Bipartite Graph Matching Research Articles

MultiTalk: A Highly-Branching Dialog Testbed for Diverse Conversations

We study conversational dialog in which there are many possible responses to a given history. We present the MultiTalk Dataset, a corpus of over 320,000 sentences of written conversational dialog that balances a high branching factor (10) with several conversation turns (6) through selective branch continuation. We make multiple contributions to study dialog generation in the highly branching setting. In order to evaluate a diverse set of generations, we propose a simple scoring algorithm, based on bipartite graph matching, to optimally incorporate a set of diverse references. We study multiple language generation tasks at different levels of predictive conversation depth, using textual attributes induced automatically from pretrained classifiers. Our culminating task is a challenging theory of mind problem, a controllable generation task which requires reasoning about the expected reaction of the listener.

Sequential End-to-end Network for Efficient Person Search

Person search aims at jointly solving Person Detection and Person Re-identification (re-ID). Existing works have designed end-to-end networks based on Faster R-CNN. However, due to the parallel structure of Faster R-CNN, the extracted features come from the low-quality proposals generated by the Region Proposal Network, rather than the detected high-quality bounding boxes. Person search is a fine-grained task and such inferior features will significantly reduce re-ID performance. To address this issue, we propose a Sequential End-to-end Network (SeqNet) to extract superior features. In SeqNet, detection and re-ID are considered as a progressive process and tackled with two sub-networks sequentially. In addition, we design a robust Context Bipartite Graph Matching (CBGM) algorithm to effectively employ context information as an important complementary cue for person matching. Extensive experiments on two widely used person search benchmarks, CUHK-SYSU and PRW, have shown that our method achieves state-of-the-art results. Also, our model runs at 11.5 fps on a single GPU and can be integrated into the existing end-to-end framework easily.

Counting matchings via capacity-preserving operators

AbstractThe notion of the capacity of a polynomial was introduced by Gurvits around 2005, originally to give drastically simplified proofs of the van der Waerden lower bound for permanents of doubly stochastic matrices and Schrijver’s inequality for perfect matchings of regular bipartite graphs. Since this seminal work, the notion of capacity has been utilised to bound various combinatorial quantities and to give polynomial-time algorithms to approximate such quantities (e.g. the number of bases of a matroid). These types of results are often proven by giving bounds on how much a particular differential operator can change the capacity of a given polynomial. In this paper, we unify the theory surrounding such capacity-preserving operators by giving tight capacity preservation bounds for all nondegenerate real stability preservers. We then use this theory to give a new proof of a recent result of Csikvári, which settled Friedland’s lower matching conjecture.

UAV-Aided Cooperative Data Collection Scheme for Ocean Monitoring Networks

In this article, we present an unmanned aerial vehicle (UAV)-aided ocean monitoring network for remote oceanic data collection, in which monitoring data are transmitted first from battery-powered underwater sensor nodes (USNs) to sea surface sink nodes (SNs) in a data collection cycle using underwater acoustic communication, and then a UAV hovering in air collects all the data from SNs and relays them to a ground base station via wireless communication links. Aiming at maximizing network lifetime, we model the resource allocation, USN-to-SN access, and SN-to-UAV access issues as a mixed-integer nonconvex optimization problem. To efficiently solve it, we decompose the optimization into two stages. The first stage is to minimize time consumption in an SN-to-UAV nonorthogonal multiple access process and we solve it by designing a UAV deployment scheme, a subchannel matching scheme, and a joint power and time allocation scheme, based on which, the second stage is to maximize the residual energies of USNs in USN-to-SN transmissions under a modified frequency-division multiple access strategy in each collection cycle. The second-stage optimization is further decomposed into some similar subproblems, and each of them is considered as a bipartite graph matching problem between USNs and underwater acoustic channels. For each subproblem, we propose improved weight-based matching and bisection-based searching algorithms. Finally, we design a low-complexity iteration algorithm to approximate the optimal solution of the original problem by solving these subproblems. The simulation results validate the effectiveness of our proposals.

On the proportion of transverse-free plane curves

We study the asymptotic proportion of smooth plane curves over a finite field Fq which are tangent to every line defined over Fq. This partially answers a question raised by Charles Favre. Our techniques include applications of Poonen's Bertini theorem and Schrijver's theorem on perfect matchings in regular bipartite graphs. Our main theorem implies that a random smooth plane curve over Fq admits a transverse Fq-line with very high probability.

