Minimum Cost Flow Algorithm Research Articles

Intra-Frame Graph Structure and Inter-Frame Bipartite Graph Matching with ReID-Based Occlusion Resilience for Point Cloud Multi-Object Tracking

Three-dimensional multi-object tracking (MOT) using lidar point cloud data is crucial for applications in autonomous driving, smart cities, and robotic navigation. It involves identifying objects in point cloud sequence data and consistently assigning unique identities to them throughout the sequence. Occlusions can lead to missed detections, resulting in incorrect data associations and ID switches. To address these challenges, we propose a novel point cloud multi-object tracker called GBRTracker. Our method integrates an intra-frame graph structure into the backbone to extract and aggregate spatial neighborhood node features, significantly reducing detection misses. We construct an inter-frame bipartite graph for data association and design a sophisticated cost matrix based on the center, box size, velocity, and heading angle. Using a minimum-cost flow algorithm to achieve globally optimal matching, thereby reducing ID switches. For unmatched detections, we design a motion-based re-identification (ReID) feature embedding module, which uses velocity and the heading angle to calculate similarity and association probability, reconnecting them with their corresponding trajectory IDs or initializing new tracks. Our method maintains high accuracy and reliability, significantly reducing ID switches and trajectory fragmentation, even in challenging scenarios. We validate the effectiveness of GBRTracker through comparative and ablation experiments on the NuScenes and Waymo Open Datasets, demonstrating its superiority over state-of-the-art methods.

Accurate prediction of RNA secondary structure including pseudoknots through solving minimum-cost flow with learned potentials

Pseudoknots are key structure motifs of RNA and pseudoknotted RNAs play important roles in a variety of biological processes. Here, we present KnotFold, an accurate approach to the prediction of RNA secondary structure including pseudoknots. The key elements of KnotFold include a learned potential function and a minimum-cost flow algorithm to find the secondary structure with the lowest potential. KnotFold learns the potential from the RNAs with known structures using an attention-based neural network, thus avoiding the inaccuracy of hand-crafted energy functions. The specially designed minimum-cost flow algorithm used by KnotFold considers all possible combinations of base pairs and selects from them the optimal combination. The algorithm breaks the restriction of nested base pairs required by the widely used dynamic programming algorithms, thus enabling the identification of pseudoknots. Using 1,009 pseudoknotted RNAs as representatives, we demonstrate the successful application of KnotFold in predicting RNA secondary structures including pseudoknots with accuracy higher than the state-of-the-art approaches. We anticipate that KnotFold, with its superior accuracy, will greatly facilitate the understanding of RNA structures and functionalities.

MAP inference algorithms without approximation for collective graphical models on path graphs via discrete difference of convex algorithm

Collective graphical model (CGM) is a probabilistic model that provides a framework for analyzing aggregated count data. Maximum a posteriori (MAP) inference of unobserved variables under given observations is one of the essential operations in CGM. Because the MAP inference problem is known to be NP-hard in general, the current mainstream approach is to solve an alternative problem obtained by approximating the objective function and applying continuous relaxation. However, this approach has two significant drawbacks. First, the quality of the solution deteriorates when the values in the count data are negligible due to the inaccuracy of Stirling’s approximation. Second, the application of continuous relaxation causes the violation of integrality constraints. This paper proposes novel algorithms for MAP inference in CGMs on path graphs to overcome these problems. Our method is based on the discrete difference of convex algorithm (DCA); DCA is a general framework to minimize the sum of a convex function and a concave function by repeatedly minimizing surrogate functions. Utilizing the particular structure of path graphs, we efficiently solve the surrogate function minimization by minimum convex cost flow algorithms. Furthermore, our approach also leads to a new method of solving another important task; MAP inference of the sample size in CGM on path graphs. Our method is naturally applicable to this task, allowing us to design very efficient algorithms. Experimental results on synthetic and real-world datasets show the effectiveness of the proposed algorithms.

