Bipartite Matching Model Research Articles

Emission-concerned coordinated dispatching of electrified autonomous mobility-on-demand system and power system incorporating heterogeneous spatiotemporal scales

Electrified autonomous mobility-on-demand (E-AMoD) systems will play a crucial role in future cities, which couple the carbon emissions generated by the transportation system and the power system. This paper proposes a joint dispatching framework to facilitate city decarbonization by coordinating the fleet operator and power system operator. Given the substantial differences in spatial and temporal dispatching scales between the two systems, this framework effectively integrates micro vehicle-level service dispatching with macro fleet-level charging scheduling. Firstly, a novel bipartite matching model efficiently solves the short-term passenger serving and rebalancing dispatching at the vehicle level. The service dispatching results are then aggregated as spatial-temporal transition flows across different areas and time intervals. Incorporating these mobility constraints, the long-term charging-discharging scheduling at the fleet level is captured as an expanded network flow model and integrated with the power system dispatching model, which aims at renewable energy utilization and carbon emission mitigation. Finally, the fleet-level scheduling results are disaggregated to the serving-rebalancing-charging sequences of each vehicle, for practical implementation. To validate the proposed framework, numerical experiments are conducted on a large-scale real-world case. Multiple charging schedule scenarios, including heuristic charging, smart charging, and smart charging-discharging, are investigated under both centralized and distributed supplied power systems. (1) The framework proves to be an effective solution for addressing the differences in dispatching spatiotemporal scales, calculation efficiencies, and privacy concerns between power and traffic systems. (2) Through power-traffic coordination, the E-AMoD fleet demonstrates its ability to alleviate 8% of average renewable energy curtailment and reduce nearly 15% of the total emissions in a power system installed with renewable distributed generators. (3) Furthermore, the extent of emission mitigation effects is influenced by critical factors such as fleet size, renewable energy profile, and power system capacity. Overall, the E-AMoD system show great potential as mobile storage devices to provide spatial-temporal flexibility to the power system and contribute to city decarbonization.

A Target Re-Identification Method Based on Shot Boundary Object Detection for Single Object Tracking

With the advantages of simple model structure and performance-speed balance, the single object tracking (SOT) model based on a Transformer has become a hot topic in the current object tracking field. However, the tracking errors caused by the target leaving the shot, namely the target out-of-view, are more likely to occur in videos than we imagine. To address this issue, we proposed a target re-identification method for SOT called TRTrack. First, we built a bipartite matching model of candidate tracklets and neighbor tracklets optimized by the Hopcroft–Karp algorithm, which is used for preliminary tracking and judging the target leaves the shot. It achieves 76.3% mAO on the tracking benchmark Generic Object Tracking-10k (GOT-10k). Then, we introduced the alpha-IoU loss function in YOLOv5-DeepSORT to detect the shot boundary objects and attained 38.62% mAP75:95 on Microsoft Common Objects in Context 2017 (MS COCO 2017). Eventually, we designed a backtracking identification module in TRTrack to re-identify the target. Experimental results confirmed the effectiveness of our method, which is superior to most of the state-of-the-art models.

Analysis of an optimal policy in dynamic bipartite matching models

A dynamic bipartite matching model is given by a bipartite matching graph which determines the possible matchings between the various types of supply and demand items. Both supply and demand items arrive to the system according to a stochastic process. Matched pairs leave the system and the others wait in the queues, which induces a holding cost. We model this problem as a Markov Decision Process and study the discounted cost and the average cost problem. We assume that the cost function is linear on the queue sizes. We show that for the N-shaped matching graph, an optimal matching control prioritizes the matchings in the pendant edges and is of threshold type for the diagonal edge. In addition, for the average cost problem, we compute the optimal threshold value. We then show how the obtained results can be used to characterize the structure of an optimal matching control for a quasi-complete graph with an arbitrary number of nodes. For arbitrary bipartite graphs, we show that, when the cost of the pendant edges is larger than in the neighbors, an optimal matching policy prioritizes the items in the pendant edges. We also study the W-shaped matching graph and, when the cost of the pendant edges is larger than the cost of the middle edge, we conjecture that an optimal matching policy is also of threshold type with priority to the pendant edges; however, when the cost of the middle edge is larger, we present simulations that show that it is not optimal to prioritize items in the pendant edges.

A product form for the general stochastic matching model

AbstractWe consider a stochastic matching model with a general compatibility graph, as introduced by Mairesse and Moyal (2016). We show that the natural necessary condition of stability of the system is also sufficient for the natural ‘first-come, first-matched’ matching policy. To do so, we derive the stationary distribution under a remarkable product form, by using an original dynamic reversibility property related to that of Adan, Bušić, Mairesse, and Weiss (2018) for the bipartite matching model.

