Showing papers on "Connectivity published in 2021"

A Distributed Optimization Algorithm Based on Multiagent Network for Economic Dispatch With Region Partitioning

Abstract: In this article, a discrete-time distributed optimization algorithm is proposed for solving the economic dispatch (ED) problem with some groups of generator units to communicate over a connected graph, which is independent of the power system. The ED problem is converted to a distributed optimization problem with an objective of the sum of individual convex functions and constraints of local generators. Based on the optimal conditions, a class of distributed algorithms is designed to find the solution to the ED problem. The distributed algorithm can be realized as a multiagent system with a connected graph, whose convergence can be proved using the dynamic analysis method. Moreover, experiments with simulations are presented to demonstrate the performance of the proposed algorithm.

Percolation and the pandemic

Abstract: This paper is dedicated to the memory of Dietrich Stauffer, who was a pioneer in percolation theory and applications of it to problems of society, such as epidemiology. An epidemic is a percolation process gone out of control, that is, going beyond the critical transition threshold p c . Here we discuss how the threshold is related to the basic infectivity of neighbors R 0 , for trees (Bethe lattice), trees with triangular cliques, and in non-planar lattice percolation with extended-range connectivity. It is shown how having a smaller range of contacts increases the critical value of R 0 above the value R 0 , c = 1 appropriate for a tree, an infinite-range system, or a large completely connected graph.

Multiple Kernel Driven Clustering With Locally Consistent and Selfish Graph in Industrial IoT

Abstract: In the cognitive computing of intelligent industrial Internet of Things, clustering is a fundamental machine learning problem to exploit the latent data relationships. To overcome the challenge of kernel choice for nonlinear clustering tasks, multiple kernel clustering (MKC) has attracted intensive attention. However, existing graph-based MKC methods mainly aim to learn a consensus kernel as well as an affinity graph from multiple candidate kernels, which cannot fully exploit the latent graph information. In this article, we propose a novel pure graph-based MKC method. Specifically, a new graph model is proposed to preserve the local manifold structure of the data in kernel space so as to learn multiple candidate graphs. Afterward, the latent consistency and selfishness of these candidate graphs are fully considered. Furthermore, a graph connectivity constraint is introduced to avoid requiring any postprocessing clustering step. Comprehensive experimental results demonstrate the superiority of our method.

The Geometry of Synchronization Problems and Learning Group Actions

Abstract: We develop a geometric framework, based on the classical theory of fibre bundles, to characterize the cohomological nature of a large class of synchronization-type problems in the context of graph inference and combinatorial optimization. We identify each synchronization problem in topological group G on connected graph $$\Gamma $$ with a flat principal G-bundle over $$\Gamma $$ , thus establishing a classification result for synchronization problems using the representation variety of the fundamental group of $$\Gamma $$ into G. We then develop a twisted Hodge theory on flat vector bundles associated with these flat principal G-bundles, and provide a geometric realization of the graph connection Laplacian as the lowest-degree Hodge Laplacian in the twisted de Rham–Hodge cochain complex. Motivated by these geometric intuitions, we propose to study the problem of learning group actions—partitioning a collection of objects based on the local synchronizability of pairwise correspondence relations—and provide a heuristic synchronization-based algorithm for solving this type of problems. We demonstrate the efficacy of this algorithm on simulated and real datasets.

On the Dα-spectra of graphs

Abstract: Let G be a connected graph with distance matrix D(G), and let Tr(G) be the diagonal matrix of vertex transmissions of G. For any α∈[0,1], the Dα-matrix of G is defined as Dα(G)=αTr(G)+(1−α)D(G). In...

IPGN: Interactiveness Proposal Graph Network for Human-Object Interaction Detection

Abstract: Human-Object Interaction (HOI) Detection is an important task to understand how humans interact with objects. Most of the existing works treat this task as an exhaustive triplet $\left \langle{ human, verb, object }\right \rangle $ classification problem. In this paper, we decompose it and propose a novel two-stage graph model to learn the knowledge of interactiveness and interaction in one network, namely, Interactiveness Proposal Graph Network (IPGN). In the first stage, we design a fully connected graph for learning the interactiveness, which distinguishes whether a pair of human and object is interactive or not. Concretely, it generates the interactiveness features to encode high-level semantic interactiveness knowledge for each pair. The class-agnostic interactiveness is a more general and simpler objective, which can be used to provide reasonable proposals for the graph construction in the second stage. In the second stage, a sparsely connected graph is constructed with all interactive pairs selected by the first stage. Specifically, we use the interactiveness knowledge to guide the message passing. By contrast with the feature similarity, it explicitly represents the connections between the nodes. Benefiting from the valid graph reasoning, the node features are well encoded for interaction learning. Experiments show that the proposed method achieves state-of-the-art performance on both V-COCO and HICO-DET datasets.

