Bipartite Graph Matching Research Articles

Energy-Efficient Joint Task Assignment and Power Control in Energy-Harvesting D2D Offloading Communications

In this article, we investigate the joint task assignment and power control problems for Device-to-Device (D2D) offloading communications with energy harvesting. Exploiting the D2D links for data offloading allows reducing the traffic load of the cellular base stations. The energy consumed by the D2D transmitters for data offloading can be compensated by energy harvesting. The main objective is to maximize the energy efficiency (EE) under energy causality and delay constraints, assuming a harvest–transmit model. Hence, the proposed model results in a nonconvex problem. We first derive an equivalent and more tractable optimization problem by exploiting nonlinear fractional programming, also known as the Dinkelbach method. We propose a layered optimization method by decoupling the EE maximization problem into power allocation and offloading assignment. The first step consists of computing the optimal power values by applying the conjugate gradient method. In the second step, the problem of the D2D pair formation for data offloading amounts to the bipartite graph matching. It can be solved to optimality using the Hungarian algorithm. Extensive simulations were performed on various network scenarios. Numerical results show that the proposed resource allocation scheme achieves remarkable improvements in terms of network EE.

Resource Allocation and Hybrid OMA/NOMA Mode Selection for Non-Coherent Joint Transmission

Supporting non-orthogonal multiple access (NOMA) in non-coherent joint transmission (NCJT) systems is beneficial for improving spectral efficiency (SE), but the interference coordination, user scheduling, and resource allocation problems in this new scenario have not been well studied. In this paper, a NOMA-enabled NCJT system is considered in which the connected users are jointly served by two multi-antenna transmitting-receiving points (TRPs) with non-ideal backhauls. Each user has two independent receiving (RX) chains that can work with orthogonal multiple access (OMA) or NOMA mode. A joint resource allocation and hybrid OMA/NOMA mode selection is proposed to maximize the throughput. The primal non-convex and NP-hard problem is decomposed into the following three subproblems, i.e., power allocation (PA) of a single TRP, hybrid mode selection (HMS) of a single TRP, and cross-TRP interference optimization (CIO). Firstly, a successive convex approximation (SCA) method is proposed to solve the non-convex PA subproblem, which achieves a local maximum solution. Secondly, the combinatorial HMS subproblem is transformed into finding the maximum matching of bipartite graphs. By constructing two weighted bipartite graphs for the OMA/near UEs and far UEs, a suboptimal solution is found. Thirdly, an alternating optimization is proposed to solve the CIO subproblem by iteratively performing PA and HMS of the two TRPs. Finally, simulation results demonstrate the superiority of throughput improvement of the proposed method, and the sum rate of the NOMA-enabled NCJT system can approach the sum rate of individual TRPs without interference.

Maximum determinant and permanent of sparse 0-1 matrices

We prove that the maximum determinant of an n×n matrix, with entries in {0,1} and at most n+k non-zero entries, is at most 2k/3, which is best possible when k is a multiple of 3. This result solves a conjecture of Bruhn and Rautenbach. We also obtain an upper bound on the number of perfect matchings in C4-free bipartite graphs based on the number of edges, which, in the sparse case, improves on the classical Bregman's inequality for permanents. This bound is tight, as equality is achieved by the graph formed by vertex disjoint union of 6-vertex cycles.

LPTD: a novel linear programming-based topology determination method for cryo-EM maps.

