algorithm of task assignment

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Hungarian Algorithm for Assignment Problem | Set 1 (Introduction)

• For each row of the matrix, find the smallest element and subtract it from every element in its row.
• Do the same (as step 1) for all columns.
• Cover all zeros in the matrix using minimum number of horizontal and vertical lines.
• Test for Optimality: If the minimum number of covering lines is n, an optimal assignment is possible and we are finished. Else if lines are lesser than n, we haven’t found the optimal assignment, and must proceed to step 5.
• Determine the smallest entry not covered by any line. Subtract this entry from each uncovered row, and then add it to each covered column. Return to step 3.

Try it before moving to see the solution

Explanation for above simple example:

  An example that doesn’t lead to optimal value in first attempt: In the above example, the first check for optimality did give us solution. What if we the number covering lines is less than n.

Time complexity : O(n^3), where n is the number of workers and jobs. This is because the algorithm implements the Hungarian algorithm, which is known to have a time complexity of O(n^3).

Space complexity :   O(n^2), where n is the number of workers and jobs. This is because the algorithm uses a 2D cost matrix of size n x n to store the costs of assigning each worker to a job, and additional arrays of size n to store the labels, matches, and auxiliary information needed for the algorithm.

In the next post, we will be discussing implementation of the above algorithm. The implementation requires more steps as we need to find minimum number of lines to cover all 0’s using a program. References: http://www.math.harvard.edu/archive/20_spring_05/handouts/assignment_overheads.pdf https://www.youtube.com/watch?v=dQDZNHwuuOY

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An adaptive distributed auction algorithm and its application to multi-AUV task assignment

• Published: 18 April 2023
• Volume 66 , pages 1235–1244, ( 2023 )

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• Yu Wang 1 ,
• HuiPing Li 1 &
• Yao Yao 2  

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The task assignment of multi-agent system has attracted considerable attention; however, the contradiction between computational complexity and assigning performance remains to be resolved. In this paper, a novel consensus-based adaptive optimization auction (CAOA) algorithm is proposed to greatly reduce the computation load while attaining enhanced system payoff. A new optimization scheme is designed to optimize the critical control parameter in the price update role of auction algorithm which can reduce the searching complexity in obtaining a better bidding price. With this new scheme, the CAOA algorithm is designed. Then the developed algorithm is applied to the multi-AUV task assignment problem for underwater detection mission in complex environments. The simulation and comparison studies verify the effectiveness and advantage of the CAOA algorithm.

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School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an, 710072, China

Yu Wang & HuiPing Li

Jiangsu Automation Research Institute, Lianyungang, 222061, China

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 62273281, U22B2039, and 61922068) .

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Wang, Y., Li, H. & Yao, Y. An adaptive distributed auction algorithm and its application to multi-AUV task assignment. Sci. China Technol. Sci. 66 , 1235–1244 (2023). https://doi.org/10.1007/s11431-022-2302-6

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Received : 08 October 2022

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Published : 18 April 2023

Issue Date : May 2023

DOI : https://doi.org/10.1007/s11431-022-2302-6

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New algorithm unlocks high-resolution insights for computer vision

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Imagine yourself glancing at a busy street for a few moments, then trying to sketch the scene you saw from memory. Most people could draw the rough positions of the major objects like cars, people, and crosswalks, but almost no one can draw every detail with pixel-perfect accuracy. The same is true for most modern computer vision algorithms: They are fantastic at capturing high-level details of a scene, but they lose fine-grained details as they process information.

Now, MIT researchers have created a system called “ FeatUp ” that lets algorithms capture all of the high- and low-level details of a scene at the same time — almost like Lasik eye surgery for computer vision.

When computers learn to “see” from looking at images and videos, they build up “ideas” of what's in a scene through something called “features.” To create these features, deep networks and visual foundation models break down images into a grid of tiny squares and process these squares as a group to determine what's going on in a photo. Each tiny square is usually made up of anywhere from 16 to 32 pixels, so the resolution of these algorithms is dramatically smaller than the images they work with. In trying to summarize and understand photos, algorithms lose a ton of pixel clarity. 

The FeatUp algorithm can stop this loss of information and boost the resolution of any deep network without compromising on speed or quality. This allows researchers to quickly and easily improve the resolution of any new or existing algorithm. For example, imagine trying to interpret the predictions of a lung cancer detection algorithm with the goal of localizing the tumor. Applying FeatUp before interpreting the algorithm using a method like class activation maps (CAM) can yield a dramatically more detailed (16-32x) view of where the tumor might be located according to the model.

FeatUp not only helps practitioners understand their models, but also can improve a panoply of different tasks like object detection, semantic segmentation (assigning labels to pixels in an image with object labels), and depth estimation. It achieves this by providing more accurate, high-resolution features, which are crucial for building vision applications ranging from autonomous driving to medical imaging.

