Speeding up the hungarian algorithm

doi:10.1016/0305-0548(90)90031-2

Computers & Operations Research

Volume 17, Issue 1, 1990, Pages 95-96

https://doi.org/10.1016/0305-0548(90)90031-2 Get rights and content

Abstract

A simple modification to the “Hungarian” algorithm for the linear assignment problem reduces execution time by up to 90%.

References (5)

R. Jonker et al.
Improving the Hungarian assignment algorithm
Opl Res. Lett.
(1986)
H.W. Kuhn
The Hungarian method for the assignment problem
Naval Res. Logist. Q.
(1955)

There are more references available in the full text version of this article.

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Large field monitoring system of vehicle load on long-span bridge based on the fusion of multiple vision and WIM data
2023, Automation in Construction
Vehicle Load Monitoring (VLM) on entire long-span bridge decks presents significant challenges due to the spatial and temporal randomness of vehicles. Existing VLM systems often suffer from limited viewing coverage and poor continuity of multi-vehicle tracking methods. This paper proposes a VLM system consisting of multi-vision image pre-processing, modified YOLO-v4 model, kinematics-enhanced vehicle tracking algorithm, and data fusion method between vision and Weigh-In-Motion sub-systems. The system was tested on a long-span bridge using six cameras, achieving vehicle monitoring of entire deck. The precision of multi-vehicle tracking achieved 99.28% built upon YOLO-v4 model with 96.2% mean Average Precision (mAP). Comparative results demonstrate that the modified YOLO-v4 model outperforms state-of-the-art approaches, and our proposed tracking method surpasses other methods. Our proposed system offers a comprehensive solution for VLM on entire bridge deck, overcoming the limitations of existing methods. Future work could extend the system's capability to include complex traffic patterns.
Optimal waypoint assignment for designing drone light show formations
2022, Results in Control and Optimization
Citation Excerpt :
Researchers [15] have also proposed an efficient GPU-based parallel algorithm for the augmenting path search, which is the most time-intensive step of the Hungarian algorithm. Further, it has been found that a minor alteration in the matrix operation can help reduce the execution time of the classical Hungarian algorithm [16]. Authors from [17] have proposed an Accelerating Hungarian Algorithm, which results in creating more than one zeroes in a single iteration that helps in the faster execution of the code.
Advancements in technology and new drone policies have boosted the adoption of drones by various industries. With active research and development, ingenious applications using drones are being developed. One such innovative and creative application of swarm drones is the drone light show. Light shows are generally performed outdoors in a dedicated clear open air space, which attracts the usage of drones for the execution. A fleet of multiple UAVs illuminates the night sky with picturesque performances in a synchronized manner. Use of drones in light shows provides an eco-friendly and reusable alternative for unique ways of advertisements, celebrations, storytelling, and entertainment. To choreograph the performance of swarm drones means allocating waypoints to each drone for every formation and the complexity of designing increases with the number of drones. An intelligent optimal assignment system is much required to allocate waypoints to drones for each transition in order to create formations. We propose a static swarm-intelligence-based assignment approach named Constrained Hungarian Method for Swarm Drones Assignment (CHungSDA) for optimally assigning multi-UAVs to waypoints. This approach uses Hungarian algorithm as a base with added constraints specific to the targeted application. Several simulations of the proposed approach — carried out for different designs have shown promising results. The work will be of best reference to the UAV manufacturers for their functional design of UAVs and development of Ground Control Station Software to communicate with multiple UAVs, along with other companies that aim to create visual illustrations using UAVs.
The Stable Marriage Problem: An interdisciplinary review from the physicist's perspective
2021, Physics Reports
Citation Excerpt :
In the following paragraphs, we will see how the Hungarian method solves this problem. For completeness, it is worth knowing that there are several variations of the Hungarian algorithm and other more recently developed algorithms that solve the assignment problem, for example in [108–110]. As Kuhn himself wrote in [111], the idea of the Hungarian algorithm came to him while reading Konig’s book on graph theory in the summer of 1953.