Adaptive Square-Root Unscented Kalman Filter Phase Unwrapping with Modified Phase Gradient Estimation

Phase unwrapping (PU) is a key program in data processing in the interferometric synthetic aperture radar (InSAR) technique, and its accuracy directly affects the quality of final SAR data products. However, PU in regions with large gradient changes and high noise has always been a difficult problem. To overcome the limitation, this article proposes an adaptive square-root unscented Kalman filter PU method. Specifically, a modified phase gradient estimation (PGE) algorithm is proposed, in which a Butterworth low-pass filter is embedded, and the PGE window can be adaptively adjusted according to phase root-mean-square errors of pixels. Furthermore, the outliers of the PGE results are detected and revised to obtain high-precision vertical and horizontal phase gradients. Finally, the unwrapped phase is calculated by the adaptive square-root unscented Kalman filter method. To the best of our knowledge, this article is the first to combine the modified PGE with an adaptive square-root unscented Kalman filter for PU. Two sets of simulated data and a set of TerraSAR-X/TanDEM-X real data were used for experimental verification. The experimental results demonstrated that the various improvement measures proposed in this article were effective. Additionally, compared with the minimum-cost flow algorithm (MCF), statistical-cost network-flow algorithm (SNAPHU) and unscented Kalman filter PU (UKFPU), the proposed method had better accuracy and model robustness.

Optimization of Multimodal Discrete Network Design Problems Based on Super Networks

In this paper, we investigate the multimodal discrete network design problem that simultaneously optimizes the car, bus, and rail transit network, in which inter-modal transfers are achieved by slow traffic modes including walking and bike-sharing. Specifically, a super network topology is presented to signify the modal interactions. Then, the generalized cost formulas of each type of links in the super network are defined. And based on the above formulas a bi-objective programming model is proposed to minimize the network operation cost and construction cost with traffic flow equilibrium constraints, investment constraints and expansion constraints. Moreover, a hybrid heuristic algorithm that combines the minimum cost flow algorithm and simulated annealing algorithm is presented to solve the proposed model. Finally, the effectiveness of the proposed model and algorithm is evaluated through two numerical tests: a simple test network and an actual multimodal transport network.

Integrated Optimization of Bipartite Matching and Its Stochastic Behavior: New Formulation and Approximation Algorithm via Min-cost Flow Optimization

The research field of stochastic matching has yielded many developments for various applications. In most stochastic matching problems, the probability distributions inherent in the nodes and edges are set a priori, and are not controllable. However, many matching services have options, which we call control variables, that affect the probability distributions and thus what constitutes an optimum matching. Although several methods for optimizing the values of the control variables have been developed, their optimization in consideration of the matching problem is still in its infancy. In this paper, we formulate an optimization problem for determining the values of the control variables so as to maximize the expected value of matching weights. Since this problem involves hard to evaluate objective values and is non-convex, we construct an approximation algorithm via a minimum-cost flow algorithm that can find 3-approximation solutions rapidly. Simulations on real data from a ride-hailing platform and a crowd-sourcing market show that the proposed method can find solutions with high profits of the service provider in practical time.

Expansion planning of offshore oilfield power systems based on minimum cost flow and global TABU search algorithm

Expansion planning of offshore oilfield power systems based on minimum cost flow and global TABU search algorithm

The minimum cost flow finding under fuzzy intuitionistic conditions

Present paper deals with the minimum cost flow finding task with fuzzy trapezoidal intuitionistic values of arc capacities and costs. Nowadays, flow tasks in networks are leading tasks in flow modelling and urban logistics. Peculiarity of the problem is in optimal paths finding, which allows decreasing the total cost of transportation and choosing the best paths for transportation. Fuzzy logic as a powerful tool for dealing with uncertainty, vagueness and inaccurate data influenced the way of presenting characteristics of networks. Arc capacities and costs can be presented as fuzzy numbers of the different form enabling researchers to get more reliable solutions. However, during the simulation a researcher is often faced with difficulties in exact specifying of arc capacities and costs. It is a commonplace that experts hesitate or have doubts choosing a specific value for parameters of the network. In such circumstances arc capacities and costs can be presented in a fuzzy intuitionistic form, in particular, as fuzzy intuitionistic triangular or trapezoidal numbers. A fuzzy intuitionistic number allows taking into account a level of hesitation by including degree of membership, non-membership and indeterminacy margin. Incorporating fuzzy intuitionistic sets into conventional flow patterns enables researchers to solve tasks in fuzzy, vague conditions even when there is a lack of necessary data for problem statement. The main contribution to the paper is the proposal for the fuzzy intuitionistic minimum cost flow algorithm using fuzzy intuitionistic flow patterns based on the ranking technique and arithmetic operations with fuzzy intuitionistic trapezoidal numbers. A case study numerical is presented to illustrate the proposed algorithm.