Adaptive Multi-Access Algorithm for Multi-Service Edge Users in 5G Ultra-Dense Heterogeneous Networks

In the 5G ultra-dense wireless heterogeneous network system, it is a crucial issue to implement an effective network selection strategy to satisfy the demands of massive edge users and novel 5G services. In this paper, we model the network selection problem of edge users requesting different services as a bipartite graph, and propose a network selection algorithm based on weighted bipartite graph matching for 5G ultra-dense heterogeneous networks, named BGMNS. The proposed algorithm combines Analytic Hierarchy Process (AHP) and Grey Relation Analysis (GRA) to analyze the preferences of multiple services for different network attributes and obtain the Quality of Experience (QoE) of different edge users for each network. Moreover, in order to realize the fair allocation of network resources, we comprehensively consider the importance of the requested services and the obtained QoE by edge users to construct system fairness index. The BGMNS algorithm can optimize the overall QoE of users under the premise of ensuring the system fairness. Simulation results show that compared to the existing network selection algorithms, the proposed BGMNS algorithm can not only provide stable access to users when network status fluctuates randomly, but also effectively reduce user blocking probability as well as total packet loss rate, and significantly improve user average energy efficiency.

On the induced matching problem in hamiltonian bipartite graphs

Abstract In this paper, we study the parameterized complexity of the induced matching problem in hamiltonian bipartite graphs and the inapproximability of the maximum induced matching problem in hamiltonian bipartite graphs. We show that, given a hamiltonian bipartite graph, the induced matching problem is W[1]-hard and cannot be solved in time n o ⁢ ( k ) {n^{o(\sqrt{k})}} , where n is the number of vertices in the graph, unless the 3SAT problem can be solved in subexponential time. In addition, we show that unless NP = P {\operatorname{NP}=\operatorname{P}} , a maximum induced matching in a hamiltonian bipartite graph cannot be approximated within a ratio of n 1 / 4 - ϵ {n^{1/4-\epsilon}} , where n is the number of vertices in the graph.

Strong structural input and state observability of linear time-invariant systems: Graphical conditions and algorithms

The paper studies input and state observability (ISO) of discrete-time linear time-invariant network systems whose dynamics are affected by unknown inputs. More precisely, we aim at reconstructing the initial state and the sequence of unknown inputs from the system outputs, and we will use the term ISO when the input reconstruction is possible with delay one, namely the inputs up to time k−1 and the states up to time k can be obtained from the outputs up to time k, while the term unconstrained ISO will refer to the case where there is some arbitrary delay in the input reconstruction. We focus on the problem of s-structural ISO (resp. s-structural unconstrained ISO) wherein the objective is to find conditions such that for all system matrices that carry the same network structure, the resulting system is ISO (resp. unconstrained ISO). We provide first a graphical characterization for s-structural unconstrained ISO, and subsequently, sufficient conditions and necessary conditions for s-structural ISO. For the latter, under the assumption of zero feedthrough, these conditions coincide and characterise ISO. The conditions presented are in terms of existence of suitable uniquely restricted matchings in bipartite graphs associated with the structured system. In order to test these conditions, we present polynomial-time algorithms. Finally, we discuss an equivalent reformulation of the main conditions in terms of coloring algorithms as in the literature of zero forcing sets.

Maximum and optimal 1-2 matching problem of the different kind

We discuss 1-2 matchings, which are matchings in bipartite graphs G = (S S′, E) where their elements are pairs of edges with common endpoints in S. An algorithm to find an optimal 1-2 matching is derived. We also discuss 1-2 matchings of the different kind, which are special kinds of 1-2 matchings. The maximum 1-2 matching problem of the different kind can be analyzed by using augmenting trails of the different kind that are analogues of augmenting paths in the usual matching problem. The optimal 1-2 matching problem of the different kind can be reduced to the minimum-cost flow problem.

Online Multiple Athlete Tracking with Pose-Based Long-Term Temporal Dependencies.

This paper addresses the Multi-Athlete Tracking (MAT) problem, which plays a crucial role in sports video analysis. There exist specific challenges in MAT, e.g., athletes share a high similarity in appearance and frequently occlude with each other, making existing approaches not applicable for this task. To address this problem, we propose a novel online multiple athlete tracking approach which make use of long-term temporal pose dynamics for better distinguishing different athletes. Firstly, we design a Pose-based Triple Stream Network (PTSN) based on Long Short-Term Memory (LSTM) networks, capable of modeling long-term temporal pose dynamics of athletes, including pose-based appearance, motion and athletes’ interaction clues. Secondly, we propose a multi-state online matching algorithm based on bipartite graph matching and similarity scores produced by PTSN. It is robust to noisy detections and occlusions due to the reliable transitions of multiple detection states. We evaluate our method on the APIDIS, NCAA Basketball and VolleyTrack databases, and the experiment results demonstrate its effectiveness.