We present a fascinating model that has lately caught attention among physicists working in complexity related fields. Though it originated from mathematics and later from economics, the model is very enlightening in many aspects that we shall highlight in this review. It is called The Stable Marriage Problem (though the marriage metaphor can be generalized to many other contexts), and it consists of matching men and women, considering preference-lists where individuals express their preference over the members of the opposite gender. This problem appeared for the first time in 1962 in the seminal paper of Gale and Shapley and has aroused interest in many fields of science, including economics, game theory, computer science, etc. Recently it has also attracted many physicists who, using the powerful tools of statistical mechanics, have also approached it as an optimization problem. Here we present a complete overview of the Stable Marriage Problem emphasizing its multidisciplinary aspect, and reviewing the key results in the disciplines that it has influenced most. We focus, in particular, in the old and recent results achieved by physicists, finally introducing two new promising models inspired by the philosophy of the Stable Marriage Problem. Moreover, we present an innovative reinterpretation of the problem, useful to highlight the revolutionary role of information in the contemporary economy.
Hungarian layer: A novel interpretable neural layer for paraphrase identification
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For the input sentences in Fig. 1, the weight between “Sunday” and “run” is lower than the weight between “yard” and “inside”, but the former weight cannot support the evidence for paraphrase/non-paraphrase, because the former two words that are most dissimilar in this case should not be compared inappropriately by alignment analysis. To extract the aligned unmatched parts, in this paper, we embed Hungarian algorithm (Wright, 1990) into neural architecture as Hungarian layer (Algorithm 2). Illustrated in Fig. 1, the alignment in sentence matching could be formulated as task-assignment problem, which can be tackled by Hungarian algorithm (Wright, 1990).
Paraphrase identification serves as an important topic in natural language processing while sequence alignment and matching underlie the principle of this task. Traditional alignment methods take advantage of attention mechanism. Attention mechanism, i.e. weighting technique, could pick out the most similar/dissimilar parts, but is weak in modeling the aligned unmatched parts, which are the crucial evidence to identify paraphrases. In this paper, we empower neural architecture with Hungarian algorithm to extract the aligned unmatched parts. Specifically, first, our model applies BiLSTM/BERT to encode the input sentences into hidden representations. Then, Hungarian layer leverages the hidden representations to extract the aligned unmatched parts. Last, we apply cosine similarity to metric the aligned unmatched parts for a final discrimination. Extensive experiments show that our model outperforms other baselines, substantially and significantly.
Seamless group target tracking using random finite sets
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Citation Excerpt :
The association result is obtained by finding the association matrix with lowest cost ℑ. This optimization problem can be solved by many optimal assignment algorithms [24,25]. In all time steps, only the association matrices with lowest costs are recorded and constitute the association history, and object trajectories are extracted from this best association history.
In many surveillance applications, target tracking algorithms have to deal with dense group targets in contrast to independently moving and well-separated targets as assumed in most scenarios. An effective strategy to handle such a group of targets is to first track the overall group and then attempt to extract the states of individual targets. Based on the Random Finite Set theory, the τ-Cardinalized Probability Hypothesis Density (τ-CPHD) filter is proposed in this paper as an effective method for group target tracking. This filter accurately extracts target states and represents the distribution of the legacy PHD. Association and track extraction are done in the post-processing step, without affecting the filtering process or overloading the computing resources. Furthermore, the group motion is modeled in conjunction with individual target motion models, with model proportion being updated by the proposed filter. Initialization process is carried out adaptively using the group motion trend through group state fitting. All these characteristics make the new filter flexible and seamlessly applicable to real-world tracking problems with group targets. Simulations demonstrate the superior performance of the proposed filter with individual target and group motion models being considered in combination or separately.

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^∗: M. B. Wright is a Lecturer in operational research at the University of Lancaster, England. Before that he was with the operational research group at the Headquarters of British Rail. His main research interests are the practical uses of heuristics and the application of OR to transport, health services and sport.

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Speeding up the hungarian algorithm

Abstract

Opl Res. Lett.

The Hungarian method for the assignment problem

Naval Res. Logist. Q.