Node Duplication Research Articles

BrepGen: A B-rep Generative Diffusion Model with Structured Latent Geometry

This paper presents BrepGen , a diffusion-based generative approach that directly outputs a Boundary representation (B-rep) Computer-Aided Design (CAD) model. BrepGen represents a B-rep model as a novel structured latent geometry in a hierarchical tree. With the root node representing a whole CAD solid, each element of a B-rep model (i.e., a face, an edge, or a vertex) progressively turns into a child-node from top to bottom. B-rep geometry information goes into the nodes as the global bounding box of each primitive along with a latent code describing the local geometric shape. The B-rep topology information is implicitly represented by node duplication. When two faces share an edge, the edge curve will appear twice in the tree, and a T-junction vertex with three incident edges appears six times in the tree with identical node features. Starting from the root and progressing to the leaf, BrepGen employs Transformer-based diffusion models to sequentially denoise node features while duplicated nodes are detected and merged, recovering the B-Rep topology information. Extensive experiments show that BrepGen advances the task of CAD B-rep generation, surpassing existing methods on various benchmarks. Results on our newly collected furniture dataset further showcase its exceptional capability in generating complicated geometry. While previous methods were limited to generating simple prismatic shapes, BrepGen incorporates free-form and doubly-curved surfaces for the first time. Additional applications of BrepGen include CAD autocomplete and design interpolation. The code, pretrained models, and dataset are available at https://github.com/samxuxiang/BrepGen.

Intra-family links in the analysis of marital networks

Marriage networks, which represent the matrimonial connections between different families in a given historical and geographical milieu, rarely take into account one aspect of internal family dynamics, namely the existence of intra-family marriages. The inclusion of such marriages, represented in the graph by self-loops, is essential to compute more accurate measures of centrality. In this paper, we discuss various procedures for incorporating these links into the analysis, with the requirement that they be compatible with the use of already available social network analysis software. We then apply them to two historical marriage networks, one from the Republic of Venice and the other from Taiwan. By comparing centrality measures for the baseline and modified networks, we found that the most satisfactory of the proposed methods is the one that duplicate nodes of families with intra-family marriages and adds new edges that link these duplicated nodes to all the families to which the original node was connected. This procedure is computationally simple and conceptually sound, making it a useful tool for analyzing marital networks.

DwMLCS: An Efficient MLCS Algorithm based on Dynamic and Weighted Directed Acyclic Graph.

The problem of finding the longest common subsequence (MLCS) for multiple sequences is a computationally intensive and challenging problem that has significant applications in various fields such as text comparison, pattern recognition, and gene diagnosis. Currently, the dominant point-based MLCS algorithms have become popular and extensively studied. Generally, they construct the directed acyclic graph (DAG) of matching points and convert the MLCS problem into a search for the longest paths in the DAG. Several improvements have been made, focusing on decreasing model size and reducing redundant computations. These include 1) hash methods for eliminating duplicated nodes, 2) dynamic structures for supporting smaller DAG and 3) path pruning strategy and so on. However, the algorithms are still too limited when facing large-scale MLCS problem due to 1) the dynamic structures are too time-consuming to maintain and 2) the path pruning relies heavily on the tightness of the lower and upper bound of the MLCS. These factors contribute to the large-scale MLCS problem remaining a challenge. We propose a novel algorithm for the large-scale MLCS problem, named dwMLCS. It is based on two models: one is a dynamic DAG model which is both space and time efficient. It can decrease the size of the DAG significantly. The other is a weighted DAG model with new successor strategies. With this model, we design the algorithm for finding a tighter lower bound of the MLCS. Then, the path pruning is conducted to further reduce the size of the DAG and eliminate redundant computation. Additionally, we propose an upper bound method for improving the efficiency of the path pruning strategy. The experimental results demonstrate that the effectiveness and efficiency of the models and algorithms proposed are better than state-of-the-art algorithms. The source codes of dwMLCS can be downloaded from web site https://github.com/BioLab310/dwMLCS.

