Related papers: Sparse Pose Graph Optimization in Cycle Space
Understanding how a vertex relates to a set of vertices is a fundamental task in graph analysis. Given a graph $G$ and a vertex set $X \subseteq V(G)$, consider the collection of subsets of the form $N(u) \cap X$ where $u$ ranges over all…
With the ever-increasing prevalence of graph data in a wide spectrum of applications, it becomes essential to analyze structural trends in dynamic graphs on a continual basis. The shortest cycle is a fundamental pattern in graph analytics.…
Finding a minimum vertex cover in a network is a fundamental NP-complete graph problem. One way to deal with its computational hardness, is to trade the qualitative performance of an algorithm (allowing non-optimal outputs) for an improved…
We describe an algorithm for finding Hamilton cycles in random graphs. Our model is the random graph $G=\gc$. In this model $G$ is drawn uniformly from graphs with vertex set $[n]$, $m$ edges and minimum degree at least three. We focus on…
Estimating 3D full-body pose from sparse sensor data is a pivotal technique employed for the reconstruction of realistic human motions in Augmented Reality and Virtual Reality. However, translating sparse sensor signals into comprehensive…
p-Cycles offer ring-like switching speed and mesh-like spare capacity efficiency for protecting network against link failures. This makes them extremely efficient and effective protection technique. p-Cycles can also protect all the links…
We present a general framework of designing efficient dynamic approximate algorithms for optimization on undirected graphs. In particular, we develop a technique that, given any problem that admits a certain notion of vertex sparsifiers,…
Autonomous navigation requires an accurate model or map of the environment. While dramatic progress in the prior two decades has enabled large-scale SLAM, the majority of existing methods rely on non-linear optimization techniques to find…
High-dimensional real-world systems can often be well characterized by a small number of simultaneous low-complexity interactions. The analysis of variance (ANOVA) decomposition and the anchored decomposition are typical techniques to find…
Hypergraph matching is a fundamental problem in computer vision. Mathematically speaking, it maximizes a polynomial objective function, subject to assignment constraints. In this paper, we reformulate the hypergraph matching problem as a…
We revisit Min-Mean-Cycle, the classical problem of finding a cycle in a weighted directed graph with minimum mean weight. Despite an extensive algorithmic literature, previous work falls short of a near-linear runtime in the number of…
We present a novel framework for collaboration amongst a team of robots performing Pose Graph Optimization (PGO) that addresses two important challenges for multi-robot SLAM: i) that of enabling information exchange "on-demand" via Active…
In this paper we give fast distributed graph algorithms for detecting and listing small subgraphs, and for computing or approximating the girth. Our algorithms improve upon the state of the art by polynomial factors, and for girth, we…
A minimum cycle basis of a weighted undirected graph $G$ is a basis of the cycle space of $G$ such that the total weight of the cycles in this basis is minimized. If $G$ is a planar graph with non-negative edge weights, such a basis can be…
This paper initiates the study of I/O algorithms (minimizing cache misses) from the perspective of fine-grained complexity (conditional polynomial lower bounds). Specifically, we aim to answer why sparse graph problems are so hard, and why…
Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into…
3D pose estimation from sparse multi-views is a critical task for numerous applications, including action recognition, sports analysis, and human-robot interaction. Optimization-based methods typically follow a two-stage pipeline, first…
This paper presents the Embedding Pose Graph (EPG), an innovative method that combines the strengths of foundation models with a simple 3D representation suitable for robotics applications. Addressing the need for efficient spatial…
Let $k \geq 2$ be an integer. Kouider and Lonc proved that the vertex set of every graph $G$ with $n \geq n_0(k)$ vertices and minimum degree at least $n/k$ can be covered by $k - 1$ cycles. Our main result states that for every $\alpha >…
We present Asynchronous Stochastic Parallel Pose Graph Optimization (ASAPP), the first asynchronous algorithm for distributed pose graph optimization (PGO) in multi-robot simultaneous localization and mapping. By enabling robots to optimize…