相关论文: Gap Amplification for Small-Set Expansion via Rand…

One of the most important properties of high dimensional expanders is that high dimensional random walks converge rapidly. This property has proven to be extremely useful in variety of fields in the theory of computer science from agreement…

Among observables characterising the random exploration of a graph or lattice, the cover time, namely the time to visit every site, continues to attract widespread interest. Much insight about cover times is gained by mapping to the…

Random walk-based node embedding algorithms have attracted a lot of attention due to their scalability and ease of implementation. Previous research has focused on different walk strategies, optimization objectives, and embedding learning…

The Forest Augmentation Problem (FAP) asks for a minimum set of additional edges (links) that make a given forest 2-edge-connected while spanning all vertices. A key special case is the Path Augmentation Problem (PAP), where the input…

We revisit the asymptotic analysis of probabilistic construction of adjacency matrices of expander graphs proposed in [4]. With better bounds we derived a new reduced sample complexity for the number of nonzeros per column of these…

We prove existence of asymptotic entropy of random walks on regular languages over a finite alphabet and we give formulas for it. Furthermore, we show that the entropy varies real-analytically in terms of probability measures of constant…

Counting integer solutions of linear constraints has found interesting applications in various fields. It is equivalent to the problem of counting lattice points inside a polytope. However, state-of-the-art algorithms for this problem…

In this paper we present linear time approximation schemes for several generalized matching problems on nonbipartite graphs. Our results include $O_\epsilon(m)$-time algorithms for $(1-\epsilon)$-maximum weight $f$-factor and…

For a graph $G$ on $n$ vertices, naively sampling the position of a random walk of at time $t$ requires work $\Omega(t)$. We desire local access algorithms supporting $\text{position}(G,s,t)$ queries, which return the position of a random…

To fully uncover the great potential of deep neural networks (DNNs), various learning algorithms have been developed to improve the model's generalization ability. Recently, sharpness-aware minimization (SAM) establishes a generic scheme…

Representing nodes in a network as dense vectors node embeddings is important for understanding a given network and solving many downstream tasks. In particular, for weighted homophilous graphs where similar nodes are connected with larger…

We investigate three aspects of weak* convergence of the $n$-step distributions of random walks on finite volume homogeneous spaces $G/\Gamma$ of semisimple real Lie groups. First, we look into the obvious obstruction to the upgrade from…

Sharpness-aware Minimization (SAM) has been proposed recently to improve model generalization ability. However, SAM calculates the gradient twice in each optimization step, thereby doubling the computation costs compared to stochastic…

In this paper we extend our recent work on two-dimensional (2D) diffusive search-and-capture processes with multiple small targets (narrow capture problems) by considering an asymptotic expansion of the Laplace transformed probability flux…

We present the analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from the regular to random behavior with increasing distance from the starting point of the…

We (claim to) prove the extremely surprising fact that NP=RP. It is achieved by creating a Fully Polynomial-Time Randomized Approximation Scheme (FPRAS) for approximately counting the number of independent sets in bounded degree graphs,…

We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…

Analyzing social graphs with limited data access is challenging for third-party researchers. To address this challenge, a number of algorithms that estimate structural properties via a random walk have been developed. However, most existing…

We define a new stochastic process on general simplicial complexes which allows to study their spectral and homological properties. Some results for random walks on graphs are shown to hold in this general setting. As an application, the…

Expander graphs, due to their mixing properties, are useful in many algorithms and combinatorial constructions. One can produce an expander graph with high probability by taking a random graph (e.g., the union of $d$ random bijections for a…