Topology determination is one of the most important intermediate steps toward building the atomic structure of proteins from their medium-resolution cryo-electron microscopy (cryo-EM) map. The main goal in the topology determination is to identify correct matches (i.e. assignment and direction) between secondary structure elements (SSEs) (α-helices and β-sheets) detected in a protein sequence and cryo-EM density map. Despite many recent advances in molecular biology technologies, the problem remains a challenging issue. To overcome the problem, this article proposes a linear programming-based topology determination (LPTD) method to solve the secondary structure topology problem in three-dimensional geometrical space. Through modeling of the protein's sequence with the aid of extracting highly reliable features and a distance-based scoring function, the secondary structure matching problem is transformed into a complete weighted bipartite graph matching problem. Subsequently, an algorithm based on linear programming is developed as a decision-making strategy to extract the true topology (native topology) between all possible topologies. The proposed automatic framework is verified using 12 experimental and 15 simulated α-β proteins. Results demonstrate that LPTD is highly efficient and extremely fast in such a way that for 77% of cases in the dataset, the native topology has been detected in the first rank topology in <2 s. Besides, this method is able to successfully handle large complex proteins with as many as 65 SSEs. Such a large number of SSEs have never been solved with current tools/methods. The LPTD package (source code and data) is publicly available at https://github.com/B-Behkamal/LPTD. Moreover, two test samples as well as the instruction of utilizing the graphical user interface have been provided in the shared readme file. Supplementary data are available at Bioinformatics online.

A collaboration approach for cloud factories based on Kuhn–Munkras algorithm

ABSTRACT Cloud manufacturing (CMfg) is a network-based and service-oriented resource-sharing manufacturing paradigm, where resources from different factories are encapsulated as services that can be jointly employed to complete manufacturing tasks. To provide an efficient collaboration strategy among the factories in CMfg, in this work, a universal framework was proposed to describe manufacturing resources under the cloud environment, in which both equipment and factory levels were considered. Moreover, a collaboration model among cloud factories was presented from the perspective of the bipartite graph. Specifically, the surplus and demands of resources were mapped to vertex vectors of the bipartite graph, respectively. Collaboration expectations of each factory, QoS (quality of service) and supply-demand balance of manufacturing capacity were evaluated as the matching degree. Furthermore, the Kuhn–Munkras(KM) algorithm, which is good at bipartite graph matching, was adopted to solve the proposed model. Finally, results from simulation confirmed that the proposed method is feasible and advanced, in comparison with the current related methods.

A Coarse-to-Fine Registration Approach for Point Cloud Data with Bipartite Graph Structure

Alignment is a critical aspect of point cloud data (PCD) processing, and we propose a coarse-to-fine registration method based on bipartite graph matching in this paper. After data pre-processing, the registration progress can be detailed as follows: Firstly, a top-tail (TT) strategy is designed to normalize and estimate the scale factor of two given PCD sets, which can combine with the coarse alignment process flexibly. Secondly, we utilize the 3D scale-invariant feature transform (3D SIFT) method to extract point features and adopt fast point feature histograms (FPFH) to describe corresponding feature points simultaneously. Thirdly, we construct a similarity weight matrix of the source and target point data sets with bipartite graph structure. Moreover, the similarity weight threshold is used to reject some bipartite graph matching error-point pairs, which determines the dependencies of two data sets and completes the coarse alignment process. Finally, we introduce the trimmed iterative closest point (TrICP) algorithm to perform fine registration. A series of extensive experiments have been conducted to validate that, compared with other algorithms based on ICP and several representative coarse-to-fine alignment methods, the registration accuracy and efficiency of our method are more stable and robust in various scenes and are especially more applicable with scale factors.

Lane-based estimation of travel time distributions by vehicle type via vehicle re-identification using low-resolution video images

Travel time estimation plays an essential role in the high-granular traffic control and management of urban roads with distinct lane-changing conditions among lanes. However, little attention has been given to the estimation of distributions of travel times among different lanes and different vehicle types in addition to their expected values. This paper proposes a new method for estimating lane-based travel time distributions with consideration of different vehicle types through matching low-resolution vehicle video images taken by conventional traffic surveillance cameras. The vehicle type classification is based on vehicle sizes and deep learning features extracted by densely connected convolutional neural networks, and the vehicle re-identification is conducted through a lane-based bipartite graph matching technique. A case study is carried out on a congested urban road in Hong Kong. Results show that the proposed method performs well in estimating the lane-level travel time distributions by vehicle type which can be very helpful for various lane-based and vehicle type-specific traffic management schemes.

Point Cloud Video Super-Resolution via Partial Point Coupling and Graph Smoothness.

