Modeling and solving the endpoint cutting problem

2021 ◽  
Author(s):  
Daniel Cuellar‐Usaquén ◽  
Alejandro Palacio ◽  
Emilia Ospina ◽  
Marcelo Botero ◽  
David Álvarez‐Martínez
Keyword(s):  
Cutting Problem

scholarly journals Deterministic, Strategyproof, and Fair Cake Cutting

2017 ◽  
Author(s):  
Vijay Menon ◽  
Kate Larson
Keyword(s):  
Mechanism Design ◽  
Impossibility Result ◽  
Restricted Class ◽  
Piecewise Constant ◽  
Incentive Compatible ◽  
Negative Results ◽  
Cake Cutting ◽  
Design Perspective ◽  
A Minor ◽  
Cutting Problem

We study the classic cake cutting problem from a mechanism design perspective, in particular focusing on deterministic mechanisms that are strategyproof and fair. We begin by looking at mechanisms that are non-wasteful and primarily show that for even the restricted class of piecewise constant valuations there exists no direct-revelation mechanism that is strategyproof and even approximately proportional. Subsequently, we remove the non-wasteful constraint and show another impossibility result stating that there is no strategyproof and approximately proportional direct-revelation mechanism that outputs contiguous allocations, again, for even the restricted class of piecewise constant valuations. In addition to the above results, we also present some negative results when considering an approximate notion of strategyproofness, show a connection between direct-revelation mechanisms and mechanisms in the Robertson-Webb model when agents have piecewise constant valuations, and finally also present a (minor) modification to the well-known Even-Paz algorithm that has better incentive-compatible properties for the cases when there are two or three agents.

Precision Generating Cutting Research of Rectangle Spline Based on Parameters Superposition

2011 ◽  
Vol 411 ◽  
pp. 117-120
Author(s):  
Jian Jun Jia ◽  
Hong Xi Wang ◽  
Ling Wang
Keyword(s):  
Simulation Experiment ◽  
Cutting Parameters ◽  
Least Square ◽  
Fusion Method ◽  
Fusion Model ◽  
Design Efficiency ◽  
Least Square Fitting ◽  
Machining Errors ◽  
Spline Shaft ◽  
Cutting Problem

Aiming at the precision generating cutting problem of rectangle spline shaft, the multi-parameter fusion method to modified cutting edge of rectangle spline hob is presented. The method based on the analysis of workpiece machining errors to establish a fusion model about the rectangle spline hob cutting parameters and the rectangle spline shaft deformation quantity, the model can indicate the connection between rectangle spling hob theoretics profile and actual cutting profile, therefore, the rectangle spline hob’s profile is modified and to simulate by polynomials. The simulation experiment indicates that the method exact approximation the hob’s modified profile. Compare with the methods of the double-circular-arc and the least square fitting, the multi-parameter fusion method can enhance both design precision and design efficiency.

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