Related papers: Cycle Basis Algorithms for Reducing Maximum Edge P…
The problem of finding the longest simple cycle in a directed graph is NP-hard, with critical applications in computational biology, scheduling, and network analysis. Existing approaches include exact algorithms with exponential runtimes,…
Pose graph optimization is a special case of the simultaneous localization and mapping problem where the only variables to be estimated are pose variables and the only measurements are inter-pose constraints. The vast majority of pose graph…
The edge list model is arguably the simplest input model for graphs, where the graph is specified by a list of its edges. In this model, we study the quantum query complexity of three variants of the triangle finding problem. The first asks…
Getting a labeling of vertices close to the structure of the graph has been proved to be of interest in many applications e.g., to follow smooth signals indexed by the vertices of the network. This question can be related to a graph…
We study the problems of finding a minimum cycle basis (a minimum weight set of cycles that form a basis for the cycle space) and a minimum homology basis (a minimum weight set of cycles that generates the $1$-dimensional…
Given an $n$-vertex $m$-edge graph $G$ with non negative edge-weights, the girth of $G$ is the weight of a shortest cycle in $G$. For any graph $G$ with polynomially bounded integer weights, we present a deterministic algorithm that…
A cycle cover of a bridgeless graph $G$ is a collection of simple cycles in $G$ such that each edge $e$ appears on at least one cycle. The common objective in cycle cover computation is to minimize the total lengths of all cycles. Motivated…
We address a specific case of the matroid intersection problem: given a set of graphs sharing the same set of vertices, select a minimum cycle basis for each graph to maximize the size of their intersection. We provide a comprehensive…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
Given a network, the critical node detection problem finds a subset of nodes whose removal disrupts the network connectivity. Since many real-world systems are naturally modeled as graphs, assessing the vulnerability of the network is…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
Acceleration of graph applications on GPUs has found large interest due to the ubiquitous use of graph processing in various domains. The inherent \textit{irregularity} in graph applications leads to several challenges for parallelization.…
Quantum machine learning holds the promise of combining the success of classical machine learning methods with the power of quantum computing, however one of the largest obstacles facing the field is the problem of barren plateaus.…
Rigidity theory studies the properties of graphs that can have rigid embeddings in a euclidean space $\mathbb{R}^d$ or on a sphere and which in addition satisfy certain edge length constraints. One of the major open problems in this field…
This paper presents the results of an experimental study of graph partitioning. We describe a new heuristic technique, path optimization, and its application to two variations of graph partitioning: the max_cut problem and the…
We propose a novel optimization-based approach to embedding heterogeneous high-dimensional data characterized by a graph. The goal is to create a two-dimensional visualization of the graph structure such that edge-crossings are minimized…
Analysis of algorithms on time-varying networks (often called evolving graphs) is a modern challenge in theoretical computer science. The edge-Markovian is a relatively simple and comprehensive model of evolving graphs: every pair of…
This paper leverages the framework of algorithms-with-predictions to design data structures for two fundamental dynamic graph problems: incremental topological ordering and cycle detection. In these problems, the input is a directed graph…
Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated…
Adaptive quantum circuits enhance flexibility and efficiency over traditional static circuits by dynamically adjusting their structure and parameters in real-time based on intermediate measurement outcomes. This paper introduces a novel…