Topology-Aware Graph Pooling Networks

Abstract: Pooling operations have shown to be effective on computer vision and natural language processing tasks. One challenge of performing pooling operations on graph data is the lack of locality that is not well-defined on graphs. Previous studies used global ranking methods to sample some of the important nodes, but most of them are not able to incorporate graph topology. In this work, we propose the topology-aware pooling (TAP) layer that explicitly considers graph topology. Our TAP layer is a two-stage voting process that selects more important nodes in a graph. It first performs local voting to generate scores for each node by attending each node to its neighboring nodes. The scores are generated locally such that topology information is explicitly considered. In addition, graph topology is incorporated in global voting to compute the importance score of each node globally in the entire graph. Altogether, the final ranking score for each node is computed by combining its local and global voting scores. To encourage better graph connectivity in the sampled graph, we propose to add a graph connectivity term to the computation of ranking scores. Results on graph classification tasks demonstrate that our methods achieve consistently better performance than previous methods.

Reeb Spaces of Smooth Functions on Manifolds

Abstract: The Reeb space of a continuous function is the space of connected components of the level sets. In this paper we first prove that the Reeb space of a smooth function on a closed manifold with finitely many critical values has the structure of a finite graph without loops. We also show that an arbitrary finite graph without loops can be realized as the Reeb space of a certain smooth function on a closed manifold with finitely many critical values, where the corresponding level sets can also be preassigned. Finally, we show that a continuous map of a smooth closed connected manifold to a finite connected graph without loops that induces an epimorphism between the fundamental groups is identified with the natural quotient map to the Reeb space of a certain smooth function with finitely many critical values, up to homotopy.

The general position number of the cartesian product of two trees

Abstract: The general position number of a connected graph is the cardinality of a largest set of vertices such that no three pairwise-distinct vertices from the set lie on a common shortest path. In this paper it is proved that the general position number is additive on the Cartesian product of two trees.

Delay Consensus Margin of First-Order Multiagent Systems With Undirected Graphs and PD Protocols

Abstract: In this article, we study robust consensus problems for continuous-time first-order multiagent systems (MASs) with time delays. We assume that the agents input is subject to an uncertain constant delay, which may arise due to interagent communication or additionally, also by self-delay in the agent dynamics. We consider dynamic feedback control protocol in the form of proportional and derivative (PD) control, and seek to determine the delay consensus margin (DCM) achievable by PD feedback protocols, whereas the DCM is a robustness measure that defines the maximal range of delay within which robust consensus can be achieved despite the uncertainty in the delay. With an undirected graph, we show that the DCM can be determined exactly by solving a unimodal concave optimization problem, which is one of univariate convex optimization and can be solved using convex optimization or gradient-based numerical methods. The results show how unstable agent dynamics and graph connectivity may limit the range of delay tolerable, so that consensus can or cannot be maintained in the presence of delay variations.

Approximate Gomory–Hu tree is faster than n – 1 max-flows

Abstract: The Gomory-Hu tree or cut tree (Gomory and Hu, 1961) is a classic data structure for reporting s−t mincuts (and by duality, the values of s−t maxflows) for all pairs of vertices s and t in an undirected graph. Gomory and Hu showed that it can be computed using n−1 exact maxflow computations. Surprisingly, this remains the best algorithm for Gomory-Hu trees more than 50 years later, even for approximate mincuts. In this paper, we break this longstanding barrier and give an algorithm for computing a (1+є)-approximate Gomory-Hu tree using log(n) maxflow computations. Specifically, we obtain the runtime bounds we describe below. We obtain a randomized (Monte Carlo) algorithm for undirected, weighted graphs that runs in O(m + n3/2) time and returns a (1+є)-approximate Gomory-Hu tree algorithm whp. Previously, the best running time known was O(n5/2), which is obtained by running Gomory and Hu’s original algorithm on a cut sparsifier of the graph. Next, we obtain a randomized (Monte Carlo) algorithm for undirected, unweighted graphs that runs in m4/3+o(1) time and returns a (1+є)-approximate Gomory-Hu tree algorithm whp. This improves on our first result for sparse graphs, namely m = o(n9/8). Previously, the best running time known for unweighted graphs was O(mn) for an exact Gomory-Hu tree (Bhalgat et al., STOC 2007); no better result was known if approximations are allowed. As a consequence of our Gomory-Hu tree algorithms, we also solve the (1+є)-approximate all pairs mincut and single source mincut problems in the same time bounds. (These problems are simpler in that the goal is to only return the s−t mincut values, and not the mincuts.) This improves on the recent algorithm for these problems in O(n2) time due to Abboud et al. (FOCS 2020).