Multi-patch isogeometric material optimization of bi-directional functionally graded plates

This study investigates an effective design methodology for the optimal material distribution of bi-directional functionally graded plates (2D-FGPs) with complex shape. In mechanical analysis, a multi-patch isogeometric method is used to analyze the statics of 2D-FGP, which is based on the third-order shear deformation theory and Nitsche’s technology. This method can effectively avoid the use of duplicate nodes in the parameterization of IGA for complex shapes to obtain C1-continuity of 2D-FGPs. In the optimal design problem, we have constructed a rectangular material design mesh (RMDM) based on the shape of 2D-FGPs, which can map the material distribution on the surface of plate to achieve the implementation of the optimization process. This two-dimensional B-spline control points of RMDM are set as the design variable with mass reduction and the first-order natural frequency maximization as optimization objectives, and limited arbitrary deflection as constraint conditions. In addition, an improved multi-objective particle swarm optimization algorithm (IMOPSO) is used to obtain a series of Pareto optimization solutions that meet the needs of the designer. The validity and applicability of this innovative combination of multi-patch isogeometric analysis and IMOPSO are demonstrated through several numerical examples in integrated design. This approach further accomplishes the numerical unified CAD/CAE optimization design of 2D-FGPs across multiple non-smooth boundaries.

RELIABLE AND ENERGY EFFICIENT CLUSTER HEAD SELECTION USING EVOLUTIONARY ALGORITHM IN WIRELESS SENSOR NETWORK

One of the most pressing problems in the industry at the moment is figuring out how to make wireless sensor networks (WSN) more reliable and extend their lifespan. The processes of selection and the development of clusters are incredibly significant; however, carrying them out is challenging and time-consuming despite the significance of the tasks. In the most recent study, researchers began their hunt by selecting a particular cluster head to use as a basis for their investigation. On the other hand, the model that was suggested utilizes evolutionary cluster head selection as one of its components. This contributes to the acceleration of computing, the improvement of selection precision, and the prevention of the selection of duplicate nodes. When the results of the simulation of the suggested model are compared to the results of simulations using other methods and techniques, we find that our method is both more accurate and more efficient. This was discovered when the results of the simulation of the proposed model were compared to the results of simulations using other approaches and techniques.

Social Networks Privacy Preservation: A Novel Framework

The development of several popular social networks and the publication of social networks’ data have led to the risk of leakage of sensitive and confidential information of individuals. This requires the preservation of privacy before the publication of a user’s data available from his Online Social Network (OSN) presence. Numerous algorithms have been proposed in the area of preserving the privacy of social network users’ information such as K-anonymity and L-diversity. Previous work has shown good results based on the concept of adding edges and noise nodes for achieving K-anonymity and L-diversity. K-anonymization techniques are able to prevent identity disclosure of users but are not sufficient to prevent the disclosure of sensitive information of users. In this direction, a number of techniques for preserving the sensitive information of social network users have been proposed. Although these techniques have shown reasonably good results to achieve anonymity, but they also lead to a substantial change in the original structure of the OSNs. In this article, the problems of preventing sensitive attribute disclosure and reducing the noisy nodes have been addressed by perturbing the sensitive attributes. Existing research uses L-diversity for preventing sensitive attribute disclosure resulting in skewness and similarity attacks. We have addressed the skewness attacks by removing the duplicate noisy nodes from the final dataset to be published for stakeholders by the OSN service providers. All the information of duplicate nodes has been stored in a table named Reference Attribute Table (RAT). This table will be accessible only to the service providers for the purpose of de-anonymizing the data of users. The proposed technique has been extensively evaluated using five metrics viz. APL, ACSPL, RRTI, number of noisy nodes, and information loss using four real-time datasets collected for OSNs namely CORA, ARNET, DBLP, and Twitter. Results of evaluation parameters viz. APL and RRTI show that there is less change in the structure of datasets after anonymization. Results of ACSPL show that our proposed technique is able to preserve sensitive attributes in the datasets. The maximum number of noisy nodes amongst all four datasets is 5.4% and the maximum information loss is 2.2%. Evaluation results make it evident that our proposed technique ensures privacy preservation with less loss of information and thus preserving the utility of published data.

