Maximum Weight Bipartite Matching Research Articles

Matching single cells across modalities with contrastive learning and optimal transport.

Understanding the interactions between the biomolecules that govern cellular behaviors remains an emergent question in biology. Recent advances in single-cell technologies have enabled the simultaneous quantification of multiple biomolecules in the same cell, opening new avenues for understanding cellular complexity and heterogeneity. Still, the resulting multimodal single-cell datasets present unique challenges arising from the high dimensionality and multiple sources of acquisition noise. Computational methods able to match cells across different modalities offer an appealing alternative towards this goal. In this work, we propose MatchCLOT, a novel method for modality matching inspired by recent promising developments in contrastive learning and optimal transport. MatchCLOT uses contrastive learning to learn a common representation between two modalities and applies entropic optimal transport as an approximate maximum weight bipartite matching algorithm. Our model obtains state-of-the-art performance on two curated benchmarking datasets and an independent test dataset, improving the top scoring method by 26.1% while preserving the underlying biological structure of the multimodal data. Importantly, MatchCLOT offers high gains in computational time and memory that, in contrast to existing methods, allows it to scale well with the number of cells. As single-cell datasets become increasingly large, MatchCLOT offers an accurate and efficient solution to the problem of modality matching.

Long-Term Matching Optimization With Federated Neural Temporal Difference Learning in Mobility-on-Demand Systems

Efficient bipartite graph matching of orders and drivers is a central operational problem in industrial mobility-on-demand (MOD) systems. Traditional studies adopt pure combinatorial optimization models for order-and-driver matching, which do not consider the long-term rewards of the dynamic MOD decision making process. Toward long-term optimization, this article presents a systemic paradigm of online matching with federated neural temporal difference learning (FedTDLearning), which encompasses learning and matching phases. During the learning phase, the long-term matching process is modeled as a Markov decision process, which is typically solved by employing data-driven reinforcement learning in an offline central training scheme. Massive amounts of data would be generated on the network by industrial MOD systems. It is impossible to send all the large-scale industrial data to the cloud server for centralized model training due to network bandwidth limitations and safety concerns. Therefore, a generic and innovative FedTDLearning is proposed to achieve long-term matching in a distributed manner. During the matching phase, a real-time bipartite matching optimization problem is formulated to maximize the learned spatiotemporal value and minimize the pickup distance, which is reducible to the minimum-cost maximum weight bipartite graph matching problem. A distance-learned-value ratio algorithm is proposed to find an optimal matching in the bipartite graph based on the joint optimization of FedTDLearning and the combinatorial fractional programming approach. Furthermore, to pursue optimal computation efficiency, we solve the real-time matching problem by constructing a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -nearest neighbor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(k$ </tex-math></inline-formula> NN) bipartite graph where each order is connected with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> NN drivers. Using openly available real-world data, the prototype system and experimental evaluations show that our proposed algorithms have effective problem-solving capability in practice.

Differentiable Multi-Granularity Human Parsing.

In this work, we study the challenging problem of instance-aware human body part parsing. We introduce a new bottom-up regime which achieves the task through learning category-level human semantic segmentation as well as multi-person pose estimation in a joint and end-to-end manner. The output is a compact, efficient and powerful framework that exploits structural information over different human granularities and eases the difficulty of person partitioning. Specifically, a dense-to-sparse projection field, which allows explicitly associating dense human semantics with sparse keypoints, is learnt and progressively improved over the network feature pyramid for robustness. Then, the difficult pixel grouping problem is cast as an easier, multi-person joint assembling task. By formulating joint association as maximum-weight bipartite matching, we develop two novel algorithms based on projected gradient descent and unbalanced optimal transport, respectively, to solve the matching problem differentiablly. These algorithms make our method end-to-end trainable and allow back-propagating the grouping error to directly supervise multi-granularity human representation learning. This is significantly distinguished from current bottom-up human parsers or pose estimators which require sophisticated post-processing or heuristic greedy algorithms. Extensive experiments on three instance-aware human parsing datasets (i.e., MHP-v2, DensePose-COCO, PASCAL-Person-Part) demonstrate that our approach outperforms most existing human parsers with much more efficient inference. Our code is available at https://github.com/tfzhou/MG-HumanParsing.