Low-altitude infrared small target detection based on fully convolutional regression network and graph matching

The high-precision infrared small target detection under low-altitude background has a high application value. The existing small IR target detection methods usually fail or cause a high probability of false alarm in the highly moving and complex low-altitude backgrounds. A detection method based on a fully convolutional network in spatial and graph matching in temporal is proposed. First, a deep fully convolution regression network for high-precision small target detection is designed to obtain accurate target probability heat maps. A weighted bipartite graph matching model is established for the target trajectory association based on the targets' temporal characteristics. It uses the motion and radiation similarity between the detection results in adjacent frames to eliminate false alarms caused by random noise and clutter. Finally, it further integrates the target optical flow information into the trajectory to distinguish between real targets and fixed ground objects. Many experimental results show that the method in this paper can accurately detect small targets in complex moving backgrounds and achieve a high detection rate in the case of a low false alarm rate.

FCFS parallel service systems and matching models

We consider three parallel service models in which customers of several types are served by several types of servers subject to a bipartite compatibility graph, and the service policy is first come first served. Two of the models have a fixed set of servers. The first is a queueing model in which arriving customers are assigned to the longest idling compatible server if available, or else queue up in a single queue, and servers that become available pick the longest waiting compatible customer, as studied by Adan and Weiss, 2014. The second is a redundancy service model where arriving customers split into copies that queue up at all the compatible servers, and are served in each queue on FCFS basis, and leave the system when the first copy completes service, as studied by Gardner et al., 2016. The third model is a matching queueing model with a random stream of arriving servers. Arriving customers queue in a single queue and arriving servers match with the first compatible customer and leave immediately with the customer, or they leave without a customer. The last model is relevant to organ transplants, to housing assignments, to adoptions and many other situations. We study the relations between these models, and show that they are closely related to the FCFS infinite bipartite matching model, in which two infinite sequences of customers and servers of several types are matched FCFS according to a bipartite compatibility graph, as studied by Adan et al., 2017. We also introduce a directed bipartite matching model in which we embed the queueing systems. This leads to a generalization of Burke’s theorem to parallel service systems.

Design heuristic for parallel many server systems

We study a parallel queueing system with multiple types of servers and customers. A bipartite graph describes which pairs of customer-server types are compatible. We consider the service policy that always assigns servers to the first, longest waiting compatible customer, and that always assigns customers to the longest idle compatible server if on arrival multiple compatible servers are available. For a general renewal stream of arriving customers, general service time distributions that depend both on customer and on server types, and general customer patience distributions, the behavior of such systems is very complicated. Key quantities for their performance are the matching rates, the fraction of services for each pair of compatible customer-server. Calculation of these matching rates in general is intractable, it depends on the entire shape of service time distributions. We suggest through a heuristic argument that if the number of servers becomes large, the matching rates are well approximated by matching rates calculated from the tractable bipartite infinite matching model. We present simulation evidence to support this heuristic argument, and show how this can be used to design systems with desired performance requirements.

Bipartite matching model with dynamic arrivals and departures

In this paper, we introduce a bipartite matching model for matching markets with dynamic arrivals and departures. Different from classical models with a finite-time horizon, our model has a long-time horizon with infinite vertices. In our model, the matching goal is to maximize the ratio of matched vertices, i.e., matched ratio. We define two types of online algorithms, i.e., Greedy and Patient, analyze their performance with evaluation metrics of both upper bounds and competitive ratios, and conduct extensive simulations to validate our analysis. To further simulate the real situation, we extend our model with the user’s strategic behavior and prove the existence of a specific Nash equilibrium under a differentiated matching mechanism.

Heterogeneous Spectrum Aggregation: Coexistence From a Queue Stability Perspective

Spectrum aggregation (SA) across heterogeneous channels, including both dedicated and shared channels, provides the potential for improving spectrum utilization and fulfilling the requirement of broadband services. Heterogeneous SA brings new technical challenges on multisystem coexistence on shared channels and the resource allocation over heterogeneous channels. In this paper, we develop an analytical framework for heterogeneous SA from a queue stability perspective. To make all systems on the shared channels stable, we design a resource allocation algorithm for the coexistence of multiple systems. Specifically, we derive the closed-form modified water-filling power control for the single-pair case by Lyapunov optimization and prove that it achieves the queue stability for all systems. Based on the results, we propose a low-complexity suboptimal resource allocation algorithm for multipair SA, which is a NP-hard problem. We partition user pairs into groups by using graph coloring and allocate the shared channels to pair groups according to the maximal weight bipartite matching model. The simulation results verify the queue stability and show that the proposed schemes outperform the conventional schemes.

Overlapping Coalition Formation Game for Resource Allocation in Network Coding Aided D2D Communications

Due to spectrum sharing, device-to-device (D2D) communications underlaying cellular networks enhance system capacity significantly that benefits services of local area. On the other hand, network coding enables highly efficient cooperation, which increases the system capacity through code-and-forward mechanism. It is a challenging problem that how to allocate resource in the network coding aided cooperative D2D communications. In this paper, we first design a network coding aided cooperative diversity scheme for D2D communication, and derive the system transmission rate with the consideration of interference. Then, we formulate the problem of joint spectrum resource allocation and relay selection as an overlapping coalition formation game, where one relay is able to serve multiple coalitions to increase the system capacity. For each coalition, maximum bipartite graph matching model is established to select the optimal relay to achieve the maximum transmission rate. Finally, to solve the formulated game problem, we propose a distributed algorithm based on switch operations with low computation complexity. Extensive numerical results demonstrate that our solution increases the system transmission rate by about 30-40 percent without bringing extra computation complexity, compared with other state-of-the-art schemes.

