 Research
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cuRnet: an R package for graph traversing on GPU
BMC Bioinformatics volume 19, Article number: 356 (2018)
 The Correction to this article has been published in BMC Bioinformatics 2018 19:456
Abstract
Background
R has become the defacto reference analysis environment in Bioinformatics. Plenty of tools are available as packages that extend the R functionality, and many of them target the analysis of biological networks. Several algorithms for graphs, which are the most adopted mathematical representation of networks, are wellknown examples of applications that require highperformance computing, and for which classic sequential implementations are becoming inappropriate. In this context, parallel approaches targeting GPU architectures are becoming pervasive to deal with the execution time constraints. Although R packages for parallel execution on GPUs are already available, none of them provides graph algorithms.
Results
This work presents cuRnet, a R package that provides a parallel implementation for GPUs of the breathfirst search (BFS), the singlesource shortest paths (SSSP), and the strongly connected components (SCC) algorithms. The package allows offloading computing intensive applications to GPU devices for massively parallel computation and to speed up the runtime up to one order of magnitude with respect to the standard sequential computations on CPU. We have tested cuRnet on a benchmark of large protein interaction networks and for the interpretation of highthroughput omics data thought network analysis.
Conclusions
cuRnet is a R package to speed up graph traversal and analysis through parallel computation on GPUs. We show the efficiency of cuRnet applied both to biological network analysis, which requires basic graph algorithms, and to complex existing procedures built upon such algorithms.
Background
Biological networks are seen as graphs, where vertices represent elements and edges are the relationships among them. Analyzing biological networks mostly means applying basic graph traversal algorithms to find, for instance, how two vertices are connected, which vertices can be reached by a source, and which part of the network is highly interconnected, i.e., every vertex is reachable from every other vertex. These tasks are commonly embedded in more crucial sophisticated analyses [1, 2] to predict, for example, protein functions [3] or to study complex diseases by relating protein interaction networks to specific conditions [4–7]. Due to the constantly increasing data set complexity, such applications require highperformance algorithms, for which classic sequential implementations are become inappropriate. Alternative solutions are given by parallel approaches, and in particular by those based on GPU architectures, which allow sensibly reducing the algorithm execution time [8].
In the context of biological network analysis and, more in general, for statistical computing in Bioinformatics, R is becoming one of the most widely used programming environment. It provides easytouse packages to programmers and analysts for efficient and flexible data modeling and analysis [9]. In this context, even though some R packages based on GPU kernels have been proposed (e.g., gpuR for algebraic operations https://cran.rproject.org/package=gpuR), none of them provides parallel implementations of algorithms for network analysis.
This work presents cuRnet, an R package that provides a wrap of parallel graph algorithms to the R environment. As an initial proof of concept, cuRnet includes basic data structures for representing graphs, a parallel implementation of BreadthFirst Search (BFS) [10], Single Source Shortest Paths (SSSP) [11], and Strongly Connected Components (SCC) [12]. The package makes available GPU solutions to R endusers in a transparent way, such that GPU modules are invoked by R functions.
cuRnet has been compared with the BFS, SSSP, and SCC implementation of the iGraph R package (http://igraph.org/r/). Tests were run over on annotated undirected protein interaction networks and on directed homology networks provided by the STRINGdb [13].
cuRnet outperformed the iGraph sequential algorithms especially on the largest networks. An average speedup of 3 × have been observed, with a maximum of 30 ×.
cuRnet SCC and SSSP were used to underscore their ability in helping researchers in providing clues on putative functional context of ncRNA molecules, and guide the selection of a relevant functional readout [14, 15]. For this aim, we used available RNA sequencing dataset of 21 prostate cancer cell lines (GEO accession number GSE25183) to predict coexpression networks. We also show how enabling the GPU implementation of graph traversal algorithms in R has a potential to speed up existing complex procedures whose implementation mainly depends on such calculations. The PCSF package for R [16] is an example, which solves the Prizecollecting Steiner Forest problem by making a massive use of SSSP. It performs userfriendly analysis of highthroughput data using the interaction networks (proteinprotein, proteinmetabolite or any other type of correlationbased interaction networks) as a template. It interprets the biological landscape of interactome with respect to the data, i.e., to detect highscoring neighbourhoods to identify functional modules. A real case application of intensive PCSF computation is reported on the analysis of Diffuse large Bcell lymphoma gene expression data.
cuRnet and the PCSF application accelerated with cuRnet are freely available on https://bitbucket.org/curnet/curnet.