Point cloud (PC) is a collection of discrete geometric samples of a physical object in 3D space. A PC video consists of temporal frames evenly spaced in time, each containing a static PC at one time instant. PCs in adjacent frames typically do not have point-to-point (P2P) correspondence, and thus exploiting temporal redundancy for PC restoration across frames is difficult. In this paper, we focus on the super-resolution (SR) problem for PC video: increase point density of PCs in video frames while preserving salient geometric features consistently across time. We accomplish this with two ideas. First, we establish partial P2P coupling between PCs of adjacent frames by interpolating interior points in a low-resolution PC patch in frame t and translating them to a corresponding patch in frame t+1 , via a motion model computed by iterative closest point (ICP). Second, we promote piecewise smoothness in 3D geometry in each patch using feature graph Laplacian regularizer (FGLR) in an easily computable quadratic form. The two ideas translate to an unconstrained quadratic programming (QP) problem with a system of linear equations as solution-one where we ensure the numerical stability by upper-bounding the condition number of the coefficient matrix. Finally, to improve the accuracy of the ICP motion model, we re-sample points in a super-resolved patch at time t to better match a low-resolution patch at time t+1 via bipartite graph matching after each SR iteration. Experimental results show temporally consistent super-resolved PC videos generated by our scheme, outperforming SR competitors that optimized on a per-frame basis, in two established PC metrics.

Envy-free matchings in bipartite graphs and their applications to fair division

A matching in a bipartite graph with parts X and Y is called envy-free, if no unmatched vertex in X is a adjacent to a matched vertex in Y. Every perfect matching is envy-free, but envy-free matchings exist even when perfect matchings do not. We prove that every bipartite graph has a unique partition such that all envy-free matchings are contained in one of the partition sets. Using this structural theorem, we provide a polynomial-time algorithm for finding an envy-free matching of maximum cardinality. For edge-weighted bipartite graphs, we provide a polynomial-time algorithm for finding a maximum-cardinality envy-free matching of minimum total weight. We show how envy-free matchings can be used in various fair division problems with either continuous resources (“cakes”) or discrete ones. In particular, we propose a symmetric algorithm for proportional cake-cutting, an algorithm for 1-out-of-(2n-2) maximin-share allocation of discrete goods, and an algorithm for 1-out-of-⌊2n/3⌋ maximin-share allocation of discrete bads among n agents.

Auction-Based VM Allocation for Deadline-Sensitive Tasks in Distributed Edge Cloud

Edge cloud computing is a new paradigm in which the computation and storage services of remote cloud data centers are moved to Edge Cloud Nodes (ECNs) in network edges. Compared to traditional cloud data centers, ECNs are geographically close to mobile users so the communication latency is significantly reduced. In this paper, we study the problem of allocating Virtual Machine (VM) resources in geo-distributed ECNs to mobile users by using the auction theory. First, we treat mobile users and ECNs as the buyers and sellers of the VM resource auction, respectively. Then, we model the VM resource allocation problem as an <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -to-one weighted bipartite graph matching problem with 0-1 knapsack constraints. Since this problem is NP-hard, we design a greedy approximation algorithm to determine the winners of the auction, based on which we propose a truthful Auction-based VM resource Allocation (AVA) mechanism to solve the problem. Moreover, we prove that the AVA mechanism not only achieves an approximately optimal solution for winner selection, but also has the properties of truthfulness, individual rationality, and computational efficiency. Finally, we conduct extensive simulations on real traces to verify the significant performances of the proposed AVA mechanism.

