Bipartite Graph Matching Research Articles

Resource allocation for virtual reality content sharing based on 5G D2D multicast communication

As the development of wireless virtual reality (VR), a great disparity exists among the huge content transmission, rigorous QoS guarantees and the limited bandwidth of cellular networks. With the increasing of cache capacity on user devices, direct content sharing between user devices is a promising solution to solve this problem. To meet the quality of service (QoS) requirement of wireless VR transmission, this paper proposes a content sharing scheme based on 5G device-to-device (D2D) Multicast Communication. In this way, some adjacent VR users can form multicasting clustering to share VR content by working on D2D communication mode. The VR D2D multicasting clusters reuse the uplink channel resource of ordinary VR cellular users in the same cell. The basic prerequisite is that the degrading on QoS of these ordinary VR cellular users can be affordable. We design a two-step scheme to solve this radio resource allocation problem for VR content sharing. Firstly, we find out the optimal transmitting power for each VR user devices by geometric proximity, which metrics are affected by wireless VR throughput, tracking accuracy and delay. In the second step, we transform the channel allocation problem into a bipartite graph matching problem based on the transmitting power metrics, which is optimally solved by the Hungarian algorithm. The simulation results show that the VR content sharing based on 5G D2D communication technology can achieve larger system throughput gain and lower transmission delay. Compared with heuristic scheme and stochastic scheme, the proposed scheme can increase the throughput of the overall network by about 50% and 12%, respectively.

Research on Network Users Archives Matching Based on Maximum Weight Matching of Bipartite Graph

Research on Network Users Archives Matching Based on Maximum Weight Matching of Bipartite Graph

SRA: Secure Reverse Auction for Task Assignment in Spatial Crowdsourcing

In this paper, we study a new type of spatial crowdsourcing, namely competitive detour tasking, where workers can make detours from their original travel paths to perform multiple tasks, and each worker is allowed to compete for preferred tasks by strategically claiming his/her detour costs. The objective is to make suitable task assignment by maximizing the social welfare of crowdsourcing systems and protecting workers’ private sensitive information. We first model the task assignment problem as a reverse auction process. We formalize the winning bid selection of reverse auction as an $n$ n -to-one weighted bipartite graph matching problem with multiple 0-1 knapsack constraints. Since this problem is NP-hard, we design an approximation algorithm to select winning bids and determine corresponding payments. Based on this, a Secure Reverse Auction (SRA) protocol is proposed for this novel spatial crowdsourcing. We analyze the approximation performance of the proposed protocol and prove that it has some desired properties, including truthfulness, individual rationality, computational efficiency, and security. To the best of our knowledge, this is the first theoretically provable secure auction protocol for spatial crowdsourcing systems. In addition, we also conduct extensive simulations on a real trace to verify the performance of the proposed protocol.

Enabling Security-Aware D2D Spectrum Resource Sharing for Connected Autonomous Vehicles

With the emergence of automated driving technology, wireless demand for secure information exchange among automated vehicles has increased dramatically. To this end, we design a security-aware dynamic device-to-device (D2D) spectrum resource sharing mechanism to enhance the security of vehicular D2D communications with the improved spectrum efficiency. Considering both resource block (RB) sharing and power control, we model this joint D2D spectrum resource sharing process as a weighted bipartite graph matching problem whose weights are obtained through deriving the closed-form solutions of power control in an algebraic method. Then, the global optimal solutions of the matching problem are obtained by using the Hungarian algorithm. Furthermore, a security-aware RB and power allocation (SA-RBPA) mechanism compatible with existing cellular networks is proposed for the small cell base station applications. Extensive simulation results have shown that, compared with existing approaches that consider RB reusing strategy or power control scheme optimization alone, the SA-RBPA scheme is able to realize a better spectrum efficiency and security performance.

Reducing Invertible Embedding Distortion Using Graph Matching Model

Invertible embedding allows the original cover and embedded data to be perfectly reconstructed. Conventional methods use a well-designed predictor and fully exploit the carrier characteristics. Due to the diversity, it is actually hard to accurately model arbitrary covers, which limits the practical use of methods relying heavily on content characteristics. It has motivated us to revisit invertible embedding operations and propose a general graph matching model to generalize them and further reduce the embedding distortion. In the model, the rate-distortion optimization task of invertible embedding is derived as a weighted bipartite graph matching problem. In the bipartite graph, the nodes represent the values of cover elements, and the edges indicate the candidate modifications. Each edge is associated with a weight indicating the corresponding embedding distortion for the connected nodes. By solving the minimum weight maximum matching problem, we can find the optimal embedding strategy under the constraint. Since the proposed work is a general model, it can be incorporated into existing works to improve their performance, or used for designing new invertible embedding systems. We incorporate the proposed work into a part of state-of-the-arts, and experiments show that it significantly improves the rate-distortion performance. To the best knowledge of the authors, it is probably the first work studying rate-distortion optimization of invertible embedding from the perspective of graph matching model.