Optimizing the Age of Information for Multi-Source Information Update in Internet of Things

Age of Information (AoI) has recently become a new performance metric that captures the freshness/timeliness of information at end users in Internet of Things (IoT). Most existing information update mechanisms mainly consider the status information from a single Source Node (SN) or from multiple SNs with independent observations. However, in a practical IoT system, each status could be observed by multiple SNs, which brings new challenge in optimizing the AoI. To consider this issue, this paper formulates two optimization problems, named AoI-aware Multi-source Information Update problem (<i>AoI-MSIU</i>) and AoI-Reduction-aware Multi-source Information Update problem (<i>AoIR-MSIU</i>) problem, respectively. Specifically, AoI-MSIU problem assumes that the status are the first time to be uploaded to the BS, while AoIR-MSIU problem supposes that the BS already maintains the status that it has received before. Besides maximizing the revenue of information update, both problems consider how to optimize the AoI of the status. For AoI-MSIU problem, we prove that it is NP-hard, and propose an efficient greedy algorithm with a guaranteed approximation ratio. For AoIR-MSIU problem, we propose a polynomial-time optimal solution, which is based on a maximum weight bipartite matching on an auxiliary graph. Finally, we evaluate the performance of the proposed schemes through simulations.

An efficient data transmission scheme through 5G D2D-enabled relays in wireless sensor networks

Energy-efficient data transmission is a key challenge in Wireless Sensor Networks (WSNs). Cluster heads (CHs) are often used to relay aggregated data from sensor nodes to a central base station (BS). However, the transmission range of such relay nodes is limited, necessitating multihop communication for forwarding data from edge relays to BS. Further, links may not be created due to the unavailability of suitable relays resulting in unreliable networks. The use of cellular device-to-device (D2D) communication eliminates the requirement of very short-range communication of WSNs and also helps in maintaining a good link throughput. In this paper, a cellular D2D-assisted relay communication scheme has been proposed for forwarding data where the issue of link disconnection is solved using dual connectivity of D2D and cellular communication among cluster heads. The proposed scheme, DSPA (D2D Relay Node (DRN) Selection and uplink Power Allocation), uses the Maximum Weight Bipartite Matching for selection of relays. Performance analysis shows that the higher sleeping probability of the sensor nodes improves the overall energy efficiency of the network and also increases the average hop gain.

A Modified Decomposition Algorithm for Maximum Weight Bipartite Matching and Its Experimental Evaluation

Let G be an undirected bipartite graph with positive integer weights on the edges. We refine the existing decomposition theorem originally proposed by Kao et al., for computing maximum weight bipartite matching. We apply it to design an efficient version of the decomposition algorithm to compute the weight of a maximum weight bipartite matching of G in O(|V |W /k(|V |, W /N))-time by employing an algorithm designed by Feder and Motwani as a subroutine, where |V | and N denote the number of nodes and the maximum edge weight of G, respectively and k(x, y) = log x/ log(x 2 /y). The parameter W is smaller than the total edge weight W, essentially when the largest edge weight differs by more than one from the second largest edge weight in the current working graph in any decomposition step of the algorithm. In best case W = O(|E|) where |E| be the number of edges of G and in worst case W = W, that is, |E| ≤ W ≤ W. In addition, we talk about a scaling property of the algorithm and research a better bound of the parameter W. An experimental evaluation on randomly generated data shows that the proposed improvement is significant in general.

Maximization of Two Techniques of Relay Networks using Co-Operative Protocols

This paper considers the transfer helped co-usable transmission in remote systems, Where numerous client pair lead bidirectional interchanges by means of different transfers dependent on Orthogonal Frequency Division Multiplexing (OFDM) transmission. The fundamental goal is to improve the general framework execution by augmenting the complete throughput. It manages the joint enhancement of channel and hand-off task, subcarrier portion just as hand-off determination. The issue is detailed as a combinatorial improvement issue. It primarily manages two-way transferring and to make it progressively manageable. It received a chart based methodology. Along these lines the issue is fathomed ideally in polynomial time by changing it into Maximum Weighted Bipartite Matching (MWBM) issue. The reproduction result shows the correlation of the proposed calculation and the seat mark alongside two handing-off conventions.

Maximization of Two Techniques of Relay Networks using Co-Operative Protocals

This study recognise the transfer-assisted co-usable transmission in remote systems, where numerous client pairs lead bidirectional interchanges through various transfers depending on the transmission of the Orthogonal Frequency Division Multiplexing. The fundamental goal is to improve the overall execution of the framework by increasing the overall performance. It manages the joint enhancement of channel and hand-off task, subcarrier portion just as hand-off determination. The issue is detailed as a combinatorial improvement issue. It primarily manages two-way transferring and to make it progressively manageable. It received a chart based methodology. Along these lines the issue is fathomed ideally in polynomial time by changing it into Maximum Weighted Bipartite Matching (MWBM) issue. The reproduction result shows the correlation of the proposed calculation and the seat mark alongside two handing-off conventions.

