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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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4.1 ★★★★★
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★★★★★ 5
Excellent solution at a great price point!!
Color: Black, Size: 5.5x8.5, Color: Black, Size: 5.5x8.5
Just received, opened package, and this is exactly what was needed. It fits certificates, documents perfectly. Needed the 8.5x5.5 size to fit a certificate and in prior years I had to to modify the document to fit a 5x7 frame (had no idea there was the perfect size available) and it was very low cost and very well made! The black frame has a soft texture which I love, and the Plexiglas material is rigid and not easily broken. It has numerous hanging or standing options.
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Reviewed in the United States on May 30, 2026
★★★★★ 4
Beautiful Non-Glass Frame
Color: Bronze, Size: 12x16
Love this frame!! I'm so in love with the new type of frame backing this one had! I hate those frames that have those tiny thin metal tabs that stick out where you have to bend up/down to remove backing but not this one! It has these really easy to use metal springs that you push down & turn & it easy pops out! Wish frames all came w actual glass! I thought this one had glass but was wrong, it has the thin plexiglass type covering where you remove the clear stickers from front/back. It will work but because I have it used in a bathroom, I will need to get a glass replacement eventually. Love the gold color, it's a really pretty gold, not overly yellow. Overall, I think its a nice frame & such a great value.
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Reviewed in the United States on March 17, 2026
★★★★★ 5
Gorgeous Distressed Bronze Frame, Easy to Hang
Color: Bronze, Size: 18x24, Color: Bronze, Size: 18x24
This bronze frame looks really, really good—honestly, it passes for real bronze at a glance. It has a nice distressed finish that gives it some character without overdoing it.
It’s also surprisingly lightweight, which makes it much easier to hang on the wall. The overall build feels solid, and I don’t see any issues with it coming apart or feeling cheap.
I especially like the back—everything is well thought out, from the sawtooth hangers to the tabs that make it easy to open and insert your print.
I didn’t have my print yet to put in it, or I would’ve included a photo of it fully set up, but I added some pictures to show the detail and the back hardware.
Great-looking frame, well made, and easy to work with. Definitely happy with it.
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Reviewed in the United States on April 1, 2026
★★★★★ 5
Overall, they’re a great way to display memories and decorate any space
Color: Black, Size: 11x17
Love these frames, They are really good quality and feel sturdy, not cheap at all. They were very easy to set up and insert my pictures, which I really appreciate. The size is perfect for posters or photos, and they make everything look much more professional and elegant on the wall. I also like how they fit well with any home decor style
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Reviewed in the United States on April 21, 2026
★★★★★ 5
Nice Frames
Color: Black, Size: 8x10
I purchased two of these frames in black. I was pleasantly surprised at how nice they are given the price was so low. I removed the film on both sides of the plexiglass as instructed and it was crystal clear. These are not high quality frames if that's what you are looking for.....real wood or glass. However, they are awesome for the price and what I needed them for. I would purchase them again.
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Reviewed in the United States on April 19, 2026