Memory and communication efficient algorithm for decentralized counting of nodes in networks

Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor networks. Thus several stochastic and naïve deterministic algorithms for distributed graph size estimation or calculation have been provided. Here we present a deterministic and distributed algorithm that allows every node of a connected graph to determine the graph size in finite time, if an upper bound on the graph size is provided. The algorithm consists in the iterative aggregation of information in local hubs which then broadcast it throughout the whole graph. The proposed node-counting algorithm is on average more efficient in terms of node memory and communication cost than its previous deterministic counterpart for node counting, and appears comparable or more efficient in terms of average-case time complexity. As well as node counting, the algorithm is more broadly applicable to problems such as summation over graphs, quorum sensing, and spontaneous hierarchy creation.

Star Topology Convolution for Graph Representation Learning

<p>We present a novel graph convolutional method called star topology convolution (STC). This method makes graph convolution more similar to conventional convolutional neural networks (CNNs) in Euclidean feature spaces. STC learns subgraphs which have a star topology rather than learning a fixed graph like most spectral methods. Due to the properties of a star topology, STC is graph-scale free (without a fixed graph size constraint). It has fewer parameters in its convolutional filter and is inductive, so it is more flexible and can be applied to large and evolving graphs. The convolutional filter is learnable and localized, similar to CNNs in Euclidean feature spaces, and maintains a good weight sharing property. To test the method, STC was compared with state-of-the-art graph convolutional methods in a supervised learning setting on six node properties prediction benchmark datasets: Cora, Citeseer, Pubmed, PPI, Ogbn-Arxiv, and Ogbn-MAG. The experimental results showed that STC achieved state-of-the-art performance on all these datasets and maintained good robustness. In an essential protein identification task, STC outperformed state-of-the-art essential protein identification methods.</p>

Empirical study prove that breadth-first search is more effective memory usage than depth-first search in frontier boundary cyclic graph

<p><span id="docs-internal-guid-06e4528a-7fff-0e38-150e-f136d6f22d84"><span>Memory consumption, of opened and closed lists in graph searching algorithms, affect in finding the solution. Using frontier boundary will reduce the memory usage for a closed list, and improve graph size expansion. The blind algorithms, depth-first frontier Searches, and breadth-first frontier Searches were used to compare the memory usage in slide tile puzzles as an example of the cyclic graph. This paper aims to prove that breadth-first frontier search is better than depth-first frontier search in memory usage. Both opened and closed lists in the cyclic graph are used. The level number and nodes count at each level for slide tile puzzles are changed when starting from different empty tile location. Eventually, the unorganized spiral path in depth-first search appears clearly through moving inside the graph to find goals.</span></span></p>

Efficiently Estimating Joining Cost of Subqueries in Regular Path Queries

Evaluating Regular Path Queries (RPQs) have been of interest since they were used as a powerful way to explore paths and patterns in graph databases. Traditional automata-based approaches are restricted in the graph size and/or highly complex queries, which causes a high evaluation cost (e.g., memory space and response time) on large graphs. Recently, although using the approach based on the threshold rare label for large graphs has been achieving some success, they could not often guarantee the minimum searching cost. Alternatively, the Unit-Subquery Cost Matrix (USCM) has been studied and obtained the viability of the usage of subqueries. Nevertheless, this method has an issue, which is, it does not cumulate the cost among subqueries that causes the long response time on a large graph. In order to overcome this issue, this paper proposes a method for estimating joining cost of subqueries to accelerate the USCM based parallel evaluation of RPQs on a large graph, namely USCM-Join. Through real-world datasets, we experimentally show that the USCM-Join outperforms others and estimating the joining cost enhances the USCM based approach up to around 20% in terms of response time.

Local classical MAX-CUT algorithm outperforms p=2 QAOA on high-girth regular graphs

The p-stage Quantum Approximate Optimization Algorithm (QAOAp) is a promising approach for combinatorial optimization on noisy intermediate-scale quantum (NISQ) devices, but its theoretical behavior is not well understood beyond p=1. We analyze QAOA2 for the maximum cut problem (MAX-CUT), deriving a graph-size-independent expression for the expected cut fraction on any D-regular graph of girth >5 (i.e. without triangles, squares, or pentagons).We show that for all degrees D≥2 and every D-regular graph G of girth >5, QAOA2 has a larger expected cut fraction than QAOA1 on G. However, we also show that there exists a 2-local randomized classical algorithm A such that A has a larger expected cut fraction than QAOA2 on all G. This supports our conjecture that for every constant p, there exists a local classical MAX-CUT algorithm that performs as well as QAOAp on all graphs.