Methods
Figure 1 shows an overview of the full cuRnet stack, by which R data is passed, as input data, to the GPU environment for parallel computation. The input network is represented, in R, through a standard R data frame, where every edge between two vertices is stored with the corresponding weight. By exploiting the Rcpp library of R, an RC++ wrapper has been developed to automatically translate the network from the standard R representation to a C++ data structure, and to link the algorithm invocation from the R to the C++ environment.
The network representation in the C++ environment relies on the coordinate list (COO) data structure, which is a mandatory step to generate the compressed sparse row (CSR) data structure for the GPU computation. CSR is a wellknown storage format to efficiently represent graphs, and it allows reaching high performance during the graph traversal on the GPU.
The C++ interface allows handling the interaction with the GPU device. It generates the host (CPU) representation of the graph starting from the rows in the data frame, it initializes the GPU kernel, it handles the host (CPU)device (GPU) data exchanging, and, finally, it runs the kernel for the parallel computation. The computation result is retrieved from the device and passed back to R through the Rcpp/C++ layers.
In what follows we briefly describe the parallel graph traversal algorithms implemented in cuRnet. Given a graph G(V,E), with a set V of vertices, a set E of edges, and a weight function \(w: E \to \mathbb {R} \), cuRnet takes G in a dataframe X having three columns listing the network edges and their weights. The dataframe can be built from an iGraph object or from a textual file (.csv). The following lines invoke the loading of the cuRnet package and the construction of the graph data structure:
We refer the reader to (https://bitbucket.org/curnet/curnet) for a complete manual of the cuRnet usage.
Parallel implementation of breadthfirst search for GPUs
The parallel graph traversal through BFS [10], which is listed and analyzed in Additional file 1: Section 1 Algorithm 1 and Figure S1, respectively, explores the reachable vertices, levelbylevel, starting from a source s. cuRnet implements the concept of frontier [17] to achieve work efficiency. A frontier holds all and only the vertices visited at each level. The algorithm checks every neighbour of a frontier vertex to see whether it has been already visited. If not, the neighbour is added into a new frontier. cuRnet implements a frontier propagation step through two data structures, F_{1} and F_{2}. F_{1} represents the actual frontier, which is read by the parallel threads to start the propagation step. F_{2} is written by the threads to generate the frontier for the next BFS step. At each step, F_{2} is filtered and swapped into F_{1} for the next iteration. When a thread visits an already visited neighbour, that neighbour is eliminated from the frontier. When more threads visit the same neighbour in the same propagation step, they generate duplicate vertices in the frontier. cuRnet implements efficient duplicate detection and correction strategies based on hash tables, advanced strategies for coalesced memory accesses, and warp shuffle instructions. Moreover, it implements different strategies to deal with the potential workload imbalance and thread divergence caused by any actual biological network nonhomogeneity. These include prefixsum procedures to efficiently handle frontiers, dynamic virtual warps, dynamic parallelism, multiple CUDA kernels, and techniques for coalesced memory accesses.
The BFS result is a matrix s×V, where s is the number of vertex sources from which the BFS is run. Each entry in the matrix is the depth of the BFS from a source to a graph vertex. The matrix is retrieved from the GPU device to R through the Rcpp/C++ layers. BFS is ran by invoking the following cuRnet function in the R environment:
Parallel implementation of singlesourceshortestpath for GPU
The cuRnet CUDA implementation of the SSSP algorithm is based on the BellmanFord’s approach [11]. The parallel algorithm is reported in Additional file 1: Section 1. cuRnet SSSP visits the graph and finds the shortest path d to reach every vertex of V from source s. Also in this case, cuRnet exploits the concept of frontier to deal with the most expensive step of the algorithm (i.e., the relax procedure). At each iteration i, the algorithm extracts, in parallel, the vertices from one frontier and inserts the active neighbours in the second frontier for the next iteration step. Each iteration concludes by swapping the contents of the second frontier (which will be the actual frontier at the next iteration) into the first one. Indeed, the frontiers allow working only on active vertices, i.e., all and only vertices whose tentative distance has been modified and, thus, that must be considered for the relax procedure at the next iteration.
