Related papers: Designing Sparse Reliable Pose-Graph SLAM: A Graph…
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…
We define a minimization problem for paths on planar graphs that, on the honeycomb lattice, is equivalent to the exploration path of the critical site percolation and than has the same scaling limit of SLE_6. We numerically study this model…
Due to its broad applications in practice, the minimum spanning tree problem and its all kinds of variations have been studied extensively during the last decades, for which a host of efficient exact and heuristic algorithms have been…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
In this paper, we present a motion planning framework for multi-modal vehicle dynamics. Our proposed algorithm employs transcription of the optimization objective function, vehicle dynamics, and state and control constraints into sparse…
We consider the minimum spanning tree problem with predictions, using the weight-arrival model, i.e., the graph is given, together with predictions for the weights of all edges. Then the actual weights arrive one at a time and an…
We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…
This paper focuses on finding a spanning tree of a graph to maximize the number of its internal vertices. We present an approximation algorithm for this problem which can achieve a performance ratio $\frac{4}{3}$ on undirected simple…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded-degree…
In this paper, we propose a tightly-coupled SLAM system fused with RGB, Depth, IMU and structured plane information. Traditional sparse points based SLAM systems always maintain a mass of map points to model the environment. Huge number of…
We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…
Neural field-based SLAM methods typically employ a single, monolithic field as their scene representation. This prevents efficient incorporation of loop closure constraints and limits scalability. To address these shortcomings, we propose a…
Random spanning trees of a graph $G$ are governed by a corresponding probability mass distribution (or "law"), $\mu$, defined on the set of all spanning trees of $G$. This paper addresses the problem of choosing $\mu$ in order to utilize…
Most existing motion planning algorithms assume that a map (of some quality) is fully determined prior to generating a motion plan. In many emerging applications of robotics, e.g., fast-moving agile aerial robots with constrained embedded…
In this letter, we propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix under the assumption that the observed signals vary smoothly over the nodes of the graph. The proposed algorithm is based on the…
Sparse decision trees are one of the most common forms of interpretable models. While recent advances have produced algorithms that fully optimize sparse decision trees for prediction, that work does not address policy design, because the…
The problem of finding a minimum-weight connected dominating set (CDS) of a given undirected graph has been studied actively, motivated by operations of wireless ad hoc networks. In this paper, we formulate a new stochastic variant of the…
A multigraph $G = (V, E)$ is $(k, \ell)$-sparse if every subset $X \subseteq V$ induces at most $\max\{k|X| - \ell, 0\}$ edges. Finding a maximum-size $(k, \ell)$-sparse subgraph is a classical problem in rigidity theory and combinatorial…
In many robotics problems, there is a significant gain in collaborative information sharing between multiple robots, for exploration, search and rescue, tracking multiple targets, or mapping large environments. One of the key implicit…
Graph-SLAM is a well-established algorithm for constructing a topological map of the environment while simultaneously attempting the localisation of the robot. It relies on scan matching algorithms to align noisy observations along robot's…