Abstract
Given an undirected graph G=(V,E;w,p), each edge e∈E has a weight w(e)∈R+ and a penalty p(e)∈R0+. We consider two types of restricted Chinese postman problems. The first problem is asked to find a tour C covering V, such that the value f(C)=w(C)+p(E∖C) is minimized. The second problem is asked to find a tour C covering V, such that the value h(C)=w(C)+pmax(E∖C) is minimized, where pmax(E∖C)=max{p(e)|e∈E∖C}. In the paper, we design some approximation algorithms to solve these problems.
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