The result is a double numeric matrix (i.e., distances and predecessors), which are retrieved from the GPU device to R through the Rcpp/C++ layer. They are obtained by invoking the cuRnet functions CURNET_SSSP and CURNET_SSSP_DISTS for the matrix of shortest paths (returned as lists of predecessor vertices) and the corresponding sourcedestination distances:
Parallel implementation of stronglyconnected components for GPU
cuRnet implements a multistep approach that applies different GPUaccelerated algorithms for SCC decomposition [12]. The algorithm is reported in Additional file 1: Section 1. The multistep approach consists of 3 phases. In the first phase it iterates a trimming procedure to identify and delete vertices of G that form trivial SCCs (i.e., vertices with no active successors or predecessors). In the second phase it iterates a forwardbackward algorithm to identify the main components. The first step is related to the choice of the pivot for each set, where heuristics can be applied to maximize vertices coverage within a single iteration. Forward and backward closure is then computed from this vertex, and up to four subgraphs are generated. The first one is the component which the pivot belongs to, and it is calculated as the intersection of the forward and backward closure. The other three sets are SCCclosed subgraphs that can be processed in parallel at the next iteration. They correspond to the nonvisited vertices in the current set, to the forward closure but not to the backward one, and to the backwardreachable vertices, respectively. In the third phase the approach runs a coloring algorithm to decompose the rest of the graph. A unique color is firstly assigned to each vertex. The max color is then propagated to the successor noneliminated vertices until no more updates are possible. Pivots are chosen as the vertices which color is unchanged. Running the backward closure from these vertices on the corresponding set, cuRnet detects the components labelled with that color.
The cuRnet SCC computation results in a vector of associations between vertices and strongly component IDs. It is retrieved from the GPU device to R through the Rcpp/C++ layer and obtained by invoking the following cuRnet function:
Results
We evaluated the cuRnet performance by comparing its execution time with the corresponding sequential implementations provided in the iGraph R package (http://igraph.org/r/). The cuRnet software requires a GPU device with compute capabilities at least 3.0. We performed tests on two different GPU devices running on a machine equipped with an AMD Phenom II X6 (3GHz) host processor, 64 GB RAM, Ubuntu 14.04 OS, and CUDA Toolkit v 8.0. The first device is an NVIDIA Maxwell GeForce GTX 980 GPU having 16 SMs (2048 CUDA cores) and 8 GB of GDDR5 memory, and it is capable of concurrently executing 32,768 threads. The second device is an NVIDIA Tesla K40 comprised of 12 GB of GDDR5 memory and 15 SMs (2880 CUDA cores), and it is able of concurrently executing 30,720 threads The two GPU devices have equal memory technology but they differ in the number of threads that they can concurrently execute and in the internal architecture. The technology of the Maxwell architecture is more recent than the Tesla one. For these reasons, the first device is expected to show better performances, compared with the second device, in many applications. In what follows, we show the main results we obtained by running tests on the Maxwell device, while we run a subset of the benchmarks on the Tesla device to show a comparison of performance between the two architectures.
Data
We used the STRING dataset [13], which mainly contains ProteinProtein Interaction (PPI) networks of several organisms, varying from microbes to eukaryotes. We used the R package STRINGdb to download the data. We refer the reader to Additional file 1: Section 2 for details on the data.
We retrieved the undirected unlabeled networks related to Homo sapiens, Danio rerio and Zea mais (see Additional file 1: Figures S2, S3 and S4 for a description of the network characteristics). Those species were chosen among the organisms having the largest networks stored in STRING, to cover the biological diversity that can be encountered in performing analysis of biological networks. For each network, we varied the threshold on the assigned edge scores to obtain sparse as well as dense networks.
We created a benchmark of undirected label networks by using the pvalues of differential expression values regarding the treatment of A549 lung cancer cells by means of Resveratrol, a natural phytoestrogen found in red wine and a variety of plants shown to have protective effects against the disease [13] (see Additional file 1: Figure S5). We used such values to label the above networks.
We also created a set of directed unlabelled networks (see Additional file 1: Figure S6) as follows. We used the complete set of 115 archaea species to create homology networks having incremental amount of involved organisms. The homology information between proteins is measured by sequence BLAST alignments. For each protein, STRING reports the best BLAST hits [18], w.r.t. the given species. Horizontal gene transfer is a frequent phenomenon in microbes [19], and homology networks are used to search for gene families shared by several organisms [20].
