All 0-1 polytopes are traveling salesman polytopes

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:35839

Billera, L; Sarangarajan, A

We study the facial structure of two important permutation polytopes in R{sup n2}, the Birkhoff or assignment polytope B{sub n}, defined as the convex hull of all n {times} n permutation matrices, and the asymmetric traveling salesman polytope T{sub n}, defined as the convex hull of those n {times} n permutation matrices corresponding to n-cycles. Using an isomorphism between the face lattice of B{sub n} and the lattice of elementary bipartite graphs, we show, for example, that every pair of vertices of B{sub n} is contained in a cubical face, showing faces of B{sub n} to be fairly special 0-1 polytopes. On the other hand, we show that T{sub n} has every 0-1 d-polytope as a face, for d {approximately} log n, by showing that every 0-1 d-polytope is the asymmetric traveling salesman polytope of some directed graph with n nodes. The latter class of polytopes is shown to have maximum diameter [n/3].

• OSTI ID: 35839
• Report Number(s): CONF-9408161--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
COMPUTERIZED SIMULATION
OPTIMIZATION
VARIATIONAL METHODS