3D Model Retrieval Using Bipartite Graph Matching Based on Attention

In this paper, we propose an attention-based bipartite graph 3D model retrieval algorithm, where many-to-many matching method, the weighted bipartite graph matching, is employed for comparison between two 3D models. Considering the panoramic views can donate the spatial and structural information, in this work, we use panoramic views to represent each 3D model. Attention mechanism is used to generate the weight of all views of each model. And then, we construct a weighted bipartite graph with the views of those models and the weight of each view. According to the bipartite graph, the matching result is used to measure the similarity between two 3D models. We experiment our method on ModelNet, NTU and ETH datasets, and the experimental results and comparison with other methods show the effectiveness of our method.

Applications of Matching in Bipartite Graph

Applications of Matching in Bipartite Graph

Scalable parallel algorithms for maximum matching and Hamiltonian circuit in convex bipartite graphs

Since bipartite convex graphs emerged from industrial applications, algorithms for this class of graphs have been devised in several research areas such as scheduling, DNA analysis, and constraint programming. A bipartite graph G=(V,W,E) is convex if there exists an ordering of the vertices of W such that, for each v∈V, the neighbors of v are consecutive in W. In this work we describe a coarse grained parallel algorithm for the maximum matching problem in a convex bipartite graph. For p processors, the algorithm runs in O((|V|/p)lg⁡(|V|/p)lg⁡p) time and uses O(lg⁡p) communication rounds. We also address a well-known problem in the area of combinatorial optimization, the Hamiltonian circuit problem, presenting a sequential linear-time algorithm to determine if a convex bipartite graph has a Hamiltonian circuit. We further show how to efficiently implement both algorithms in PRAM and coarse grained parallel models. Experimental tests performed on commercial machines show the algorithms are robust and scalable.

A Faster Algorithm for Cuckoo Insertion and Bipartite Matching in Large Graphs

Hash tables are ubiquitous in computer science for efficient access to large datasets. However, there is always a need for approaches that offer compact memory utilisation without substantial degradation of lookup performance. Cuckoo hashing is an efficient technique of creating hash tables with high space utilisation and offer a guaranteed constant access time. We are given n locations and m items. Each item has to be placed in one of the $$k\ge 2$$ locations chosen by k random hash functions. By allowing more than one choice for a single item, cuckoo hashing resembles multiple choice allocations schemes. In addition it supports dynamically changing the location of an item among its possible locations. We propose and analyse an insertion algorithm for cuckoo hashing that runs in linear time with high probability and in expectation. Previous work on total allocation time has analysed breadth first search, and it was shown to be linear only in expectation. Our algorithm finds an assignment (with probability 1) whenever it exists. In contrast, the other known insertion method, known as random walk insertion, may run indefinitely even for a solvable instance. We also present experimental results comparing the performance of our algorithm with the random walk method, also for the case when each location can hold more than one item. As a corollary we obtain a linear time algorithm (with high probability and in expectation) for finding perfect matchings in a special class of sparse random bipartite graphs. We support this by performing experiments on a real world large dataset for finding maximum matchings in general large bipartite graphs. We report an order of magnitude improvement in the running time as compared to the Hopkraft–Karp matching algorithm.

Bipartite Graphs Associated with Pell, Mersenne and Perrin Numbers

Abstract In this paper, we consider the relationships between the numbers of perfect matchings (1-factors) of bipartite graphs and Pell, Mersenne and Perrin Numbers. Then we give some Maple procedures in order to calculate the numbers of perfect matchings of these bipartite graphs.

Approximating maximum uniquely restricted matchings in bipartite graphs

A matching in a graph is uniquely restricted if no other matching covers exactly the same set of vertices. This notion was defined by Golumbic, Hirst, and Lewenstein (2001) and studied in a number of articles. We provide approximation algorithms for computing a uniquely restricted matching of maximum size in some bipartite graphs, namely those excluding a C4 or with maximum degree at most three. In particular, we achieve a ratio of 5∕9 for subcubic bipartite graphs, improving over a 1∕2-approximation algorithm proposed by Mishra (2011).

