Related papers: Smoothed Analysis of Dynamic Graph Algorithms
We study dynamic algorithms in the model of algorithms with predictions. We assume the algorithm is given imperfect predictions regarding future updates, and we ask how such predictions can be used to improve the running time. This can be…
Real-world graph data environments intrinsically exist noise (e.g., link and structure errors) that inevitably disturb the effectiveness of graph representation and downstream learning tasks. For homogeneous graphs, the latest works use…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…
We present a new approach for finding matchings in dense graphs by building on Szemer\'edi's celebrated Regularity Lemma. This allows us to obtain non-trivial albeit slight improvements over longstanding bounds for matchings in streaming…
We consider the problem of aggregating data in a dynamic graph, that is, aggregating the data that originates from all nodes in the graph to a specific node, the sink. We are interested in giving lower bounds for this problem, under…
We study fundamental directed graph (digraph) problems in the streaming model. An initial investigation by Chakrabarti, Ghosh, McGregor, and Vorotnikova [SODA'20] on streaming digraphs showed that while most of these problems are provably…
In recent years, Graph Neural Networks (GNNs) have achieved remarkable success in many graph mining tasks. However, scaling them to large graphs is challenging due to the high computational and storage costs of repeated feature propagation…
We consider directed graph algorithms in a streaming setting, focusing on problems concerning orderings of the vertices. This includes such fundamental problems as topological sorting and acyclicity testing. We also study the related…
Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an…
The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the…
The 3-domatic number problem asks whether a given graph can be partitioned intothree dominating sets. We prove that this problem can be solved by a deterministic algorithm in time 2.695^n (up to polynomial factors). This result improves the…
The simplex method for linear programming is known to be highly efficient in practice, and understanding its performance from a theoretical perspective is an active research topic. The framework of smoothed analysis, first introduced by…
We propose a unifying framework for smoothed analysis of combinatorial local optimization problems, and show how a diverse selection of problems within the complexity class PLS can be cast within this model. This abstraction allows us to…
Researchers have designed many algorithms to measure the distances between graph nodes, such as average hitting times of random walks, cosine distances from DeepWalk, personalized PageRank, etc. Successful although these algorithms are,…
Accurate and robust trajectory prediction is essential for safe and efficient autonomous driving, yet recent work has shown that even state-of-the-art prediction models are highly vulnerable to inputs being mildly perturbed by adversarial…
We present an algorithm for the maximum matching problem in dynamic (insertion-deletions) streams with *asymptotically optimal* space complexity: for any $n$-vertex graph, our algorithm with high probability outputs an $\alpha$-approximate…
We present a novel gradient-free algorithm to solve a convex stochastic optimization problem, such as those encountered in medicine, physics, and machine learning (e.g., adversarial multi-armed bandit problem), where the objective function…
Randomized smoothing is a popular certified defense against adversarial attacks. In its essence, we need to solve a problem of statistical estimation which is usually very time-consuming since we need to perform numerous (usually $10^5$)…
We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity,…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…