A variant selection framework for genome graphs

MotivationVariation graph representations are projected to either replace or supplement conventional single genome references due to their ability to capture population genetic diversity and reduce reference bias. Vast catalogues of genetic variants for many species now exist, and it is natural to ask which among these are crucial to circumvent reference bias during read mapping.ResultsIn this work, we propose a novel mathematical framework for variant selection, by casting it in terms of minimizing variation graph size subject to preserving paths of length α with at most δ differences. This framework leads to a rich set of problems based on the types of variants (SNPs, indels), and whether the goal is to minimize the number of positions at which variants are listed or to minimize the total number of variants listed. We classify the computational complexity of these problems and provide efficient algorithms along with their software implementation when feasible. We empirically evaluate the magnitude of graph reduction achieved in human chromosome variation graphs using multiple α and δ parameter values corresponding to short and long-read resequencing characteristics. When our algorithm is run with parameter settings amenable to long-read mapping (α = 10 kbp, δ = 1000), 99.99% SNPs and 73% indel structural variants can be safely excluded from human chromosome 1 variation graph. The graph size reduction can benefit downstream pan-genome analysis.Implementationhttps://github.com/at-cg/[email protected], [email protected], [email protected]

Grus

Today’s GPU graph processing frameworks face scalability and efficiency issues as the graph size exceeds GPU-dedicated memory limit. Although recent GPUs can over-subscribe memory with Unified Memory (UM), they incur significant overhead when handling graph-structured data. In addition, many popular processing frameworks suffer sub-optimal efficiency due to heavy atomic operations when tracking the active vertices. This article presents Grus, a novel system framework that allows GPU graph processing to stay competitive with the ever-growing graph complexity. Grus improves space efficiency through a UM trimming scheme tailored to the data access behaviors of graph workloads. It also uses a lightweight frontier structure to further reduce atomic operations. With easy-to-use interface that abstracts the above details, Grus shows up to 6.4× average speedup over the state-of-the-art in-memory GPU graph processing framework. It allows one to process large graphs of 5.5 billion edges in seconds with a single GPU.

Shallow Graph Convolutional Network for Skeleton-Based Action Recognition

Graph convolutional networks (GCNs) have brought considerable improvement to the skeleton-based action recognition task. Existing GCN-based methods usually use the fixed spatial graph size among all the layers. It severely affects the model’s abilities to exploit the global and semantic discriminative information due to the limits of receptive fields. Furthermore, the fixed graph size would cause many redundancies in the representation of actions, which is inefficient for the model. The redundancies could also hinder the model from focusing on beneficial features. To address those issues, we proposed a plug-and-play channel adaptive merging module (CAMM) specific for the human skeleton graph, which can merge the vertices from the same part of the skeleton graph adaptively and efficiently. The merge weights are different across the channels, so every channel has its flexibility to integrate the joints. Then, we build a novel shallow graph convolutional network (SGCN) based on the module, which achieves state-of-the-art performance with less computational cost. Experimental results on NTU-RGB+D and Kinetics-Skeleton illustrates the superiority of our methods.

RDF graph validation using rule-based reasoning

The correct functioning of Semantic Web applications requires that given RDF graphs adhere to an expected shape. This shape depends on the RDF graph and the application’s supported entailments of that graph. During validation, RDF graphs are assessed against sets of constraints, and found violations help refining the RDF graphs. However, existing validation approaches cannot always explain the root causes of violations (inhibiting refinement), and cannot fully match the entailments supported during validation with those supported by the application. These approaches cannot accurately validate RDF graphs, or combine multiple systems, deteriorating the validator’s performance. In this paper, we present an alternative validation approach using rule-based reasoning, capable of fully customizing the used inferencing steps. We compare to existing approaches, and present a formal ground and practical implementation “Validatrr”, based on N3Logic and the EYE reasoner. Our approach – supporting an equivalent number of constraint types compared to the state of the art – better explains the root cause of the violations due to the reasoner’s generated logical proof, and returns an accurate number of violations due to the customizable inferencing rule set. Performance evaluation shows that Validatrr is performant for smaller datasets, and scales linearly w.r.t. the RDF graph size. The detailed root cause explanations can guide future validation report description specifications, and the fine-grained level of configuration can be employed to support different constraint languages. This foundation allows further research into handling recursion, validating RDF graphs based on their generation description, and providing automatic refinement suggestions.

Determining Exact Solutions for Structural Parameters on Hierarchical Networks With Density Feature

The problem of determining closed-form solutions for some structural parameters of great interest on networked models is meaningful and intriguing. In this paper, we propose a family of networked models $\mathcal{G}_{n}(t)$ with hierarchical structure where $t$ represents time step and $n$ is copy number. And then, we study some structural parameters on the proposed models $\mathcal{G}_{n}(t)$ in more detail. The results show that (i) models $\mathcal{G}_{n}(t)$ follow power-law distribution with exponent $2$ and thus exhibit density feature; (ii) models $\mathcal{G}_{n}(t)$ have both higher clustering coefficients and an ultra-small diameter and so display small-world property; and (iii) models $\mathcal{G}_{n}(t)$ possess rich mixing structure because Pearson-correlated coefficients undergo phase transitions unseen in previously published networked models. In addition, we also consider trapping problem on networked models $\mathcal{G}_{n}(t)$ and then precisely derive a solution for average trapping time $ATT$. More importantly, the analytic value for $ATT$ can be approximately equal to the theoretical lower bound in the large graph size limit, implying that models $\mathcal{G}_{n}(t)$ are capable of having most optimal trapping efficiency. As a result, we also derive exact solution for another significant parameter, Kemeny’s constant. Furthermore, we conduct extensive simulations that are in perfect agreement with all the theoretical deductions.