WGDTree: a phylogenetic software tool to examine conditional probabilities of retention following whole genome duplication events

BackgroundMultiple processes impact the probability of retention of individual genes following whole genome duplication (WGD) events. In analyzing two consecutive whole genome duplication events that occurred in the lineage leading to Atlantic salmon, a new phylogenetic statistical analysis was developed to examine the contingency of retention in one event based upon retention in a previous event. This analysis is intended to evaluate mechanisms of duplicate gene retention and to provide software to generate the test statistic for any genome with pairs of WGDs in its history.ResultsHere a software package written in Python, ‘WGDTree’ for the analysis of duplicate gene retention following whole genome duplication events is presented. Using gene tree-species tree reconciliation to label gene duplicate nodes and differentiate between WGD and SSD duplicates, the tool calculates a statistic based upon the conditional probability of a gene duplicate being retained after a second whole genome duplication dependent upon the retention status after the first event. The package also contains methods for the simulation of gene trees with WGD events. After running simulations, the accuracy of the placement of events has been determined to be high. The conditional probability statistic has been calculated for Phalaenopsis equestris on a monocot species tree with a pair of consecutive WGD events on its lineage, showing the applicability of the method.ConclusionsA new software tool has been created for the analysis of duplicate genes in examination of retention mechanisms. The software tool has been made available on the Python package index and the source code can be found on GitHub here: https://github.com/cnickh/wgdtree.

A scheduling algorithm based on reinforcement learning for heterogeneous environments

Efficient application scheduling is critical for achieving high performance in heterogeneous computing environments. For heterogeneous static scheduling problems, applications with a set of distributed tasks are modeled as directed acyclic graphs (DAG). The goal of scheduling is to properly allocate processors to DAG nodes and minimize the average completion time of all DAG applications. Most existing scheduling algorithms cannot fully utilize scheduling information, and are designed to schedule one DAG application at a time. Therefore, this study proposes a scheduling algorithm based on reinforcement learning for heterogeneous computing environments. A convolutional neural network with graph attention is first used to fully process and encode the scheduling information. Then, a fully connected neural network selects an appropriate node from the DAG applications for execution. Finally, a heuristic method is employed to allocate a processor to the selected node based on the earliest finish time and node duplication. This process is then repeated for every DAG node. The proximal policy optimization algorithm is used to tune all network hyperparameters. The training phase employs a reward function suitable for multi-DAG scheduling to ensure optimal performance when multiple DAG applications are scheduled concurrently. Experiments of various scheduling scenarios and types of applications were conducted, and the results show that the proposed algorithm reduces the average termination time of applications by 13.03% over that of existing algorithms.

Generalized Simultaneous Localization and Mapping (G-SLAM) as unification framework for natural and artificial intelligences: towards reverse engineering the hippocampal/entorhinal system and principles of high-level cognition.