Socially Aware Device-to-multi-device User Grouping for Popular Content Distribution

The distribution of popular videos incurs a large amount of traffic at the base stations (BS) of networks. Device-to-multi-device (D2MD) communication has emerged an efficient radio access technology for offloading BS traffic in recent years. However, traditional studies have focused on synchronous user requests whereas asynchronous user requests are more common. Hence, offloading BS traffic in case of asynchronous user requests while considering their time-varying characteristics and the quality of experience (QoE) of video request users (VRUs) is a pressing problem. This paper uses social stability (SS) and video loading duration (VLD)-tolerant property to group VRUs and seed users (SUs) to offload BS traffic. We define the average amount of data transmission (AADT) to measure the network’s capacity for offloading BS traffic. Based on this, we formulate a time-varying bipartite graph matching optimization problem. We decouple the problem into two subproblems which can be solved separately in terms of time and space. Then, we propose the socially aware D2MD user selection (SA-D2MD-S) algorithm based on finite horizon optimal stopping theory, and propose the SA-D2MD user matching (SA-D2MD-M) algorithm to solve the two subproblems. The results of simulations show that our algorithms outperform prevalent algorithms.

Solving the α-helix correspondence problem at medium-resolution Cryo-EM maps through modeling and 3D matching

Cryo-electron microscopy (cryo-EM) has recently emerged as a prominent biophysical method for macromolecular structure determination. Many research efforts have been devoted to produce cryo-EM images, density maps, at near-atomic resolution. Despite many advances in technology, the resolution of the generated density maps may not be sufficiently adequate and informative to directly construct the atomic structure of proteins. At medium-resolution (∼4-10 Å), secondary structure elements (α-helices and β-sheets) are discernible, whereas finding the correspondence of secondary structure elements detected in the density map with those on the sequence remains a challenging problem. In this paper, an automatic framework is proposed to solve α-helix correspondence problem in three-dimensional space. Through modeling of the sequence with the aid of a novel strategy, the α-helix correspondence problem is initially transformed into a complete weighted bipartite graph matching problem. An innovative correlation-based scoring function based on a well-known and robust statistical method is proposed for weighting the graph. Moreover, two local optimization algorithms, which are Greedy and Improved Greedy algorithms, have been presented to find α-helix correspondence. A widely used data set including 16 reconstructed and 4 experimental cryo-EM maps were chosen to verify the accuracy and reliability of the proposed automatic method. The experimental results demonstrate that the automatic method is highly efficient (86.25% accuracy), robust (11.3% error rate), fast (∼1.4 s), and works independently from cryo-EM skeleton.

FIT: Inspect vulnerabilities in cross-architecture firmware by deep learning and bipartite matching

Widely deployed IoT devices expose serious security threats because the firmware in them contains vulnerabilities, which are difficult to detect due to two main factors: 1) The firmware’s code is usually not available; 2) A same vulnerability often exists in multiple firmware with different architectures and/or release versions. In this paper, we propose a novel neural network-based staged approach to inspect vulnerabilities in firmware, which first learns semantics in binary code and utilizes neural network model to screen out the potential vulnerable functions, then performs bipartite graph matching upon three-level features between two binary functions. We implement the approach in a tool called FIT and evaluation results show that FIT outperforms state-of-the-art approaches, i.e., Gemini, CVSSA and discovRE, on both effectiveness and efficiency. FIT also detects vulnerabilities in real-world firmware of IoT devices, such as D-Link routers. Moreover, we make our tool and dataset publicly available in the hope of facilitating further researches in the firmware security field.

Multiple UAV-Mounted Base Station Placement and User Association With Joint Fronthaul and Backhaul Optimization

In this paper, we study a joint placement, resource allocation, and user association problem for UAV-assisted wireless networks with constrained backhaul links, where multiple UAV-mounted base stations (UBSs) are deployed to provide wireless services for ground users. We propose a novel framework to maximize the user throughput within the flight-time of UBSs and provides fairness among the users. We first obtain the optimal resource allocation schemes based on different fronthaul and backhaul conditions, and an efficient iterative algorithm is then developed to jointly optimize user association and UBS placement. The optimal UBS placement can be achieved by solving an unconstrained optimization problem which is a simplification of the initial constrained optimization problem based on the optimal resource allocation. We develop a dual-domain coordinated descent and bipartite graph matching based sub-process to identify an optimal user association that prefers the nearby UBSs, as the user association under constrained backhaul links have non-unique optimal solutions. Extensive simulations are conducted to verify the effectiveness of the proposed algorithm, and results show that our proposed method under constrained backhaul can improve both the average throughput by 49% and the fairness among the users by 47% in comparison with the method under ideal backhaul.

An Optimum Lower Bound for the Weights of Maximum Weight Matching in Bipartite Graphs

Let $\Ga$ be the collection of all weighted bipartite graphs each having $\sigma$ and $m$, as the size of a vertex partition and the total weight, respectively. We give a tight lower bound $\lceil \frac{m-\sigma}{\sigma} \rceil+1$ for the set $\{\textit{Wt}(\textit{mwm}(G))~|~G \in \Ga\}$ which denotes the collection of weights of maximum weight bipartite matchings of all graphs in $\Ga$.