Sum-Rate Maximization for Multi-Reconfigurable Intelligent Surface-Assisted Device-to-Device Communications

This paper proposes to deploy multiple reconfigurable intelligent surfaces (RISs) in device-to-device (D2D)-underlaid cellular systems. The uplink sum-rate of the system is maximized by jointly optimizing the transmit powers of the users, the pairing of the cellular users (CUs) and D2D links, the receive beamforming of the base station (BS), and the configuration of the RISs, subject to the power limits and quality-of-service (QoS) of the users. To address the non-convexity of this problem, we develop a new block coordinate descent (BCD) framework which decouples the D2D-CU pairing, power allocation and receive beamforming, from the configuration of the RISs. Specifically, we derive closed-form expressions for the power allocation and receive beamforming under any D2D-CU pairing, which facilitates interpreting the D2D-CU pairing as a bipartite graph matching solved using the Hungarian algorithm. We transform the configuration of the RISs into a quadratically constrained quadratic program (QCQP) with multiple quadratic constraints. A low-complexity algorithm, named Riemannian manifold-based alternating direction method of multipliers (RM-ADMM), is developed to decompose the QCQP into simpler QCQPs with a single constraint each, and solve them efficiently in a decentralized manner. Simulations show that the proposed algorithm can significantly improve the sum-rate of the D2D-underlaid system with a reduced complexity, as compared to its alternative based on semidefinite relaxation (SDR).

Multi-stage online task assignment driven by offline data under spatio-temporal crowdsourcing

In the era of the Internet of Things (IoT), the crowdsourcing process is driven by data collected by devices that interact with each other and with the physical world. As a part of the IoT ecosystem, task assignment has become an important goal of the research community. Existing task assignment algorithms can be categorized as offline (performs better with datasets but struggles to achieve good real-life results) or online (works well with real-life input but is difficult to optimize regarding in-depth assignments). This paper proposes a Cross-regional Online Task (CROT) assignment problem based on the online assignment model. Given the CROT problem, an Online Task Assignment across Regions based on Prediction (OTARP) algorithm is proposed. OTARP is a two-stage graphics-driven bilateral assignment strategy that uses edge cloud and graph embedding to complete task assignments. The first stage uses historical data to make offline predictions, with a graph-driven method for offline bipartite graph matching. The second stage uses a bipartite graph to complete the online task assignment process. This paper proposes accelerating the task assignment process through multiple assignment rounds and optimizing the process by combining offline guidance and online assignment strategies. To encourage crowd workers to complete crowd tasks across regions, an incentive strategy is designed to encourage crowd workers’ movement. To avoid the idle problem in the process of crowd worker movement, a drop-by-rider problem is used to help crowd workers accept more crowd tasks, optimize the number of assignments, and increase utility. Finally, through comparison experiments on real datasets, the performance of the proposed algorithm on crowd worker utility value and the matching number is evaluated.

The spanning k-trees, perfect matchings and spectral radius of graphs

A k-tree is a spanning tree in which every vertex has degree at most k. In this paper, we provide a sufficient condition for the existence of a k-tree in a connected graph with fixed order in terms of the adjacency spectral radius and the signless Laplacian spectral radius, respectively. Also, we give a similar condition for the existence of a perfect matching in a balanced bipartite graph with fixed order and minimum degree.

Multi-robot task allocation in disaster response: Addressing dynamic tasks with deadlines and robots with range and payload constraints

This paper tackles a class of multi-robot task allocation (MRTA) problems called “Single-Task Robots and Single-Robot Tasks” or SR–ST problems, subject to the following additional characteristics: tasks with deadlines, tasks that are generated during the mission, and robots with range and payload constraints (thus requiring multiple tours per robot). While these characteristics are typical of various disaster response and commercial applications, there is a lack of online MRTA solutions to address them. To solve this class of complex MRTA problems, an efficient online method (which is also suitable for decentralized deployment) is developed based on the construction and weighted matching of bipartite graphs. An exact integer linear programming (ILP) formulation of this class of MRTA problems is also developed, the solution of which serves both as an offline MRTA approach and as a provably optimal benchmark against which the online method is compared. The new methods are applied to a flood response problem where multiple unmanned aerial vehicles must respond to victims spread out over a large area. The results show that the new online algorithm closely trails the offline ILP method in terms of task completion performance, while being >103 times more computationally efficient compared to the ILP method. Dedicated case studies provide further insights into the favorable scalability of the online method with an increasing number of UAVs — offering up to 46% higher task completion compared to a random walk baseline in huge 1000-task problems. Lastly, application to a slightly different class of SR–ST problems and comparison of the ensuing results with that of corresponding state-of-the-art methods demonstrate the potential wider applicability of the proposed online MRTA method.