Simultaneous localization and mapping (SLAM) represents a fundamental problem for autonomous embodied systems, for which the hippocampal/entorhinal system (H/E-S) has been optimized over the course of evolution. We have developed a biologically-inspired SLAM architecture based on latent variable generative modeling within the Free Energy Principle and Active Inference (FEP-AI) framework, which affords flexible navigation and planning in mobile robots. We have primarily focused on attempting to reverse engineer H/E-S “design” properties, but here we consider ways in which SLAM principles from robotics may help us better understand nervous systems and emergent minds. After reviewing LatentSLAM and notable features of this control architecture, we consider how the H/E-S may realize these functional properties not only for physical navigation, but also with respect to high-level cognition understood as generalized simultaneous localization and mapping (G-SLAM). We focus on loop-closure, graph-relaxation, and node duplication as particularly impactful architectural features, suggesting these computational phenomena may contribute to understanding cognitive insight (as proto-causal-inference), accommodation (as integration into existing schemas), and assimilation (as category formation). All these operations can similarly be describable in terms of structure/category learning on multiple levels of abstraction. However, here we adopt an ecological rationality perspective, framing H/E-S functions as orchestrating SLAM processes within both concrete and abstract hypothesis spaces. In this navigation/search process, adaptive cognitive equilibration between assimilation and accommodation involves balancing tradeoffs between exploration and exploitation; this dynamic equilibrium may be near optimally realized in FEP-AI, wherein control systems governed by expected free energy objective functions naturally balance model simplicity and accuracy. With respect to structure learning, such a balance would involve constructing models and categories that are neither too inclusive nor exclusive. We propose these (generalized) SLAM phenomena may represent some of the most impactful sources of variation in cognition both within and between individuals, suggesting that modulators of H/E-S functioning may potentially illuminate their adaptive significances as fundamental cybernetic control parameters. Finally, we discuss how understanding H/E-S contributions to G-SLAM may provide a unifying framework for high-level cognition and its potential realization in artificial intelligences.

A multivariable hybrid prediction system of wind power based on outlier test and innovative multi-objective optimization

Wind power forecasting is critical to the safe running of the power grid. However, due to the strong intermittence and instability of wind, reliable forecast of wind power remains a significant difficulty. In this study, a novel multivariable machine learning hybrid prediction system that incorporates data preprocessing, prediction, and multi-objective system optimization is designed to quantify the certainty and uncertainty of wind power. To increase the quality of data input, the data preparation module performs outlier tests based on the correlation between wind power and wind speed, as well as feature extraction, on the original data. In the prediction process, this paper offers an incremental kernel extreme learning machine (IK-elm), the parameters of which are set synchronously by an enhanced multi-objective optimization technique (MOCEHHO) developed in this paper. It overcomes the restrictions of duplicated hidden layer nodes and low learning efficiency caused by classic ELM and successfully maximizes the model's prediction capabilities. The simulation results on four datasets from Turkish wind farms show that the hybrid forecasting system outperforms the benchmark and may be utilized as a useful tool for wind power forecasting.

Low-loss belief propagation decoder with Tanner graph in quantum error-correction codes

Quantum error-correction codes are immeasurable resources for quantum computing and quantum communication. However, the existing decoders are generally incapable of checking node duplication of belief propagation (BP) on quantum low-density parity check (QLDPC) codes. Based on the probability theory in the machine learning, mathematical statistics and topological structure, a GF(4) (the Galois field is abbreviated as GF) augmented model BP decoder with Tanner graph is designed. The problem of repeated check nodes can be solved by this decoder. In simulation, when the random perturbation strength p=0.0115–0.0116 and number of attempts N = 60–70, the highest decoding efficiency of the augmented model BP decoder is obtained, and the low-loss frame error rate (FER) decreases to 7.1975 ×10−5. Hence, we design a novel augmented model decoder to compare the relationship between GF(2) and GF(4) for quantum code [[450,200]] on the depolarization channel. It can be verified that the proposed decoder provides the widely application range, and the decoding performance is better in QLDPC codes.

Hybrid Stochastic Ranking and Opposite Differential Evolution-Based Enhanced Firefly Optimization Algorithm for Extending Network Lifetime Through Efficient Clustering in WSNs

