A Study on the Mathematical Equivalence and $\varepsilon$-Relaxation of Auction Algorithm for PCB Design

PCB 설계를 위한 Auction 알고리즘의 수학적 등가와 $\varepsilon$-이완법에 관한 연구

Minimum-cost linear network flow problems could be transformed with equal to assignment problems. Traditional method to solve the linear network flow problems are improved source-cost by transform the simple cycle flow. Auction algorithm could be applied to same element using the initial target price and dispersion calculation. Also, each elements are obtained by $\varepsilon$-relaxation methods. In this paper we proposed; 1)minimum-cost flow problem, 2)minimum-cost flow problem by the mathematical equivalent and 3) extraction $\varepsilon$-relaxation & expand transfer problem with minimum-cost flow. It can be applicant to PCB design by above mentioned.