A hybrid heuristic for the maximum dispersion problem

In this paper we propose a hybrid heuristic for the Maximum Dispersion Problem of finding a balanced partition of a set of objects such that the shortest intra-part distance is maximized. In contrast to clustering problems, dispersion problems aim for a large spread of objects in the same group. They arise in many practical applications such as waste collection and the formation of study groups. The heuristic alternates between finding a balanced solution, and increasing the dispersion. Balancing is achieved by a combination of a minimum cost flow algorithm to find promising pairs of parts and a branch-and-bound algorithm that searches for an optimal balance, and the dispersion is increased by a local search followed by an ejection chain method for escaping local minima. We also propose new upper bounds for the problem. In computational experiments we show that the heuristic is able to find solutions significantly faster than previous approaches. Solutions are close to optimal and in many cases provably optimal.

A theoretical and experimental study of a new algorithm for minimum cost flow in dynamic graphs

This work focuses on the minimum cost flow problem in dynamic graphs. The model here proposed does not have travel time nor storage but all other parameters are time-dependent. The most popular method to solve this kind of problem uses the time-expanded graph but due to the large size of this graph, this solution technique is not manageable on a long time horizon. We propose a new approach that does not use the time-expanded graph. Our algorithm is based on the computation of successive shortest paths on static graphs, which are much smaller compared to the time-expanded graph. It has a significantly better computational complexity. Our method was implemented using the GraphStream library and experiments showed that it is also much faster than the classical method in practice.

Research on abundance adaptive frequency control strategy of household temperature-control load

Based on the method of space state, state division of household temperature-control load group is proposed. State sequence method is used to analyze the influence of load group abundance on aggregated power. Based on the minimum cost and maximum flow algorithm, the temperature-control load group’s abundance recovery strategy is proposed, which could achieves the goal of fast and smooth recovery load group abundance. The simulation of household temperature-control load respond to the power system primary frequency adjustment is carried out under the circumstances of good abundance, excess abundance and lack of abundance. The simulation results show that the effect of temperature control load on the power grid primary frequency adjustment is fine. and the effectiveness of the proposed frequency adjustment control strategy is verified.

Efficient algorithm for Minimum cost flow problem with partial lane reversals

In this paper, we investigate the minimum cost flow problem in two terminal series parallel network. We present modified minimum cost flow algorithm that computes the maximum dynamic and the earliest arrival flows in strongly polynomial time and also preserves all unused arc capacities. We also present strongly polynomial time minimum cost partial contraflow algorithm that solves both problems with partial reversals of arc capacities on two terminal series parallel networks.

A New 3-D Minimum Cost Flow Phase Unwrapping Algorithm Based on Closure Phase

Phase unwrapping (PU) is a critical step in interferometric synthetic aperture radar (InSAR) processing chain, which can directly affect the quality of the final results. In order to improve the accuracy and robustness of PU algorithm, especially for the interferograms that have relatively long perpendicular baselines, in this article, we propose a new 3-D minimum cost flow (MCF) algorithm based on closure phase. Different from current 3-D PU algorithms that aim to solve the unwrapped phase gradients (UPGs) among different interferograms and usually follow a 1+2D mode, this new approach establishes a mathematical constraint within the closure phases and unwraps them jointly. This constraint is based on a prior knowledge that the sums of UPGs, where the UPGs are in the azimuth/range plane whereas belongs to different interferograms in the closure phase, can be obtained before PU. The main advantage of this new approach is that neither a temporal deformation model nor a preliminary atmospheric phase calibration is required before PU. Besides, this new approach combines the MCF model and phase consistency, showing advantages in reducing the chance of phase aliasing. We implement our new approach in both continuous and discrete interferograms and use real SAR data to validate the performance by comparing with the 2-D MCF algorithm in SNAPHU and the 3-D PU algorithm in StaMPS.

Sketch Recognition Using LSTM with Attention Mechanism and Minimum Cost Flow Algorithm

Sketch Recognition Using LSTM with Attention Mechanism and Minimum Cost Flow Algorithm

On the Analysis of the Phase Unwrapping Process in a D-InSAR Stack with Special Focus on the Estimation of a Motion Model

This paper analyses the critical phase unwrapping step in a differential interferometric phase (D-InSAR) stack where both the solving of conventional methods and alternative approaches are discussed. It can be shown that including the temporal relationship between interferograms in the phase unwrapping step improves the results. This leads to the three-dimensional extended minimum cost flow algorithm. To unwrap the phase in a multitemporal way a motion model has to be considered. The estimation of these parameters is an important step. By default, the parameters are estimated in an iterative search process, where in each step, a linear program has to be solved. The best parameters are defined by the minimal costs. Often the choice of this search space is not straightforward. Furthermore, with this discrete optimization function, the solution is often not unique. This paper presents an alternative way to estimate the motion model parameters by maximizing a continuous function, the ensemble phase coherence. With the help of a closed-loop simulation and real data, both methods, the standard and the alternative way, are numerically compared and analyzed. Consequently, it is shown that maximizing the ensemble phase coherence is a good alternative to the established iterative procedure. It offers the advantage that the run time can be reduced considerably and is thus well suited in the processing of large data sets.

