On the symmetric circuit polytope
Given an undirected graph G = (V,e) and a cost vector c {element_of} R{sup E}, the weighted girth problem is to find a circuit, i.e. simple cycle, in G having minimum total cost. Since the traveling salesman problem can be reduced to it, this problem is in general NP-hard. We consider the case where G is the complete graph K{sub n} and investigate the facial structure of the circuit polytope P{sub C}{sup n}, which is the convex hull of the incidence vectors of circuits of K{sub n}. We introduce several new classes of facets, partly obtained from the traveling salesman polyhedron, and give some separation routines. Moreover, we shown how the results on P{sub C}{sup n} can be transferred to the case where we restrict to circuits of length at most k < n.
- OSTI ID:
- 35814
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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