Shape correspondence based on Kendall shape space and RAG for 2D animation

We introduce a 2D vectorized shape correspondence method based on Kendall shape space and region adjacency graph. We regard shape correspondence in 2D animation as a weighted bipartite graph matching problem and optimize it by means of various weights, including geometric attribute, local topological information, and global topological information in 2D animation drawing. The measuring method in Kendall shape space is introduced to determine similarity between two regions and a local adjacent region matching method is presented to associate the vicinity of the corresponding region by utilizing local topology information. Ultimately, we propose a globally optimal shape matching method, which exploits the global topological information to get the final result of the shape correspondence. Our approach can efficiently match associated regions that have exaggerated deformation and unstable topology between two shapes in 2D animation. It is also robust to the similarity transformation of shapes.

Towards cost-efficient resource provisioning with multiple mobile users in fog computing

Fog computing is an emerging paradigm that brings computing capabilities closer to distributed IoT devices, which provides networking services between end devices and traditional cloud data centers. One important mission is to further reduce the monetary cost of fog resources while meeting the ever-growing demands of multiple users. In this paper, we focus on minimizing the total cost for multiple mobile users to provide an efficient resource provisioning scheme in fog computing. The total cost includes two aspects: the replication cost and the transmission cost. We consider three cases for the resource provision problem by focusing on different cost models. First, one simple case where users can only upload one replication is discussed, and an optimal solution is proposed by converting the original problem into a bipartite graph matching. Then we consider a more complicated case in which each user can upload multiple replications on fog nodes in the resource provisioning. Specifically, two models are discussed: the 0–1 transmission cost model and the different transmission cost model. For the 0–1 transmission cost model, each user can upload multiple replications with a constant transmission cost, and one optimal greedy solution is proposed. For the different transmission cost model, the transmission cost is related to the distance of each pair of fog nodes. This problem is proven to be NP-hard. We first propose a non-adaptive algorithm which is proved to be bounded by 23W+13OPT. Another 3+ϵ-approximation algorithm is proposed based on local search, which has better performance with higher complexity. Extensive simulations also prove the efficiency of our schemes.

A bipartite matching-based feature selection for multi-label learning

Many real-world data have multiple class labels known as multi-label data, where the labels are correlated with each other, and as such, they are not independent. Since these data are usually high-dimensional, and the current multi-label feature selection methods have not been precise enough, then a new feature selection method is necessary. In this paper, for the first time, we have modeled the problem of multi-label feature selection to a bipartite graph matching process. The proposed method constructs a bipartite graph of features (as the left vertices) and labels (as the right vertices), called Feature-Label Graph (FLG), where each feature is connected to the set of labels, where the weight of the edge between each feature and label is equal to their correlation. Then, the Hungarian algorithm estimates the best matching in FLG. The selected features in each matching are sorted by weighted correlation distance and added to the ranking vector. To select the discriminative features, the proposed method considers both the redundancy of features and the relevancy of each feature to the class labels. The results indicate the superiority of the proposed method against the other methods in classification measures.

Scaling matrices and counting the perfect matchings in graphs

We investigate efficient randomized methods for approximating the number of perfect matchings in bipartite graphs and general undirected graphs. Our approach is based on assigning probabilities to edges, randomly selecting an edge to be in a perfect matching, and discarding edges that cannot be put in a perfect matching. The probabilities are set according to the entries in the doubly stochastically scaled version of the adjacency matrix of the given graph. The experimental analysis on random and real-life graphs shows improvements in the approximation over previous and similar methods from the literature.

Mallows permutations as stable matchings

AbstractWe show that the Mallows measure on permutations of $1,\dots ,n$ arises as the law of the unique Gale–Shapley stable matching of the random bipartite graph with vertex set conditioned to be perfect, where preferences arise from the natural total ordering of the vertices of each gender but are restricted to the (random) edges of the graph. We extend this correspondence to infinite intervals, for which the situation is more intricate. We prove that almost surely, every stable matching of the random bipartite graph obtained by performing Bernoulli percolation on the complete bipartite graph $K_{{\mathbb Z},{\mathbb Z}}$ falls into one of two classes: a countable family $(\sigma _n)_{n\in {\mathbb Z}}$ of tame stable matchings, in which the length of the longest edge crossing k is $O(\log |k|)$ as $k\to \pm \infty $ , and an uncountable family of wild stable matchings, in which this length is $\exp \Omega (k)$ as $k\to +\infty $ . The tame stable matching $\sigma _n$ has the law of the Mallows permutation of ${\mathbb Z}$ (as constructed by Gnedin and Olshanski) composed with the shift $k\mapsto k+n$ . The permutation $\sigma _{n+1}$ dominates $\sigma _{n}$ pointwise, and the two permutations are related by a shift along a random strictly increasing sequence.