Big Data Analytics and Network Calculus Enabling Intelligent Management of Autonomous Vehicles in a Smart City

Artificial intelligence (AI) and big data analytics enable autonomous vehicles (AVs) to dramatically change future intelligent transportation in smart cities. AVs are envisaged to evolve to a service rather than a product in the future. To provide best user experience of such services, three primary factors, namely, waiting time, travel time, and supply of AV services, are taken into consideration in a multiobjective optimization. Conventional optimization of services relies on traffic flow analysis over a queuing network model. However, due to the mobility of vehicles and the transfer uncertainty of road networks, the queuing network analysis is too complicated and practically intractable. For accuracy and convenient processing, network calculus (NC) is extended to model the queueing problem in this paper. The optimal number of available AVs can be identified by guaranteeing the waiting time of customers. The satisfaction of AV services can be viewed as a supply and demand problem, and optimized by bipartite graph matching. In order to reduce the average travel time, especially for rush hours with heavy traffic, we further propose a new online AVs fleet management scheme with congestion control for smart cities. It is shown that the intelligent management of AV fleet can be efficiently achieved, outperforming the cases of traditional vehicles. NC-assisted AI enables an efficient intelligent transportation paradigm in smart cities, while achieving substantial energy saving.

A weighted approach to the maximum cardinality bipartite matching problem with applications in geometric settings

We present a weighted approach to compute a maximum cardinality matching in an arbitrary bipartite graph. Our main result is a new algorithm that takes as input a weighted bipartite graph $G(A\cup B,E)$ with edge weights of $0$ or $1$. Let $w \leq n$ be an upper bound on the weight of any matching in $G$. Consider the subgraph induced by all the edges of $G$ with a weight $0$. Suppose every connected component in this subgraph has $O(r)$ vertices and $O(mr/n)$ edges. We present an algorithm to compute a maximum cardinality matching in $G$ in $\tilde{O}( m(\sqrt{w}+ \sqrt{r}+\frac{wr}{n}))$ time.When all the edge weights are $1$ (symmetrically when all weights are $0$), our algorithm will be identical to the well-known Hopcroft-Karp (HK) algorithm, which runs in $O(m\sqrt{n})$ time. However, if we can carefully assign weights of $0$ and $1$ on its edges such that both $w$ and $r$ are sub-linear in $n$ and $wr=O(n^{\gamma})$ for $\gamma < 3/2$, then we can compute a maximum cardinality matching in $o(m\sqrt{n})$ time. Using our algorithm, we obtain a new $\tilde{O}(n^{4/3}/\varepsilon^3)$ time algorithm to compute an $\varepsilon$-approximate bottleneck matching of $A,B\subset \mathbb{R}^2$ and a $\frac{1}{\varepsilon^{O(d)}}n^{1+\frac{d-1}{2d-1}}\mathrm{poly}\log n$ time algorithm for computing an $\varepsilon$-approximate bottleneck matching in $d$-dimensions. All previous algorithms take $\Omega(n^{3/2})$ time.Our algorithm also applies to any graph $G(A \cup B,E)$ that has an easily computable balanced vertex separator of size $|V'|^{\delta}$, for every subgraph $G'(V',E')$ where $\delta\in [1/2,1)$. By applying our algorithm, we can compute a maximum matching in $\tilde{O}(mn^{\frac{\delta}{1+\delta}})$ time, improving upon the $O(m\sqrt{n})$ time taken by the HK-Algorithm.

A deterministic parallel algorithm for bipartite perfect matching

A fundamental quest in the theory of computing is to understand the power of randomness. It is not known whether every problem with an efficient randomized algorithm also has one that does not use randomness. One of the extensively studied problems under this theme is that of perfect matching. The perfect matching problem has a randomized parallel (NC) algorithm based on the Isolation Lemma of Mulmuley, Vazirani, and Vazirani. It is a long-standing open question whether this algorithm can be derandomized. In this article, we give an almost complete derandomization of the Isolation Lemma for perfect matchings in bipartite graphs. This gives us a deterministic parallel (quasi-NC) algorithm for the bipartite perfect matching problem. Derandomization of the Isolation Lemma means that we deterministically construct a weight assignment so that the minimum weight perfect matching is unique. We present three different ways of doing this construction with a common main idea.

A 2/3-Approximation Algorithm for Vertex Weighted Matching in Bipartite Graphs

We consider the maximum vertex-weighted matching problem (MVM), in which nonnegative weights are assigned to the vertices of a graph, the weight of a matching is the sum of the weights of the match...

Energy Disaggregation of Appliances Consumptions Using HAM Approach

Non-intrusive load monitoring (NILM) makes it possible for users to track the energy consumption of a household. In this paper, we present a new hybrid energy disaggregation approach named HAM. This event-based load disaggregation algorithm uses an improved multi-layer Hungarian algorithm to match appliances transient features and a supervised adaptive resonance theory mapping neural network (ARTMAP) to cluster steady features. This approach using a modified dual sliding window-based cumulative sum control chart algorithm (DSWC) to detect the transient event first, and we convert the multi-dimensional electrical features of appliances into a bipartite graph matching problem. This way, an improved Hungarian algorithm is proposed to find the perfect matching when appliances are in different states. For classification and identification, the ARTMAP network is used to learn and classify the steady features of appliances. Furthermore, we introduced a grey correlation evaluation and multiple matching strategies to increase the fitness and accuracy of the approach. Experimental results demonstrate that the proposed HAM outperforms the comparative algorithm in both our resident appliances dataset (RAD) and BLUED public dataset. The proposed approach could also facilitate NILM more applicable for common households.