On Partition Dimension of Some Cycle-Related Graphs

Abstract: Let be a simple connected graph. Suppose an - partition of . A partition representation of a vertex is the vector , denoted by . Any partition is referred as resolving partition if such that . The smallest integer is referred as the partition dimension of if the - partition is a resolving partition. In this article, we discuss the partition dimension of kayak paddle graph, cycle graph with chord, and a graph generated by chain of cycles. It has been shown that the partition dimension of the said families of graphs is constant.

Transductive Zero-Shot Action Recognition via Visually Connected Graph Convolutional Networks

Abstract: With the explosive growth of action categories, zero-shot action recognition aims to extend a well-trained model to novel/unseen classes. To bridge the large knowledge gap between seen and unseen classes, in this brief, we visually associate unseen actions with seen categories in a visually connected graph, and the knowledge is then transferred from the visual features space to semantic space via the grouped attention graph convolutional networks (GAGCNs). In particular, we extract visual features for all the actions, and a visually connected graph is built to attach seen actions to visually similar unseen categories. Moreover, the proposed grouped attention mechanism exploits the hierarchical knowledge in the graph so that the GAGCN enables propagating the visual–semantic connections from seen actions to unseen ones. We extensively evaluate the proposed method on three data sets: HMDB51, UCF101, and NTU RGB + D. Experimental results show that the GAGCN outperforms state-of-the-art methods.

Brouwer type conjecture for the eigenvalues of distance signless Laplacian matrix of a graph

Abstract: Let G be a simple connected graph with n vertices, m edges and having distance signless Laplacian eigenvalues ρ1≥ρ2≥…≥ρn≥0. For 1≤k≤n, let Mk(G)=∑i=1kρi and Nk(G)=∑i=0k−1ρn−i be respectivel...

Constructing dual-CISTs of pancake graphs and performance assessment of protection routings on some Cayley networks

Abstract: For a connected graph $$G=(V,E)$$ , two spanning trees $$T_1$$ and $$T_2$$ of G are said to be a pair of completely independent spanning trees (or a dual-CIST for short) if for any two vertices $$u,v\in V$$ , the paths joining u and v in the two trees have no common vertex except for u and v. Although the existence of a dual-CIST in the underlying graph of a network has the practical application of protection routing on fault-tolerance, it has been proved that determining whether a graph G admits a dual-CIST is NP-complete. As we know that Cayley graphs are a large family of graphs, some of its subclasses have been attracted and thus graphs in these subclasses have been adopted as the topologies of interconnection networks, such as the n-dimensional star graphs $$S_n$$ , bubble sort graphs $$BS_n$$ , pancake graph $$P_n$$ , alternating group networks $$AGN_n$$ and so on. Pai and Chang (IEEE/ACM Trans Netw 27(3): 1112–1123, 2019) recently showed that there exist dual-CISTs in $$S_n$$ , $$BS_n$$ , $$AGN_n$$ for $$n\geqslant 5$$ and provided their corresponding protection routings. So far, the problem of constructing dual-CISTs on $$P_n$$ has not been dealt with yet. In this sequel, we continue the investigation of the construction of dual-CISTs in pancake graphs as a complementary result. Since $$P_n$$ , $$S_n$$ , and $$BS_n$$ are with the same scale, we experimentally assess the performance of protection routing through simulation results for comparing them when $$n=5,6,7$$ .