The running time to create graph data structures in cuRnet and iGraph from the above datasets is reported in Additional file 1: Figures S7 and S8. In general, cuRnet requires half the time of iGraph to perform such a task.
cuRnet performance
We tested cuRnet BFS on undirected unlabeled networks and SSSP on undirected labeled networks related to Homo sapiens, Danio rerio and Zea mais by varying the number of sources ranging from just to few vertices to a 20% of vertices. Figures 2 and 3 (see also Additional file 1: Figures S9 and S10) show the execution time of the BFS and SSSP, as well as the corresponding speedup w.r.t. the sequential counterpart. Running times were evaluated as an average of 10 runs.
Additional file 1: Figures S11, S12, S13 and S14 show the total running time including the call to the function primitives, plus the time required for building the graph data structures. Highly functional networks have small sizes and the execution time of the two implementations is in terms of few seconds, obtaining however speedups up to 5 ×. The time of both packages highly depends on the number of source vertices, but the slope of cuRnet is sensibly lower than iGraph. On average, iGraph shows similar performance up to a small percentage of sources (0.5%). Above that, cuRnet shows up to 15 × speedup w.r.t. the sequential counterpart. The time requirements and the general speedup are similar for the three species.
We tested cuRnet SCC performance on directed unlabelled networks representing interspecies proteins homology. Figure 4 shows the running time and corresponding speedups by increasing the size of the extracted homology networks, up to the final one of 114 species. As for the previous benchmarks, running times were evaluated as an average of 10 runs. Additional file 1: Figure S15 reports the total running time including the graph data structure generation. cuRnet shows an extremely low slope w.r.t. iGraph, and the speedup increases by increasing the network size up to a maximum of 14 ×. Additional file 1: Figures S16, S17 and S18 report the performance of cuRnet measured by running the software on two different GPU architectures. Regarding BFS, the device with the Maxwell architecture outperforms the Tesla device, however also the less recent device shows good speedups, up to 10 ×, w.r.t. iGraph.
Finally, we tested a modified version of PCSF R package [16] where the original sequential SSSP implementation has been replaced by the parallel SSSP implementation of cuRnet. PCSF, taken an input network, may give prizes to vertices according to the measurements of differential expression, copy number, or number of gene mutations. After scoring the interactome, the PCSF identifies highconfidence subnetworks, the neighborhoods in interaction networks potentially belonging to the key pathways that are altered in a disease. It also interactively visualizes the resulting subnetworks with functional enrichment analysis. The running time of the PCSF module is highly dominated by SSSP computations and the application of the cuRnet SSSP provided up to 9 × speedup for the total execution times of the PCSF (see Fig. 5). This allows for even more rigorous computations on larger networks.
Discussion
cuRnet allows users to quickly retrieve ncRNApathway associations and individual genes contributing to them. To evaluate the cuRnet performance in making highly confident ncRNA function predictions, we analysed a case study with the wellknown lncRNA involved in cancer called MALAT1. Noncoding RNAs (ncRNAs) are emerging as key molecules in human cancer but only a small number of them has been functionally annotated [15]. Using the guiltbyassociation principle is possible to infer functions of lncRNAs on a genomewide scale [21]. This approach identifies protein coding genes significantly correlated with a given lncRNA using geneexpression analysis. In combination with enrichment strategies, it projects functional protein coding gene sets onto mRNAs correlated with the lncRNA of interest, generating hypotheses for functions and potential regulators of the candidate lncRNA. We used a public RNA sequencing dataset of 21 prostate cancer cell lines sequenced on the Illumina Genome Analyzer and GAII (GEO accession number GSE25183) and built up a largescale gene association network using cuRnet SCC (Pearson method as pairwise correlations). We extracted the subnetworks where MALAT1 is present and calculated singlesource shortest paths, mean distance of shortest paths within this subnetwork, and mean distance of shortest paths over the whole big graph. Gene Set Enrichment Analysis (GSEA) was carried out to identify associated biological processes and signalling pathways [22]. We computed overlaps of genes in the MALAT1 subnetworks with gene sets in MSigDB C2 CP (Canonical pathways) and hallmark gene sets [22]. Several cancer related pathways such as epithelial mesenchymal transition (EMT) and DNA replication were enriched, which implies that MALAT1 subnetworks might be involved in the metastasis related pathways [23]. In addition, we identified an overrepresentation of gene sets that corresponds to the validated MALAT1 functionality reported in the literature: cell cycle, e2ftargets, proliferation, BMYBrelated, and G2M checkpoint [14, 24].
