Related papers: Designing Sparse Reliable Pose-Graph SLAM: A Graph…
Finding spanning trees under various constraints is a classic problem with applications in many fields. Recently, a novel notion of "dense" ("sparse") tree, and in particular spanning tree (DST and SST respectively), is introduced as the…
Autonomous exploration requires a robot to explore an unknown environment while constructing an accurate map using Simultaneous Localization and Mapping (SLAM) techniques. Without prior information, the exploration performance is usually…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider a relaxed version of this problem in the setting of local algorithms. The relaxation is that the constructed subgraph is a sparse spanning…
Pose-graph SLAM is the de facto standard framework for constructing large-scale maps from multi-session experiences of relative observations and motions during visual robot navigation. It has received increasing attention in the context of…
When adapting Simultaneous Mapping and Localization (SLAM) to real-world applications, such as autonomous vehicles, drones, and augmented reality devices, its memory footprint and computing cost are the two main factors limiting the…
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…
In spatially embedded networks such as transportation and power grids, understanding how edge removals affect connectivity is crucial for robustness analysis. This paper studies a planar graph dismantling problem under an edge-budget…
We consider the minimum spanning tree problem in a setting where the edge weights are stochastic from unknown distributions, and the only available information is a single sample of each edge's weight distribution. In this setting, we…
A longstanding problem in spectral graph theory asks for graphs with maximum number of spanning trees among all connected simple graphs with a prescribed number of vertices and edges. Such graphs are called t-optimal graphs. Petingi and…
Structured sparse optimization is an important and challenging problem for analyzing high-dimensional data in a variety of applications such as bioinformatics, medical imaging, social networks, and astronomy. Although a number of structured…
We consider the probability that a spanning tree chosen uniformly at random from a graph can be partitioned into a fixed number $k$ of trees of equal size by removing $k-1$ edges. In that case, the spanning tree is called {\em splittable}.…
In this paper, we address the lack of datasets for - and the issue of reproducibility in - collaborative SLAM pose graph optimizers by providing a novel pose graph generator. Our pose graph generator, kollagen, is based on a random walk in…
We give an asymptotic expression for the expected number of spanning trees in a random graph with a given degree sequence $\boldsymbol{d}=(d_1,\ldots, d_n)$, provided that the number of edges is at least $n + \textstyle{\frac{1}{2}}…
We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a connected graph. It is motivated by a particular problem in epidemiology, and may be useful in studies of various dynamical processes in…
The ability for an agent to localize itself within an environment is crucial for many real-world applications. For unknown environments, Simultaneous Localization and Mapping (SLAM) enables incremental and concurrent building of and…
With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The…
We show variants of spectral sparsification routines can preserve the total spanning tree counts of graphs, which by Kirchhoff's matrix-tree theorem, is equivalent to determinant of a graph Laplacian minor, or equivalently, of any SDDM…
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…
Numerous Simultaneous Localization and Mapping (SLAM) algorithms have been presented in last decade using different sensor modalities. However, robust SLAM in extreme weather conditions is still an open research problem. In this paper,…
Collaborative Simultaneous Localization and Mapping (CSLAM) is a critical capability for enabling multiple robots to operate in complex environments. Most CSLAM techniques rely on the transmission of low-level features for visual and…