Ensuring stability and extending network lifetime in Wireless Sensor Networks (WSNs) achieved through significantly reduced energy consumption is considered as a potential challenge. The selection of Cluster Head (CH) during the process of clustering is determined to be highly complicated in spite of its role in facilitating efficient and balanced energy consumption in the network. In this paper, Hybrid Stochastic Ranking and Opposite Differential Evolution enhanced Firefly Algorithm (HSRODE-FFA)-based clustering protocol is proposed for handling the issues of location-based CH selection approaches that select duplicate nodes with increased computation and poor selection accuracy. This HSRODE-FFA clustering scheme includes the process of sampling for selecting the CHs from among the sensor nodes that exist in the sample population and address the problems introduced by different locations of nodes and CHs. It is proposed as an attempt to improve stability and lifetime of WSNs based on the merits of Stochastic Firefly Ranking (SFR) that enhances the exploration capability of Firefly Algorithm (FFA). The hybridization of the enhanced FFA with Opposition Differential Evolution (ODE) aids in speeding and ensuring optimal exploitation in the selection of CHs. The proposed HSRODE-FFA thereby maintains a balance between the rate of exploitation and exploration for deriving mutual benefit of rapid and potential selection of CHs from the sampling population. The experimental results of the proposed HSRODE-FFA scheme confirm an enhanced stability period and network lifetime of 16.21% and 13.86% respectively in contrast to the benchmarked Harmony Search and Firefly Algorithm-based Cluster Head Selection (HSFFA-CHS), Krill Herd Optimization and Genetic Algorithm-based Cluster Head Selection (KHOGA-CHS), Particle Swarm Optimization with Energy Centers Searching-based Cluster Head Selection (PSO-ECS-CHS) and Spider Monkey Optimization-based Cluster Head Selection (SMO-CHS) schemes.

Efficient parallel A* search on multi-GPU system

A* search is a best-first search algorithm that is widely used in pathfinding and graph traversal. To meet the ever-increasing demand of performance, various high-performance architectures (e.g., multi-core CPU and GPU) have been explored to accelerate the A* search. However, the current GPU based A* search approaches are merely designed based on single-GPU architecture. Nowadays, the amount of data grows at an exponential rate, making it inefficient or even infeasible for the current A* to process the data sets entirely on a single GPU.In this paper, we propose DA*, a parallel A* search algorithm based on the multi-GPU architecture. DA* enables the efficient acceleration of the A* algorithm using multiple GPUs with effective graph partitioning and data communication strategies. To make the most of the parallelism of multi-GPU architecture, in the state extension phase, we adopt the method of multiple priority queues for the open list, which allows multiple states being calculated in parallel. In addition, we use the parallel hashing of replacement and frontier search mechanism to address node duplication detection and memory bottlenecks respectively. The evaluation shows that DA* is effective and efficient in accelerating A* based computational tasks on the multi-GPU system. Compared to the state-of-the-art A* search algorithm based on a single GPU, our algorithm can achieve up to 3× performance speedup with four GPUs.

Evaluation of Internal Forces and Support Reaction of Column and Shearwall in 15th Building Design

In the case of 15th building, the structure type to earthquake resistant code is dual system reinforced concrete consists of frame and shear wall. The structure is analysis by dynamic analysis for whole structure and compare base shear by static analysis. By several trial position of shear wall can give first and second mode is translation and the third mode is rotation. In this case planar shear wall is used and placed in two direction of axis. The category of structural system is Other Structure for calculation of fundamental period (T). Fundamental Period (T) of structure is more than T maximum, so value of static seismic coefficient (Cs) taken from T maximum. Each of important element is column where the dimension and reinforcement are must satisfied for requirements. Shear wall have joint together with others shear wall, so one node used by several shear wall, make duplication forces in support reaction. For foundation design we can used 1st story internal forces in finding forces and compare them with after correction of support reaction caused duplication node in used with several shear walls. This exercise could solve the problem to anticipate duplication forces in several planar shear wall using one foundation assembly from several shear walls. The results of preliminary design column based on axial forces is 23,12 % lower than internal forces. From preliminary design based on axial forces. The dimension of preliminary design columns are lower than ideal dimension with 3 % reinforcement ratio. The result of difference between internal forces columns and support reaction columns is 12,99 %. The result of difference between internal forces shear walls and support reaction shear wall is 0,80 %.