DAMS: D2D-assisted multimedia streaming service with minimized BS transmit power in cellular networks

This paper presents a scheme, named D2D-assisted Multimedia Streaming (DAMS), for selecting relay nodes to assist low-battery active users in a cellular network. The scheme also minimizes the transmission power of base stations (BSs) by transmitting data through D2D relay nodes (DRNs). The proposed scheme uses a maximum-weight bipartite matching and transmission power allocation algorithm to obtain optimal power allocation at the BS. We show that the energy required at the BS for transmitting D2D control signals is negligible in comparison to the transmission power that is saved. Simulation results verify the improved performance of the proposed scheme.

Optimal Channel and Relay Assignment in Ofdmbased Multi-Relay Multi-Pair Two-Way Communication Networks

Efficient utilization of radio resources in wireless networks is crucial and has been investigated extensively. This letter considers a wireless relay network where multiple user pairs conduct bidirectional communications via multiple relays based on orthogonal frequency-division multiplexing (OFDM) transmission. The joint optimization of channel and relay assignment, including subcarrier pairing, subcarrier allocation as well as relay selection, for total throughput maximization is formulated as a combinatorial optimization problem. Using a graph theoretical approach, we solve the problem optimally in polynomial time by transforming it into a maximum weighted bipartite matching (MWBM) problem. Simulation studies are carried out to evaluate the network total throughput versus transmit power per node and the number of relay nodes

Maximizing throughput gain via resource allocation in D2D communications

By reusing the cellular resources, device-to-device (D2D) communication is becoming a very promising technology that greatly enhances the spectrum utilization. To harvest the benefits that D2D communications can offer, efficient resource allocation strategy is required to guarantee the demands of quality of service (QoS) for both cellular and D2D users. This paper proposes a resource allocation scheme to alleviate the performance deterioration of the D2D communications with spectrum reuse. To maximize the overall throughput gain, the proposed scheme is designed to reduce the rate loss of cellular users and improve the rate of D2D users simultaneously in a two-step manner. Specifically, it first calculates the reuse gain for a single D2D pair and a single cellular user. Next, a maximum weight bipartite matching is further proposed to select the reuse pair to maximize the overall network throughput gain. Numerical results demonstrate that the proposed resource allocation scheme can significantly improve the network throughput performance with average user rate guaranteed.

Systematic module approach identifies altered genes and pathways in four types of ovarian cancer.

The present study aimed to identify altered genes and pathways associated with four histotypes of ovarian cancer, according to the systematic tracking of dysregulated modules of reweighted protein-protein interaction (PPI) networks. Firstly, the PPI network and gene expression data were initially integrated to infer and reweight normal ovarian and four types of ovarian cancer (endometrioid, serous, mucinous and clear cell carcinoma) PPI networks based on Spearman's correlation coefficient. Secondly, modules in the PPI network were mined using a clique-merging algorithm and the differential modules were identified through maximum weight bipartite matching. Finally, the gene compositions in the altered modules were analyzed, and pathway functional enrichment analyses for disrupted module genes were performed. In five conditional-specific networks, universal alterations in gene correlations were revealed, which leads to the differential correlation density among disrupted module pairs. The analyses revealed 28, 133, 139 and 33 altered modules in endometrioid, serous, mucinous and clear cell carcinoma, respectively. Gene composition analyses of the disrupted modules revealed five common genes (mitogen-activated protein kinase 1, phosphoinositide 3-kinase-encoding catalytic 110-KDα, AKT serine/threonine kinase 1, cyclin D1 and tumor protein P53) across the four subtypes of ovarian cancer. In addition, pathway enrichment analysis confirmed one common pathway (pathways in cancer), in the four histotypes. This systematic module approach successfully identified altered genes and pathways in the four types of ovarian cancer. The extensive differences of gene correlations result in dysfunctional modules, and the coordinated disruption of these modules contributes to the development and progression of ovarian cancer.

Systematic tracking of disrupted modules identifies significant genes and pathways in hepatocellular carcinoma.