Three-Dimensional Diffusion Model in Sports Dance Video Human Skeleton Detection and Extraction

The research in this paper mainly includes as follows: for the principle of action recognition based on the 3D diffusion model convolutional neural network, the whole detection process is carried out from fine to coarse using a bottom-up approach; for the human skeleton detection accuracy, a multibranch multistage cascaded CNN structure is proposed, and this network structure enables the model to learn the relationship between the joints of the human body from the original image and effectively predict the occluded parts, allowing simultaneous prediction of skeleton point positions and skeleton point association information on the one hand, and refinement of the detection results in an iterative manner on the other. For the combination problem of discrete skeleton points, it is proposed to take the limb parts formed between skeleton points as information carriers, construct the skeleton point association information model using vector field, and consider it as a feature, to obtain the relationship between different skeleton points by using the detection method. It is pointed out that the reorganization problem of discrete skeleton points in multiperson scenes is an NP-Hard problem, which can be simplified by decomposing it into a set of subproblems of bipartite graph matching, thus proposing a matching algorithm for discrete skeleton points and optimizing it for the skeleton dislocation and algorithm problems of human occlusion. Compared with traditional two-dimensional images, audio, video, and other multimedia data, the 3D diffusion model data describe the 3D geometric morphological information of the target scene and are not affected by lighting changes, rotation, and scale transformation of the target and thus can describe the realistic scene more comprehensively and realistically. With the continuous updating of diffusion model acquisition equipment, the rapid development of 3D reconstruction technology, and the continuous enhancement of computing power, the research on the application of 3D diffusion model in the detection and extraction of a human skeleton in sports dance videos has become a hot direction in the field of computer vision and computer graphics. Among them, the feature detection description and model alignment of 3D nonrigid models are a fundamental problem with very important research value and significance and challenging at the same time, which has received wide attention from the academic community.

Crater Detection and Recognition Method for Pose Estimation

A crater detection and recognition algorithm is the key to pose estimation based on craters. Due to the changing viewing angle and varying height, the crater is imaged as an ellipse and the scale changes in the landing camera. In this paper, a robust and efficient crater detection and recognition algorithm for fusing the information of sequence images for pose estimation is designed, which can be used in both flying in orbit around and landing phases. Our method consists of two stages: stage 1 for crater detection and stage 2 for crater recognition. In stage 1, a single-stage network with dense anchor points (dense point crater detection network, DPCDN) is conducive to dealing with multi-scale craters, especially small and dense crater scenes. The fast feature-extraction layer (FEL) of the network improves detection speed and reduces network parameters without losing accuracy. We comprehensively evaluate this method and present state-of-art detection performance on a Mars crater dataset. In stage 2, taking the encoded features and intersection over union (IOU) of craters as weights, we solve the weighted bipartite graph matching problem, which is matching craters in the image with the previously identified craters and the pre-established craters database. The former is called “frame-frame match”, or FFM, and the latter is called “frame-database match”, or FDM. Combining the FFM with FDM, the recognition speed is enabled to achieve real-time on the CPU (25 FPS) and the average recognition precision is 98.5%. Finally, the recognition result is used to estimate the pose using the perspective-n-point (PnP) algorithm and results show that the root mean square error (RMSE) of trajectories is less than 10 m and the angle error is less than 1.5 degrees.

Perfect matching and distance spectral radius in graphs and bipartite graphs

A perfect matching in a graph G is a set of nonadjacent edges covering every vertex of G. Motivated by recent progress on the relations between the eigenvalues and the matching number of a graph, in this paper, we aim to present a distance spectral radius condition to guarantee the existence of a perfect matching. Let G be an n-vertex connected graph where n is even and λ1(D(G)) be the distance spectral radius of G. Then the following statements are true.(I) If 4≤n≤8 and λ1(DG)≤λ1(D(Sn,n2−1)), then G contains a perfect matching unless G≅Sn,n2−1 where Sn,n2−1≅Kn2−1∨(n2+1)K1.(II) If n≥10 and λ1(DG)≤λ1(D(G∗)), then G contains a perfect matching unless G≅G∗ where G∗≅K1∨(Kn−3∪2K1).Moreover, if G is a connected 2n-vertex balanced bipartite graph with λ1(D(G))≤λ1(D(Bn−1,n−2)), then G contains a perfect matching, unless G≅Bn−1,n−2 where Bn−1,n−2 is obtained from Kn,n−2 by attaching two pendent vertices to a vertex in the n-vertex part.

