03711nam 22006735 450 991076028300332120240619172911.03-031-42354-210.1007/978-3-031-42354-3(MiAaPQ)EBC30870270(Au-PeEL)EBL30870270(DE-He213)978-3-031-42354-3(CKB)28781949800041(EXLCZ)992878194980004120231106d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierTropical Circuit Complexity Limits of Pure Dynamic Programming /by Stasys Jukna1st ed. 2023.Cham :Springer International Publishing :Imprint: Springer,2023.1 online resource (138 pages)SpringerBriefs in Mathematics,2191-8201Print version: Jukna, Stasys Tropical Circuit Complexity Cham : Springer International Publishing AG,c2023 9783031423536 Chapter. 1. Basics -- Chapter. 2. Combinatorial Bounds -- Chapter. 3. Rectangle Bounds -- Chapter. 4. Bounds for Approximating Circuits -- Chapter. 5. Tropical Branching Programs -- Chapter. 6. Extended Tropical Circuits.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. In this work, the reader will find lower-bound ideas and methods that have emerged in the last few years, with detailed proofs. Largely self-contained, this book is meant to be approachable by graduate students in mathematics and computer science with a special interest in circuit complexity.SpringerBriefs in Mathematics,2191-8201Discrete mathematicsComputational complexityMathematical optimizationComputer scienceMathematicsDiscrete MathematicsComputational ComplexityDiscrete OptimizationMathematical Applications in Computer ScienceOptimització matemàticathubComplexitat computacionalthubLlibres electrònicsthubDiscrete mathematics.Computational complexity.Mathematical optimization.Computer scienceMathematics.Discrete Mathematics.Computational Complexity.Discrete Optimization.Mathematical Applications in Computer Science.Optimització matemàticaComplexitat computacional511.1Jukna Stasys550822MiAaPQMiAaPQMiAaPQBOOK9910760283003321Tropical Circuit Complexity3598771UNINA