Parallel graph-grammar-based algorithm for the longest-edge refinement of triangular meshes and the pollution simulations in Lesser Poland area

In this paper, we propose parallel graph-grammar-based algorithm for the longest-edge refinements and the pollution simulations in Lesser Poland area. We introduce graph-grammar productions for Rivara’s longest-edged algorithm for the local refinement of unstructured triangular meshes. We utilize the hyper-graph to represent the computational mesh and the graph-grammar productions to express the longest-edge mesh refinement algorithm. The parallelism in the original Rivara’s longest edge refinement algorithm is obtained by processing different longest edge refinement paths in different three ads. Our graph-grammar-based algorithm allows for additional parallelization within a single longest-edge refinement path. The graph-grammar-based algorithm automatically guarantees the validity and conformity of the generated mesh; it prevents the generation of duplicated nodes and edges, elongated elements with Jacobians converging to zero, and removes all the hanging nodes automatically from the mesh. We test the algorithm on generating a surface mesh based on a topographic data of Lesser Poland area. The graph-grammar productions also generate the layers of prismatic three-dimensional elements on top of the triangular mesh, and they break each prismatic element into three tetrahedral elements. Next, we propose graph-grammar productions generating element matrices and right-hand-side vectors for each tetrahedral element. We utilize the Streamline Upwind Petrov–Galerkin (SUPG) stabilization for the pollution propagation simulations in Lesser Poland area. We use the advection–diffusion-reaction model, the Crank–Nicolson time integration scheme, and the graph-grammar-based interface to the GMRES solver.

Hybrid shuffled frog leaping and improved biogeography‐based optimization algorithm for energy stability and network lifetime maximization in wireless sensor networks

SummaryWireless sensor networks are significantly used for data sensing and aggregating dusts from a remote area environment in order to utilize them in a diversified number of engineering applications. The data transfer among the sensor nodes is attained through the inclusion of energy efficient routing protocols. These energy efficient routing necessitates optimal cluster head selection procedure for handling the challenge of energy consumption to extend the stability and lifetime in the sensor networks. The implementation of energy efficient routing is still complicated even when the process of clustering is enhanced through the cluster head selection. The majority of the existing cluster head selection schemes suffer from the issues of poor selection accuracy, increased computation, and duplicate nodes' selection. In this paper, hybrid shuffled frog leaping and improved biogeography‐based optimization algorithm (HSFLBOA) for optimal cluster head selection is proposed for resolving issues that are common in cluster head selection schemes. This proposed HSFLBOA used the objective function that used the parameters of node energy, data packet transmission delay, cluster traffic density, and internode distance in the cluster. The simulation results of the proposed HSFLBOA is determined to be significant in achieving superior throughput and network energy compared to benchmarked metaheuristic optimal cluster head schemes.

On Comparing the Similarity and Dissimilarity Between Two Distinct Vehicular Trajectories

In this paper, we study the problem of comparing the similarity and dissimilarity between two distinct vehicular trajectories by proposing an adjacency-based metric. This approach has a broad application in building truthfulness by comparing the similarity between two vehicles and evaluating the dissimilarity between two distinct paths in hazardous materials transportation. Given two sequences $A$ and $B$ of Point of Interests (POIs) visited by two vehicles in a road/transportation network, the problem is to delete some nodes from $A$ and $B$ to obtain $A'$ and $B'$ such that the number of adjacencies in $A'$ and $B'$ is maximized. In the sequences $A'$ and $B'$ duplicated nodes are allowed, e.g., to represent road edges. We prove that this problem is NP-hard when noisy POIs are deleted and all the remaining POIs must be involved in some adjacency. On the other hand, when the adjacency involvement constraint is dropped, a variation of the problem is as hard as Exact Set Cover hence cannot be approximated within a constant factor unless P=NP. At last, we design a practical approach based on local search and show that the algorithm is very effective on simulation data.