Analysis of ground state in random bipartite matching

Bipartite matching problems emerge in many human social phenomena. In this paper, we study the ground state of the Gale–Shapley model, which is the most popular bipartite matching model. We apply the Kuhn–Munkres algorithm to compute the numerical ground state of the model. For the first time, we obtain the number of blocking pairs which is a measure of the system instability. We also show that the number of blocking pairs formed by each person follows a geometric distribution. Furthermore, we study how the connectivity in the bipartite matching problems influences the instability of the ground state.

Stability of the Bipartite Matching Model

We consider the bipartite matching model of customers and servers introduced by Caldentey, Kaplan and Weiss (2009). Customers and servers play symmetrical roles. There are finite sets C and S of customer and server classes, respectively. Time is discrete and at each time step one customer and one server arrive in the system according to a joint probability measure μ on C× S, independently of the past. Also, at each time step, pairs of matched customers and servers, if they exist, depart from the system. Authorized matchings are given by a fixed bipartite graph (C, S, E⊂ C × S). A matching policy is chosen, which decides how to match when there are several possibilities. Customers/servers that cannot be matched are stored in a buffer. The evolution of the model can be described by a discrete-time Markov chain. We study its stability under various admissible matching policies, including ML (match the longest), MS (match the shortest), FIFO (match the oldest), RANDOM (match uniformly), and PRIORITY. There exist natural necessary conditions for stability (independent of the matching policy) defining the maximal possible stability region. For some bipartite graphs, we prove that the stability region is indeed maximal for any admissible matching policy. For the ML policy, we prove that the stability region is maximal for any bipartite graph. For the MS and PRIORITY policies, we exhibit a bipartite graph with a non-maximal stability region.

Stability of the Bipartite Matching Model

We consider the bipartite matching model of customers and servers introduced by Caldentey, Kaplan and Weiss (2009). Customers and servers play symmetrical roles. There are finite sets C and S of customer and server classes, respectively. Time is discrete and at each time step one customer and one server arrive in the system according to a joint probability measure μ on C× S, independently of the past. Also, at each time step, pairs of matched customers and servers, if they exist, depart from the system. Authorized matchings are given by a fixed bipartite graph (C, S, E⊂ C × S). A matching policy is chosen, which decides how to match when there are several possibilities. Customers/servers that cannot be matched are stored in a buffer. The evolution of the model can be described by a discrete-time Markov chain. We study its stability under various admissible matching policies, including ML (match the longest), MS (match the shortest), FIFO (match the oldest), RANDOM (match uniformly), and PRIORITY. There exist natural necessary conditions for stability (independent of the matching policy) defining the maximal possible stability region. For some bipartite graphs, we prove that the stability region is indeed maximal for any admissible matching policy. For the ML policy, we prove that the stability region is maximal for any bipartite graph. For the MS and PRIORITY policies, we exhibit a bipartite graph with a non-maximal stability region.

Stability of the bipartite matching model

We consider the bipartite matching model of customers and servers introduced by Caldentey, Kaplan, and Weiss (Adv. Appl. Probab., 2009). There is a finite set C , resp. S , of customer, resp. server, classes. Time is discrete and at each time step, one customer and one server arrive in the system according to a joint probability measure ¼ on C×S , independently of the past. Allowed matchings are given by a fixed bipartite graph ( C, S,E ? C × S ), and customers/servers that cannot be matched are stored in a buffer. In this paper, we study the stability of the associated discrete time Markov chain under various admissible matching policies including: ML (Match-the-Longest), MS (Match-the-Shortest), FIFO (match the oldest), priorities. For the ML policy, we prove via a Lyapunov function argument that the stability region is maximal for any bipartite graph. On the other hand, we exhibit a bipartite graph for which the MS and priority policies have non-maximal stability regions. Finally, we prove that the stability of the bipartite model is implied by the stability of the associate fluid limits, and use this result to establish maximal stability region for the FIFO matching policy.

Resource assignment in high school timetabling

This paper explores one aspect of the high school timetabling problem, namely the assignment of resources, such as teachers and rooms, to meetings after times are assigned. Several algorithms, with run times of just a few seconds, are presented and tested on real-world data. The best of these is currently in operation within KTS, a free, public web site for high school timetabling created by the author. A large bipartite matching model, called the global tixel matching, is used to preserve optimality of one key measure of quality as resource assignment proceeds.

Exact solution of the random bipartite matching model

In this paper we present the exact solution for the average minimum energy of the random bipartite matching model with an arbitrary finite number of elements where random paired interactions are described by independent exponential distribution. This solution confirms the Parisi conjecture proposed for this model earlier, as well as the result of the replica solution of this model in the thermodynamic limit.