Joint Radio Resource Allocation and Control for Vehicle Platooning in LTE-V2V Network

To improve safety and efficiency of transportation system, an effective approach is vehicle platooning, in which a group of vehicles maintains a pre-defined moving pattern by minimizing tracking error of each vehicle. As a networked control process, platooning control relies on the cooperative awareness messages (CAM) periodically exchanged in the vehicle platoon. In meeting communication and control expectations, we propose to jointly optimize the radio resource allocation in LTE-vehicle-to-vehicle (V2V) network for the CAM transmission and control parameters of vehicle, in order to minimize the tracking error while guaranteeing the reliability requirements of V2V communication and string stability of platoon. To solve the formulated problem, we develop a sub-optimal solution. First, we present a tracking error based scheduling criterion and then obtain a radio resource allocation scheme by bipartite graph matching. Then, control parameters of vehicle are adapted to minimize the tracking error by heuristic gradient descent based method. Simulation results show that the proposed scheme can reduce the tracking error as well as ensure the platoon stability compared to the existing schemes.

3D object retrieval with graph-based collaborative feature learning

3D object retrieval has attractive extensive research focus in recent years. Among various schemes, view based 3D object retrieval is regarded as a promising direction. In this paper, we present a novel view-based 3D object retrieval framework, which is deployed over a graph-based collaborative learning scheme to intelligently fuse multiple features. In particular, we introduce a hypergraph based collaborative feature learning scheme to fuse complement descriptors from both the contour and the interior region of 3D object effectively. Then, the view-based 3D object retrieval is done via a greedy bipartite graph matching algorithm, which achieves highly accurate and efficient 3D object matching. With the above bipartite graph matching and feature concatenation, significant performance improvement is achieved in the 3D object retrieval task, on either widely-used benchmark datasets or open competitions like SHREC15 challenge. In both evaluations, the proposed graph-based collaborative feature learning scheme has beaten a serial of existing approaches and state-of-the-art schemes.

Perfect Matchings in Õ (n1.5) Time in Regular Bipartite Graphs

In this paper we consider the well-studied problem of finding a perfect matching in a d-regular bipartite graph on 2n nodes with m=nd edges. The best-known algorithm for general bipartite graphs (due to Hopcroft and Karp) takes time O(m\sqrt{n}). In regular bipartite graphs, however, a matching is known to be computable in O(m) time (due to Cole, Ost and Schirra). In a recent line of work by Goel, Kapralov and Khanna the O(m) time algorithm was improved first to \tilde O(min{m, n^{2.5}/d}) and then to \tilde O(min{m, n^2/d}). It was also shown that the latter algorithm is optimal up to polylogarithmic factors among all algorithms that use non-adaptive uniform sampling to reduce the size of the graph as a first step. In this paper, we give a randomized algorithm that finds a perfect matching in a d-regular graph and runs in O(n\log n) time (both in expectation and with high probability). The algorithm performs an appropriately truncated random walk on a modified graph to successively find augmenting paths. Our algorithm may be viewed as using adaptive uniform sampling, and is thus able to bypass the limitations of (non-adaptive) uniform sampling established in earlier work. We also show that randomization is crucial for obtaining o(nd) time algorithms by establishing an \Omega(nd) lower bound for any deterministic algorithm. Our techniques also give an algorithm that successively finds a matching in the support of a doubly stochastic matrix in expected time O(n\log^2 n) time, with O(m) pre-processing time; this gives a simple O(m+mn\log^2 n) time algorithm for finding the Birkhoff-von Neumann decomposition of a doubly stochastic matrix.

The train frequency compatibility problem

How should trains that arrive at a railway station in constant intervals be scheduled so that the safety interval between two trains is maximum? This is a timetabling problem which we call the train frequency compatibility (TFC) problem that can be mathematically stated as follows. Given a collection A of N (possible repeated) positive integers ai (the train frequencies), find δi≥0 (the starting time of the periodic trip i), for i=1,…,N, such that z=min|naj+δj−(mai+δi)|, with i,j=1,…,N,i≠j and m,n∈N0, is maximum. We present Mixed Integer Linear Programming (MILP) formulations for the problem, describe a procedure to obtain bounds on maximum z, and report computational results. We also consider a restricted version of the TFC which yields more realistic solutions regarding the train scheduling applications. For the restricted version we give a formulation based on matchings in bipartite graphs, compare the computational performance of this formulation with the MILP model, and prove that the problem is NP-hard.