We applied the PCSF to analyze Diffuse large Bcell lymphoma (DLBCL), which is the most common form of human lymphoma. Based on gene expression profiling studies DLBCL can be divided into two subgroups, the germinal center Bcell (GCB) and the activated Bcell like (ABC), with different clinical outcome and response to therapies [25, 26]. Therefore, it is important to understand underlying molecular mechanism of two subtypes. A public gene expression datasets GSE10846 from Gene Expression Omnibus online repository (https://www.ncbi.nlm.nih.gov/geo) has been used in the analysis. The dataset is composed of 350 patients being 167 ABC and 183 GCB. We run the PCSF separately for ABC and GCB patients providing top 100 differentially expressed genes as terminals and their absolute fold changes as prizes. The STRING database (version 13) [27] is provided as a template network by applying some filtering steps described in [6], which afterwards had 15,405 nodes and 175,821 genes.
An interactive visualization of the subnetwork for ABC patients is shown in Fig. 6. PCSF also performs enrichment analysis on subnetworks by employing either EnrichR [28] API or topGO [29] that can be specified by the user. For the resulting subnetwork of ABC patients, the hallmark of ABCDLBCL, as constitutive activation of nuclear factor kappaB (NFKB) signalling, was confirmed by the enrichment of NFKB pathway (cluster in purple) and upregulation of well defined ABC genes including IRF4, FOXP1, IL6, BATF and PIM2 among others [30]. In parallel, PCSF subnetwork for GCB patients (see Additional file 1: Figure S19) showed activation of the PI3K/Akt/mTOR signalling pathway (cluster in red) and overexpression of germinal center markers such as BCL6, LMO2, MME (CD10) and MYBL1, reproducing the findings given in [30, 31].
Conclusion
cuRnet has been developed to be easy to use both as a standalone analysis application and as a core primitive to be incorporated in more complex algorithmic frameworks. cuRnet has been structured to modularly include, as current and future work, a wide collection of algorithms for biological network analysis.
Change history
27 November 2018
After publication of this supplement article [1], it was brought to our attention that reference 10 and reference 12 in the article are incorrect.
Abbreviations
 BFS:

Breadthfirst search
 GPU:

Graphic processing unit
 PCSF:

Prizecollecting steiner forest
 SCC:

Strongly connected component
 SSSP:

Single source shortest path
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Acknowledgements
We thank the Fondo Sociale Europeo provided by Regione del Veneto for partially supported this work.
Funding
This work has been partially supported by the following projects: GNCSINDAM, Fondo Sociale Europeo, and National Research Council Flagship Projects Interomics; JOINT PROJECTS 2016JPVR16FNCL; JOINT PROJECTS 2017B33C17000440003; project of the Italian Ministry of Education, Universities and Research (MIUR) “Dipartimenti di Eccellenza 20182022”. Publication costs have been founded by the Department of Computer Science, University of Verona (Italy), and the Institute of Oncology Research (Switzerland).
Availability of data and materials
Data and materials are available at the web site https://bitbucket.org/curnet/curnet.
About this supplement
This article has been published as part of BMC Bioinformatics Volume 19 Supplement 10, 2018: Italian Society of Bioinformatics (BITS): Annual Meeting 2017. The full contents of the supplement are available online at https://bmcbioinformatics.biomedcentral.com/articles/supplements/volume19supplement10.
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LC, NB, IK and RG designed the model. VB, FB (Busato), SA, MA implemented the model. AAC and FB (Bertoni) validated the model. All authors contributed to the writing of the manuscript. All authors read and approved the final manuscript.
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Bonnici, V., Busato, F., Aldegheri, S. et al. cuRnet: an R package for graph traversing on GPU. BMC Bioinformatics 19, 356 (2018). https://doi.org/10.1186/s1285901823103
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Keywords
 Graph traversal
 GPU parallel implementation
 Biological network analysis
 Highthroughput omics network annotation
 Topological network analysis
 Prizecollecting Steiner forest