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Description
Partitions: Optimality & Clustering (V19)The need of optimal partition arises from many real world problems involving the distribution of limited resources to many users. The "clustering" problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting
The need of optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The "clustering" problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion.Many well-known practical problems of optimal partitions are dealt with. The authors show how they can be solved using the theory -- or why they cannot be. These problems include: allocation of components to maximize system reliability; experiment design to identify defectives; design of circuit card library and of blood analyzer lines; abstraction of finite state machines and assignment of cache items to pages; the division of property and partition bargaining as well as touching on those well-known research areas such as scheduling, inventory, nearest neighbor assignment, the traveling salesman problem, vehicle routing, and graph partitions. The authors elucidate why the last three problems cannot be solved in the context of the theory.Shipping Notes
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Product Reviews
★★★★★ 5
Balls
Size: Medium
My dog loves chasing these balls. He seems to love the squeak! They fit the chuck it stick perfectly, and are great replacements for the originals that came with the stick.
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Reviewed in the United States on February 7, 2026
★★★★★ 5
Nice set of balls
Size: Medium
The squeaker quickly became my dog’s favorite ball and has replaced the fuzzy tennis balls. My dog is a nonstop fetcher and these chuck it balls are durable and fun.
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Reviewed in the United States on January 9, 2026
★★★★★ 5
Perfect ball
Size: Medium
Our dog loves these!
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Reviewed in the United States on May 26, 2026
★★★★★ 4
Soild
Size: Medium
The orange and blue ball is perfect. Once start taken because the because the blue noisy one was a little to easy for my dog to start ripping pieces off. Will say most toys do not survive his chewing.
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Reviewed in the United States on January 24, 2026
★★★★★ 5
Aggressive chewer who loves fetch approved!!
Size: Medium, Size: Medium
I highly recommend the Chuck-It brand in general, especially for dogs with an aggressive bite. These balls are awesome and are the most durable balls I’ve bought for my 50 lbs lab mix. He has not been able to break one of them yet and we’ve had a few of the squeaky balls for months. They are a bit pricey but worth it.
The one in the pic has been used for months, lives outside and you can see it’s still in great shape.
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Reviewed in the United States on June 22, 2025
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