Integrated reconfiguration of both supply and demand for evacuation planning

Evacuation planning is a challenging task due to the suddenly increased large transportation demand in emergency situations. The imbalance between demand and supply of transportation systems is the key problem during evacuation. Existing literature has tried to increase the traffic capacity but not to reduce the demand. This paper proposes a novel integrated reconfiguration strategy that reconfigures both the supply and demand sides of transportation systems; in particular, the evacuation demand is reconfigured using a heterogeneous fleet of vehicles and the traffic capacity supply is reconfigured through a heterogeneous contraflow technique. Four strategies, i.e., do-nothing, supply reconfiguration, demand reconfiguration, and integrated reconfiguration, are compared. The general integrated strategy is formulated as a bi-level programming model which is solved by a two-layer algorithm composed of the tabu search (TS) and priority-based minimum cost flow (P-MCF) algorithm. The experimental results justify the effectiveness of the reconfiguration method and show that the integrated reconfiguration strategy performs best under any circumstance while the ranking of the other three strategies depends on the number of vehicles and evacuees.

DISPERSE: A Decentralized Architecture for Content Replication Resilient to Node Failures

This paper introduces DISPERSE, a distributed scalable architecture for delivery of content and services that provides resilience against node failure through location-independent storage and replication of content. Current content delivery networks (CDNs) have, at least to some degree, a centralized structure thus susceptible to a single point of failure. DISPERSE addresses this limitation by implementing a fully de-centralized structure. DISPERSE is a two-layer architecture: the first layer (front-end layer) exposes services (e.g., Web, SFTP) to clients; the second layer (back-end layer) provides reliable distributed storage of content and application state. Content in DISPERSE's back-end layer is stored and exchanged as Named Data Network (NDN) content objects. This allows DISPERSE to implement fine-grained, location-independent, fully decentralized content replication mechanisms. We validate the performance of DISPERSE under two node failure scenarios. In the first scenario, content can be stored in any DISPERSE node, and all nodes are equally likely to fail. In this scenario, we use non-linear optimization techniques to determine the optimal number of content copies under availability and latency constraints. In the second scenario, different nodes fail with different probabilities, and content is stored in nodes according to its value, node failure probability, and resource availability. This scenario is addressed as an instance of the minimum cost flow problem. Our results show that DISPERSE reduces the failure of content retrieval by five orders of magnitude compared to common CDN implementations, without significantly increasing content retrieval delay. Further, numerical results show that DISPERSE improves content availability by a factor of 1.3× - 2.3× when deploying the minimum cost flow algorithm.

Multiple object tracking by reliable tracklets

This paper proposes a novel network flow model for multi-target tracking, which uses short and highly reliable detection responses as the basic unit, namely the tracklet, in the model. Our model exploits the local information of the tracklet and deploys the global strategy of data association in tracking. The method is divided into two phases: a local phase and a global phase. In the local phase, our method is used to track targets using the detection results, namely the tracking by detection, where the boosted particle filter is used to generate high-confidence detection responses and they are connected into reliable tracklets. In the global phase, the multi-object tracking is modeled as data association problem, and the problem is represented by the maximum posterior probability. Finally, the model is solved by the minimum cost flow algorithm. When dealing with the target occlusion, this paper designs a two-step optimization algorithm to solve the long-term occlusion that affects tracking. A large number of experimental results show that our method is more effective in multi-object tracking than other state-of-the-art methods.

Minimum-cost flow algorithms: a performance evaluation using the Brazilian road network

Minimum-cost flow algorithms: a performance evaluation using the Brazilian road network

Minimum-cost flow algorithms: a performance evaluation using the Brazilian road network

In this paper, we evaluate the practical performance of four algorithms for solving the minimum-cost flow problem on road networks. While most computational testing has been based on artificially generated networks, for this study we used 215 real-world test instances, solved over the Brazilian road network. We verified that, differently from the literature, Network Simplex was the best performing algorithm in practice for this context, both in terms of speed and robustness. Features such as the number of supply and demand nodes influenced runtime, besides network topology and spatial syntax. On the other hand, the supplied volume and the ratio of supply/demand nodes were not good performance predictors. Our evaluation also showed that efficiency may be tied to algorithmic structure. The results should be particularly useful to support the choice of a MCF algorithm for evaluation of transportation networks, allowing reduction of cost for processing analyses of flow allocation.