Randomized sequential importance sampling for estimating the number of perfect matchings in bipartite graphs

We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we establish various non-standard central limit theorems. We expect our methods to be useful for other applied problems.

Dynamic server placement in edge computing toward Internet of Vehicles

Facing serious challenges in bandwidth and delay, currently adopted cloud computing is no longer effective for providing real-time Internet of Vehicles (IoV) services in the intelligent transportation system (ITS). A newly introduced computing paradigm with a distributed feature, i.e., edge computing, can be a complement to the centralized cloud computing with computation offloaded to the distributed edge servers (ESs). Typically, edge servers are the host of IoV services in edge computing, which requires an appropriate quantification and placement before the implementation of computation offloading. To pursue a higher quality of service (QoS), the quantity and locations of the ESs need to be thoroughly discussed ahead. Otherwise, additional delay and network congestion will occur. Simultaneously, as the ITS is continuously developing, the existing placement of ESs ought to be adjusted to be in line with the dynamic change of IoV traffic. However, ES placement schemes are often devised by clustering methods with a fixed ES quantity and are unaware of the extensibility of the placement. To address the problems that mentioned, a dynamic ES placement approach (DEP) is developed. Technically, DEP leverages the non-dominated sorting genetic algorithm III (NSGA-III) for placements with better performance and less reconstruction of existing placement. The population of NSGA-III is initialized with clustering algorithms for a higher accuracy and convergence speed, and the fitness of minimum reconstruction cost is calculated based on Kuhn–Munkres bipartite graph matching algorithm. A real-world traffic data with 436 deployed roadside units in the provincial capital city Nanjing, China, is leveraged for comparative experiments. The experimental results verify the effectiveness of DEP with a 17.64% lower latency and 25.82% lower workload standard deviation comparing to the clustering method.

Achieving arbitrary throughput-fairness trade-offs in the inter cell interference coordination with fixed transmit power problem

We study the problem of inter cell interference coordination (ICIC) with fixed transmit power in OFDMA-based cellular networks, in which each base station (BS) needs to decide as to which subchannel, if any, to allocate to each of its associated mobile stations (MS) for data transmission. In general, there exists a trade-off between the total throughput (sum of throughputs of all the MSs) and fairness under the allocations found by resource allocation schemes. We introduce the concept of \(\tau -\alpha -\)fairness by modifying the concept of \(\alpha -\)fairness, which was earlier proposed in the context of congestion control for packet-switched networks. The concept of \(\tau -\alpha -\)fairness allows us to achieve arbitrary trade-offs between total throughput and fairness by selecting an appropriate value of \(\alpha\) in \([0,\infty )\). We show that for every \(\alpha \in [0,\infty )\) and every \(\tau > 0\), the problem of finding a \(\tau -\alpha -\)fair allocation is NP-Complete. Further, we show that for every \(\alpha \in [0, \infty )\), there exist thresholds such that if the potential interference levels experienced by each MS on every subchannel are above the threshold values, then the problem can be optimally solved in polynomial time by reducing it to the bipartite graph matching problem. Also, we propose a simple, distributed subchannel allocation algorithm for the ICIC problem, which is flexible, requires a small amount of time to operate, and requires information exchange among only neighboring BSs. We investigate via simulations as to how the algorithm parameters should be selected so as to achieve any desired trade-off between the total throughput and fairness. Finally, we compare the performance of the proposed algorithm with those of the simulated annealing based and opportunistic subchannel allocation algorithms in terms of the total throughput, fairness index and computational complexity.