“The essence of all computer vision lies in these deep, intelligent features that emerge from the depths of deep learning architectures. The big challenge of modern algorithms is that they reduce large images to  very small grids of 'smart' features, gaining intelligent insights but losing the finer details,” says Mark Hamilton, an MIT PhD student in electrical engineering and computer science, MIT Computer Science and Artificial Intelligence Laboratory (CSAIL) affiliate, and a co-lead author on a paper about the project. “FeatUp helps enable the best of both worlds: highly intelligent representations with the original image’s resolution. These high-resolution features significantly boost performance across a spectrum of computer vision tasks, from enhancing object detection and improving depth prediction to providing a deeper understanding of your network's decision-making process through high-resolution analysis.” 

Resolution renaissance 

As these large AI models become more and more prevalent, there’s an increasing need to explain what they’re doing, what they’re looking at, and what they’re thinking. 

But how exactly can FeatUp discover these fine-grained details? Curiously, the secret lies in wiggling and jiggling images. 

In particular, FeatUp applies minor adjustments (like moving the image a few pixels to the left or right) and watches how an algorithm responds to these slight movements of the image. This results in hundreds of deep-feature maps that are all slightly different, which can be combined into a single crisp, high-resolution, set of deep features. “We imagine that some high-resolution features exist, and that when we wiggle them and blur them, they will match all of the original, lower-resolution features from the wiggled images. Our goal is to learn how to refine the low-resolution features into high-resolution features using this 'game' that lets us know how well we are doing,” says Hamilton. This methodology is analogous to how algorithms can create a 3D model from multiple 2D images by ensuring that the predicted 3D object matches all of the 2D photos used to create it. In FeatUp’s case, they predict a high-resolution feature map that’s consistent with all of the low-resolution feature maps formed by jittering the original image.

The team notes that standard tools available in PyTorch were insufficient for their needs, and introduced a new type of deep network layer in their quest for a speedy and efficient solution. Their custom layer, a special joint bilateral upsampling operation, was over 100 times more efficient than a naive implementation in PyTorch. The team also showed this new layer could improve a wide variety of different algorithms including semantic segmentation and depth prediction. This layer improved the network’s ability to process and understand high-resolution details, giving any algorithm that used it a substantial performance boost. 

“Another application is something called small object retrieval, where our algorithm allows for precise localization of objects. For example, even in cluttered road scenes algorithms enriched with FeatUp can see tiny objects like traffic cones, reflectors, lights, and potholes where their low-resolution cousins fail. This demonstrates its capability to enhance coarse features into finely detailed signals,” says Stephanie Fu ’22, MNG ’23, a PhD student at the University of California at Berkeley and another co-lead author on the new FeatUp paper. “This is especially critical for time-sensitive tasks, like pinpointing a traffic sign on a cluttered expressway in a driverless car. This can not only improve the accuracy of such tasks by turning broad guesses into exact localizations, but might also make these systems more reliable, interpretable, and trustworthy.”

Regarding future aspirations, the team emphasizes FeatUp’s potential widespread adoption within the research community and beyond, akin to data augmentation practices. “The goal is to make this method a fundamental tool in deep learning, enriching models to perceive the world in greater detail without the computational inefficiency of traditional high-resolution processing,” says Fu.

“FeatUp represents a wonderful advance towards making visual representations really useful, by producing them at full image resolutions,” says Cornell University computer science professor Noah Snavely, who was not involved in the research. “Learned visual representations have become really good in the last few years, but they are almost always produced at very low resolution — you might put in a nice full-resolution photo, and get back a tiny, postage stamp-sized grid of features. That’s a problem if you want to use those features in applications that produce full-resolution outputs. FeatUp solves this problem in a creative way by combining classic ideas in super-resolution with modern learning approaches, leading to beautiful, high-resolution feature maps.”

“We hope this simple idea can have broad application. It provides high-resolution versions of image analytics that we’d thought before could only be low-resolution,” says senior author William T. Freeman, an MIT professor of electrical engineering and computer science professor and CSAIL member. Lead authors Fu and Hamilton are accompanied by MIT PhD students Laura Brandt SM ’21 and Axel Feldmann SM ’21, as well as Zhoutong Zhang SM ’21, PhD ’22, all current or former affiliates of MIT CSAIL. Their research is supported, in part, by a National Science Foundation Graduate Research Fellowship , by the National Science Foundation and Office of the Director of National Intelligence, by the U.S. Air Force Research Laboratory, and by the U.S. Air Force Artificial Intelligence Accelerator. The group will present their work in May at the International Conference on Learning Representations.

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• FeatUp project page
• William Freeman
• Mark Hamilton
• Computer Science and Artificial Intelligence Laboratory (CSAIL)
• Department of Electrical Engineering and Computer Science

Related Topics

• Computer vision
• Artificial intelligence
• Computer science and technology
• Electrical Engineering & Computer Science (eecs)
• National Science Foundation (NSF)

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