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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Tropical Circuit Complexity: Limits of Pure Dynamic Programming

Tropical Circuit Complexity: Limits of Pure Dynamic Programming

Jukna, Stasys

Paperback

Series: Springerbriefs in Mathematics

General ComputersGeneral Mathematics

ISBN10: 3031423534
ISBN13: 9783031423536
Publisher: Springer Nature
Published: Nov 8 2023
Pages: 129
Weight: 0.45
Height: 0.30 Width: 6.14 Depth: 9.21
Language: English
This book presents an enticing introduction to tropical circuits and their use as a rigorous mathematical model for dynamic programming (DP), which is one of the most fundamental algorithmic paradigms for solving combinatorial, discrete optimization problems.
In DP, an optimization problem is broken up into smaller subproblems that are solved recursively. Many classical DP algorithms are pure in that they only use the basic (min, +) or (max, +) operations in their recursion equations. In tropical circuits, these operations are used as gates. Thanks to the rigorous combinatorial nature of tropical circuits, elements from the Boolean and arithmetic circuit complexity can be used to obtain lower bounds for tropical circuits, which play a crucial role in understanding the limitations and capabilities of these computational models. This book aims to offer a toolbox for proving lower bounds on the size of tropical circuits.

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