Dynamic Node Allocation-Based Multirobot Path Planning

The previous multirobot path planning algorithm stipulated that more than two channels must be included in the map, causing the algorithm to malfunction in more demanding environments such as narrow passages or crossroads. In contrast, a path planning method based on heuristic search is proposed in this paper. The method truncates the path of robots and disables inverse edges so that it enables multirobots to run in a coordinated way under space-limited circumstances. First, real-time communication between the server and the robots is established. Then, the server uses heuristic search to plot a short path for the robot according to the obtained robot position and state information, during which the inverse edges of the node sequence allocated to other robots and the nodes occupied by stationary robots are not allowed to be visited. Finally, since the server has searched the paths for all the robots, the duplicated nodes are eliminated while the remnant nodes are sent to the corresponding robots. The above process loops until each robot reaches the target position. Experimental results show that this method improves the traffic efficiency of multirobots in narrow passages and allows robots to operate in an orderly manner.

Object Detection With Component-Graphs in Multi-Band Images: Application to Source Detection in Astronomical Images

In the context of mathematical morphology, component-graphs are complex but powerful structures for multi-band image modeling, processing, and analysis. In this work, we propose a novel multi-band object detection method relying on the component-graphs and statistical hypothesis tests. Our analysis shows that component-graphs are better at capturing image structures compared to the classical component-trees, with significantly higher detection capacity. Besides, we introduce two filtering algorithms to identify duplicated and partial nodes in the component-graphs. The proposed method, applied to the detection of sources on astronomical images, demonstrates a significant improvement in detecting faint objects on both multi-band simulated and real astronomical images compared to the state of the art.

The Origin of the Legumes is a Complex Paleopolyploid Phylogenomic Tangle Closely Associated with the Cretaceous–Paleogene (K–Pg) Mass Extinction Event

The consequences of the Cretaceous–Paleogene (K–Pg) boundary (KPB) mass extinction for the evolution of plant diversity remain poorly understood, even though evolutionary turnover of plant lineages at the KPB is central to understanding assembly of the Cenozoic biota. The apparent concentration of whole genome duplication (WGD) events around the KPB may have played a role in survival and subsequent diversification of plant lineages. To gain new insights into the origins of Cenozoic biodiversity, we examine the origin and early evolution of the globally diverse legume family (Leguminosae or Fabaceae). Legumes are ecologically (co-)dominant across many vegetation types, and the fossil record suggests that they rose to such prominence after the KPB in parallel with several well-studied animal clades including Placentalia and Neoaves. Furthermore, multiple WGD events are hypothesized to have occurred early in legume evolution. Using a recently inferred phylogenomic framework, we investigate the placement of WGDs during early legume evolution using gene tree reconciliation methods, gene count data and phylogenetic supernetwork reconstruction. Using 20 fossil calibrations we estimate a revised timeline of legume evolution based on 36 nuclear genes selected as informative and evolving in an approximately clock-like fashion. To establish the timing of WGDs we also date duplication nodes in gene trees. Results suggest either a pan-legume WGD event on the stem lineage of the family, or an allopolyploid event involving (some of) the earliest lineages within the crown group, with additional nested WGDs subtending subfamilies Papilionoideae and Detarioideae. Gene tree reconciliation methods that do not account for allopolyploidy may be misleading in inferring an earlier WGD event at the time of divergence of the two parental lineages of the polyploid, suggesting that the allopolyploid scenario is more likely. We show that the crown age of the legumes dates to the Maastrichtian or early Paleocene and that, apart from the Detarioideae WGD, paleopolyploidy occurred close to the KPB. We conclude that the early evolution of the legumes followed a complex history, in which multiple auto- and/or allopolyploidy events coincided with rapid diversification and in association with the mass extinction event at the KPB, ultimately underpinning the evolutionary success of the Leguminosae in the Cenozoic. [Allopolyploidy; Cretaceous–Paleogene (K–Pg) boundary; Fabaceae, Leguminosae; paleopolyploidy; phylogenomics; whole genome duplication events]