Approximation Algorithms for Maximally Balanced Connected Graph Partition

Abstract: Given a simple connected graph \(G = (V, E)\), we seek to partition the vertex set V into k non-empty parts such that the subgraph induced by each part is connected, and the partition is maximally balanced in the way that the maximum cardinality of these k parts is minimized. We refer this problem to as min-max balanced connected graph partition into k parts and denote it as k -BGP. The general vertex-weighted version of this problem on trees has been studied since about four decades ago, which admits a linear time exact algorithm; the vertex-weighted 2-BGP and 3-BGP admit a 5/4-approximation and a 3/2-approximation, respectively; but no approximability result exists for k -BGP when \(k \ge 4\), except a trivial k-approximation. In this paper, we present another 3/2-approximation for our cardinality 3-BGP and then extend it to become a k/2-approximation for k -BGP, for any constant \(k \ge 3\). Furthermore, for 4-BGP, we propose an improved 24/13-approximation. To these purposes, we have designed several local improvement operations, which could be useful for related graph partition problems.

Roadmap Learning for Probabilistic Occupancy Maps With Topology-Informed Growing Neural Gas

Abstract: We address the problem of generating navigation roadmaps for uncertain and cluttered environments represented with probabilistic occupancy maps. A key challenge is to generate roadmaps that provide connectivity through tight passages and paths around uncertain obstacles. We propose the topology-informed growing neural gas algorithm that leverages estimates of probabilistic topological structures computed using persistent homology theory. These topological structure estimates inform the random sampling distribution to focus the roadmap learning on challenging regions of the environment that have not yet been learned correctly. We present experiments for three real-world indoor point-cloud datasets represented as Hilbert maps. Our method outperforms baseline methods in terms of graph connectivity, path solution quality, and search efficiency. Compared to a much denser PRM*, our method achieves similar performance while enabling a 27× faster query time for shortest-path searches.

Dynamic Point Cloud Denoising via Manifold-to-Manifold Distance

Abstract: 3D dynamic point clouds provide a natural discrete representation of real-world objects or scenes in motion, with a wide range of applications in immersive telepresence, autonomous driving, surveillance, etc . Nevertheless, dynamic point clouds are often perturbed by noise due to hardware, software or other causes. While a plethora of methods have been proposed for static point cloud denoising, few efforts are made for the denoising of dynamic point clouds, which is quite challenging due to the irregular sampling patterns both spatially and temporally. In this paper, we represent dynamic point clouds naturally on spatial-temporal graphs, and exploit the temporal consistency with respect to the underlying surface (manifold). In particular, we define a manifold-to-manifold distance and its discrete counterpart on graphs to measure the variation-based intrinsic distance between surface patches in the temporal domain, provided that graph operators are discrete counterparts of functionals on Riemannian manifolds. Then, we construct the spatial-temporal graph connectivity between corresponding surface patches based on the temporal distance and between points in adjacent patches in the spatial domain. Leveraging the initial graph representation, we formulate dynamic point cloud denoising as the joint optimization of the desired point cloud and underlying graph representation, regularized by both spatial smoothness and temporal consistency. We reformulate the optimization and present an efficient algorithm. Experimental results show that the proposed method significantly outperforms independent denoising of each frame from state-of-the-art static point cloud denoising approaches, on both Gaussian noise and simulated LiDAR noise.

A Proof of Brouwer's Toughness Conjecture

Abstract: The toughness $t(G)$ of a connected graph $G$ is defined as $t(G)=\min\{\frac{|S|}{c(G-S)}\}$, in which the minimum is taken over all proper subsets $S\subset V(G)$ such that $c(G-S)>1$, where $c(G...

Structural Adapters in Pretrained Language Models for AMR-to-text Generation

Abstract: Pretrained language models (PLM) have recently advanced graph-to-text generation, where the input graph is linearized into a sequence and fed into the PLM to obtain its representation. However, efficiently encoding the graph structure in PLMs is challenging because such models were pretrained on natural language, and modeling structured data may lead to catastrophic forgetting of distributional knowledge. In this paper, we propose StructAdapt, an adapter method to encode graph structure into PLMs. Contrary to prior work, StructAdapt effectively models interactions among the nodes based on the graph connectivity, only training graph structure-aware adapter parameters. In this way, we incorporate task-specific knowledge while maintaining the topological structure of the graph. We empirically show the benefits of explicitly encoding graph structure into PLMs using StructAdapt, outperforming the state of the art on two AMR-to-text datasets, training only 5.1% of the PLM parameters.