques like localized…

Given a super-critical branching random walk on $\mathbb R$ started from the origin, let $M_n$ be the maximal position of individuals at the $n$-th generation. Under some mild conditions, it is known from \cite{A13} that as…

Given a supercritical branching random walk $\{Z_n\}_{n\geq 0}$ on $\mathbb{R}$, let $Z_n([y,\infty))$ be the number of particles located in $[y,\infty)\subset\mathbb{R}$ at generation $n$. Let $m$ be the mean of the offspring law of…

PageRank, the prestige measure for Web pages used by Google, is the stationary probability of a peculiar random walk on directed graphs, which interpolates between a pure random walk and a process where all nodes have the same probability…

The choice of the PageRank damping factor is not evident. The Google's choice for the value c=0.85 was a compromise between the true reflection of the Web structure and numerical efficiency. However, the Markov random walk on the original…

In the decremental $(1+\epsilon)$-approximate Single-Source Shortest Path (SSSP) problem, we are given a graph $G=(V,E)$ with $n = |V|, m = |E|$, undergoing edge deletions, and a distinguished source $s \in V$, and we are asked to process…

How large a fraction of a graph must one explore to rank a small set of nodes according to their PageRank scores? We show that the answer is quite nuanced, and depends crucially on the interplay between the correctness guarantees one…

Given the damping factor $\alpha$ and precision tolerance $\epsilon$, \citet{andersen2006local} introduced Approximate Personalized PageRank (APPR), the \textit{de facto local method} for approximating the PPR vector, with runtime bounded…