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We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…

Data Structures and Algorithms · Computer Science 2007-05-23 David R. Karger

The subject of this work is the patrolling of an environment with the aid of a team of autonomous agents. We consider both the design of open-loop trajectories with optimal properties, and of distributed control laws converging to optimal…

Combinatorics · Mathematics 2015-03-17 Fabio Pasqualetti , Antonio Franchi , Francesco Bullo

Attack Trees (ATs) are a widely used tool for security analysis. ATs can be employed in quantitative security analysis through metrics, which assign a security value to an AT. Many different AT metrics exist, and there exist multiple…

Cryptography and Security · Computer Science 2024-01-19 Milan Lopuhaä-Zwakenberg

Suppose we are given a bipartite graph that admits a perfect matching and an adversary may delete any edge from the graph with the intention of destroying all perfect matchings. We consider the task of adding a minimum cost edge-set to the…

Data Structures and Algorithms · Computer Science 2018-12-06 Felix Hommelsheim , Moritz Mühlenthaler , Oliver Schaudt

Attack Trees are a graphical model of security used to study threat scenarios. While visually appealing and supported by solid theories and effective tools, one of their main drawbacks remains the amount of effort required by security…

Cryptography and Security · Computer Science 2024-09-13 Alyzia-Maria Konsta , Gemma Di Federico , Alberto Lluch Lafuente , Andrea Burattin

Attack graphs provide a representation of possible actions that adversaries can perpetrate to attack a system. They are used by cybersecurity experts to make decisions, e.g., to decide remediation and recovery plans. Different approaches…

Cryptography and Security · Computer Science 2022-02-09 Kéren Saint-Hilaire , Frédéric Cuppens , Nora Cuppens , Joaquin Garcia-Alfaro

We present sublinear-time (randomized) algorithms for finding simple cycles of length at least $k\geq 3$ and tree-minors in bounded-degree graphs. The complexity of these algorithms is related to the distance of the graph from being…

Data Structures and Algorithms · Computer Science 2012-04-04 Artur Czumaj , Oded Goldreich , Dana Ron , C. Seshadhri , Asaf Shapira , Christian Sohler

Recent studies have shown that graph convolution networks (GCNs) are vulnerable to carefully designed attacks, which aim to cause misclassification of a specific node on the graph with unnoticeable perturbations. However, a vast majority of…

Cryptography and Security · Computer Science 2020-04-30 Jihong Wang , Minnan Luo , Fnu Suya , Jundong Li , Zijiang Yang , Qinghua Zheng

Provenance analysis based on system audit data has emerged as a fundamental approach for investigating Advanced Persistent Threat (APT) attacks. Due to the high concealment and long-term persistence of APT attacks, they are only represented…

Cryptography and Security · Computer Science 2025-10-28 Qi Sheng

(see paper for full abstract) Cut problems and connectivity problems on digraphs are two well-studied classes of problems from the viewpoint of parameterized complexity. After a series of papers over the last decade, we now have (almost)…

Data Structures and Algorithms · Computer Science 2019-10-07 Rajesh Chitnis , Andreas Emil Feldmann

Computing a (short) path between two vertices is one of the most fundamental primitives in graph algorithmics. In recent years, the study of paths in temporal graphs, that is, graphs where the vertex set is fixed but the edge set changes…

Discrete Mathematics · Computer Science 2021-05-27 Arnaud Casteigts , Anne-Sophie Himmel , Hendrik Molter , Philipp Zschoche

In the Disjoint Paths problem, the input consists of an $n$-vertex graph $G$ and a collection of $k$ vertex pairs, $\{(s_i,t_i)\}_{i=1}^k$, and the objective is to determine whether there exists a collection $\{P_i\}_{i=1}^k$ of $k$…

Data Structures and Algorithms · Computer Science 2020-08-20 Daniel Lokshtanov , Saket Saurabh , Meirav Zehavi

Edit distance is a measurement of similarity between two sequences such as strings, point sequences, or polygonal curves. Many matching problems from a variety of areas, such as signal analysis, bioinformatics, etc., need to be solved in a…

Computational Geometry · Computer Science 2020-09-10 Kyle Fox , Xinyi Li

We study spreading processes in temporal graphs, i. e., graphs whose connections change over time. These processes naturally model real-world phenomena such as infectious diseases or information flows. More precisely, we investigate how…

Data Structures and Algorithms · Computer Science 2021-07-21 Hendrik Molter , Malte Renken , Philipp Zschoche

We consider the task of estimating a high-dimensional directed acyclic graph, given observations from a linear structural equation model with arbitrary noise distribution. By exploiting properties of common random graphs, we develop a new…

Machine Learning · Statistics 2019-12-30 Arjun Sondhi , Ali Shojaie

We give an algorithm that takes a directed graph $G$ undergoing $m$ edge insertions with lengths in $[1, W]$, and maintains $(1+\epsilon)$-approximate shortest path distances from a fixed source $s$ to all other vertices. The algorithm is…

Data Structures and Algorithms · Computer Science 2025-06-25 Yang P. Liu

We consider the problem of testing graph cluster structure: given access to a graph $G=(V, E)$, can we quickly determine whether the graph can be partitioned into a few clusters with good inner conductance, or is far from any such graph?…

Data Structures and Algorithms · Computer Science 2018-09-19 Ashish Chiplunkar , Michael Kapralov , Sanjeev Khanna , Aida Mousavifar , Yuval Peres

Graph data structures offer a versatile and powerful means to model relationships and interconnections in various domains, promising substantial advantages in data representation, analysis, and visualization. In games, graph-based data…

Machine Learning · Computer Science 2024-09-10 Florian Rupp , Kai Eckert

Finding the graphs that are most similar to a query graph in a large database is a common task with various applications. A widely-used similarity measure is the graph edit distance, which provides an intuitive notion of similarity and…

Databases · Computer Science 2021-10-05 Franka Bause , David B. Blumenthal , Erich Schubert , Nils M. Kriege

Dynamic techniques are a scalable and effective way to analyze concurrent programs. Instead of analyzing all behaviors of a program, these techniques detect errors by focusing on a single program execution. Often a crucial step in these…

Logic in Computer Science · Computer Science 2025-09-16 Umang Mathur , Andreas Pavlogiannis , Hünkar Can Tunç , Mahesh Viswanathan