The objective of the present study is to identify significant genes and pathways associated with hepatocellular carcinoma (HCC) by systematically tracking the dysregulated modules of re-weighted protein-protein interaction (PPI) networks. Firstly, normal and HCC PPI networks were inferred and re-weighted based on Pearson correlation coefficient. Next, modules in the PPI networks were explored by a clique-merging algorithm, and disrupted modules were identified utilizing a maximum weight bipartite matching in non-increasing order. Then, the gene compositions of the disrupted modules were studied and compared with differentially expressed (DE) genes, and pathway enrichment analysis for these genes was performed based on Expression Analysis Systematic Explorer. Finally, validations of significant genes in HCC were conducted using reverse transcription-quantitative polymerase chain reaction (RT-qPCR) analysis. The present study evaluated 394 disrupted module pairs, which comprised 236 dysregulated genes. When the dysregulated genes were compared with 211 DE genes, a total of 26 common genes [including phospholipase C beta 1, cytochrome P450 (CYP) 2C8 and CYP2B6] were obtained. Furthermore, 6 of these 26 common genes were validated by RT-qPCR. Pathway enrichment analysis of dysregulated genes demonstrated that neuroactive ligand-receptor interaction, purine and drug metabolism, and metabolism of xenobiotics mediated by CYP were significantly disrupted pathways. In conclusion, the present study greatly improved the understanding of HCC in a systematic manner and provided potential biomarkers for early detection and novel therapeutic methods.

Optimal Channel and Relay Assignment in Ofdmbased Multi-Relay Multi-Pair Two-Way Communication Networks

The aim of the paper lies in maximizing the system total throughput by optimally coordinating the relay and subcarrier assignment among the multiple pairs of two-way users .In this Paper, consider an OFDM-based network where multiple relays help multiple pairs of source nodes to conduct Bidirectional communications.. The joint optimization problem of subcarrier pairing based subcarrier assignment and relay selection for multiple two-way users is considered as a combinatorial optimization problem. Hence graph based approach is implemented to establish the equivalence between the proposed problem and a maximum weighted bipartite matching (MWBM) problem. Then the problem is solved by the corresponding graph based algorithm optimally in polynomial time

An Optimal Resource Allocation Method for Multi-User Multi-Relay DF Cognitive Radio Networks

This letter investigates the resource optimization problem for the multi-user multi-relay decode-forward (DF) cognitive radio networks. The novel optimization metric, namely the bandwidth-power product (BPP), is applied to achieve the optimal spectrum sharing. The formulated problem is found to be a mixed-integer programming problem. Hence, a suboptimal and tractable algorithm with low complexity called the joint optimal relay matching and greedy resource allocation (JRMRA) algorithm is proposed. The optimal relay selection is first regulated by solving the equivalent maximum weighted bipartite matching (MWBM) problem with the Hungarian method in terms of statistic expectation. Then applying the greedy-based clustering method, the resource allocation is performed to minimize the overall BPP. Simulation results show that the JRMRA algorithm achieves the acceptable performance with great reduction of computational complexity and validate the superiority of the proposed scheme compared to conventional spectrum sharing scheme using the water-filling method.

Maximum bipartite matchings with low rank data: Locality and perturbation analysis

The maximum-weighted bipartite matching problem between two sets U=V=[1:n] is defined by a matrix W=(wij)n×n of “affinity” data. Its goal is to find a permutation π over [1:n] whose total weight ∑iwi,π(i) is maximized. In various practical applications,3 the affinity data may be of low rank (or approximately low rank): we say W has rank at most r if there are 2r vectors u1,…,ur,v1,…vr∈Rn such thatW=∑i=1ruiviT.In this paper, we partially address a question raised by David Karger who asked for a characterization of the structure of the maximum-weighted bipartite matchings when the rank of the affinity data is low. In particular, we study the following locality property: For an integer k>0, we say that the bipartite matchings of G have locality at most k if for every sub-optimal matching π of G, there exists a matching σ of larger total weight that can be reached from π by an augmenting cycle of length at most k.We prove the following main theorem: For every W∈[0,1]n×n of rank r and ϵ∈[0,1], there exists W˜∈[0,1]n×n such that (i) W˜ has rank at most r+1, (ii) the entry-wise ∞-norm ‖W−W˜‖∞≤ϵ, and (iii) the weighted bipartite graph with affinity data W˜ has locality at most ⌈r/ϵ⌉r. In contrast, this property is not true if perturbations are not allowed. We also give a tight bound for the binary case.

Systematic tracking of altered modules identifies disrupted pathways in teratozoospermia.

