In each step of the cup game on n cups, a filler distributes up to 1" water among the cups, and then an emptier removes 1 unit of water from a single cup. The emptier’s goal is to minimize the height of the fullest cup, also known as the backlog. The cup emptying game has found extensive applications to processor scheduling, network- switch buffer management, quality of service guarantees, and data- structure deamortization. The greedy emptying algorithm (i.e., always remove from the fullest cup) is known to achieve backlog O(log n) and to be the optimal deterministic algorithm. Randomized algorithms can do significantly better, achieving backlog O(log log n) with high probability, as long as " is not too small. In order to achieve these improvements, the known randomized algorithms require that the filler is an oblivious adversary, unaware of which cups the emptier chooses to empty out of at each step. Such randomized guarantees are known to be impossible against fully adaptive fillers. We show that, even when the filler is just slightly non- adaptive, randomized emptying algorithms can still guarantee a backlog of O(log log n). In particular, we give randomized ran- domized algorithms against an elevated adaptive filler, which is an adaptive filler that can see the precise fills of every cup containing more than 3 units of water, but not of the cups containing less than 3 units. 
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                            Automated Handling and Feeding Techniques for Skewering Operations
                        
                    
    
            Barbecue kebab skewers typically consist of various meat choices, including chicken, lamb, pork, or seafood, and vegetables such as onion and pepper. Traditionally, manual kebab-making is a time-consuming and labor-intensive process, which is considered to be replaced by semi-auto and full-auto skewering machines. Currently, semi-auto skewering machines still require two main manual preparation processes: align the small meat and vegetable pieces into lines for skewering operations; superpose the large pieces of meat and vegetables, then do skewering and cutting operations. Fully automated skewering machines also have two different strategies. The first one is to use rotating scrappers and cups with a respective depth to ensure only one item can be loaded into each cup. All the cups are arranged into sequential cup rows and cup lines for skewering operations. However, the cups are frequently left empty because the rotating scrapper design often blocks any items falling into cups. Thus, some processing facilities still need extra labor to manually fill these empty cups. Another solution is the pick-and-place method by using robot arms and real-time image processing equipment, which cannot process irregular food pieces, such as shrimps (C-shape). In this paper, a novel fully automated handling and feeding system has been developed to prepare and connect the skewering operations to establish unattended kebab production lines. The performances of singulation, handling, and feeding operations have been investigated with different parameter settings and food items. Besides, the presented machine system is the first realization of unattended kebab production lines to process shrimps (C-shape), and the first design of using horizontal skewering operation to produce meat and vegetable kebabs (cube+ square piece) and shrimp and vegetable kebabs (C-shape+ square piece). This study will be beneficial for developing more effective next-generation skewering technologies and better value-added meat and seafood products. 
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                            - Award ID(s):
- 2431189
- PAR ID:
- 10625021
- Publisher / Repository:
- American Society of Agricultural and Biological Engineers
- Date Published:
- Journal Name:
- Journal of the ASABE
- Volume:
- 67
- Issue:
- 5
- ISSN:
- 2769-3295
- Page Range / eLocation ID:
- 1181 to 1190
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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