The objective of this study was to identify disrupted pathways in teratozoospermia by systematically tracking dysregulated modules in reweighted protein-protein interaction (PPI) networks. We inferred and reweighted the PPI networks of normal and teratozoospermia groups based on Spearman correlation coefficients. Modules in the PPI networks were explored via a clique-merging algorithm and altered modules were identified based on maximum weight bipartite matching. Furthermore, pathway-enrichment analyses of genes in altered modules were performed by Database for Annotation, Visualization, and Integrated Discovery (DAVID) to illuminate the biological pathways in teratozoospermia. A total of 20,102 genes were screened from the expression profile. We explored 2406 and 2101 modules in normal and disease PPI networks, respectively. Moreover, we obtained 875 altered modules by comparing modules in normal and teratozoospermia PPI networks. At P < 0.01, the genes involved in 2855 interactions with score changes >1 were mainly enriched in 66 pathways and the genes in altered modules were enriched in 71 pathways. The activity genes (missed and added genes in the disrupted modules) were enriched in 41 common pathways. There were 36 mutual enriched pathways under the five different conditions. Moreover, the cell cycle pathway was disrupted in the first 10 pathways of each condition. This study provides a powerful biomarker discovery platform to better understand the progression of teratozoospermia by systematically tracking dysregulated modules. This method uncovered potential diagnostic and therapeutic targets of teratozoospermia. This information might lead to improved monitoring and treatment of teratozoospermia.

Systematic Tracking of Disrupted Modules Identifies Altered Pathways Associated with Congenital Heart Defects in Down Syndrome.

BackgroundThis work aimed to identify altered pathways in congenital heart defects (CHD) in Down syndrome (DS) by systematically tracking the dysregulated modules of reweighted protein-protein interaction (PPI) networks.Material/MethodsWe performed systematic identification and comparison of modules across normal and disease conditions by integrating PPI and gene-expression data. Based on Pearson correlation coefficient (PCC), normal and disease PPI networks were inferred and reweighted. Then, modules in the PPI network were explored by clique-merging algorithm; altered modules were identified via maximum weight bipartite matching and ranked in non-increasing order. Finally, pathways enrichment analysis of genes in altered modules was carried out based on Database for Annotation, Visualization, and Integrated Discovery (DAVID) to study the biological pathways in CHD in DS.ResultsOur analyses revealed that 348 altered modules were identified by comparing modules in normal and disease PPI networks. Pathway functional enrichment analysis of disrupted module genes showed that the 4 most significantly altered pathways were: ECM-receptor interaction, purine metabolism, focal adhesion, and dilated cardiomyopathy.ConclusionsWe successfully identified 4 altered pathways and we predicted that these pathways would be good indicators for CHD in DS.

Temporal Identification of Dysregulated Genes and Pathways in Clear Cell Renal Cell Carcinoma Based on Systematic Tracking of Disrupted Modules.

Objective. The objective of this work is to identify dysregulated genes and pathways of ccRCC temporally according to systematic tracking of the dysregulated modules of reweighted Protein-Protein Interaction (PPI) networks. Methods. Firstly, normal and ccRCC PPI network were inferred and reweighted based on Pearson correlation coefficient (PCC). Then, we identified altered modules using maximum weight bipartite matching and ranked them in nonincreasing order. Finally, gene compositions of altered modules were analyzed, and pathways enrichment analyses of genes in altered modules were carried out based on Expression Analysis Systematic Explored (EASE) test. Results. We obtained 136, 576, 693, and 531 disrupted modules of ccRCC stages I, II, III, and IV, respectively. Gene composition analyses of altered modules revealed that there were 56 common genes (such as MAPK1, CCNA2, and GSTM3) existing in the four stages. Besides pathway enrichment analysis identified 5 common pathways (glutathione metabolism, cell cycle, alanine, aspartate, and glutamate metabolism, arginine and proline metabolism, and metabolism of xenobiotics by cytochrome P450) across stages I, II, III, and IV. Conclusions. We successfully identified dysregulated genes and pathways of ccRCC in different stages, and these might be potential biological markers and processes for treatment and etiology mechanism in ccRCC.

Collision Bottleneck Throughput in Bacterial Conjugation-based Nanonetworks

Bacterial conjugation-based nanonetwork has been recently proposed as a novel molecular communication paradigm, in which the bacteria act as carriers. This is the foundational work proposing the phenomenon of collision which occurs in the form of multi-conjugation of multiple carrier bacteria at the side of receiver nanodevice. We show the effect of this conjugation-based collision on the maximum achievable throughput of the network, using a simple graph-theoretic approach, namely, Maximum Weight Bipartite Matching. One of the several interesting results that emerges concerns the maximum achievable throughput, which is bounded by Θ(n/p) in case of homogeneous nodes, where n and p refer to the total number of nodes, and the vertical layers in the network, respectively.