M. Grotschel, M. Padberg (1979). On the symmetric traveling salesman problem I: Inequalities. Math. Program. 16, 265-280.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....facet de ning mod k cuts for the symmetric TSP. We rst address mod 2 cuts that can be obtained from (6) 8) A well known class of such cuts is that of comb inequalities, as introduced by Edmonds [14] in the context of matching theory, and extended by Chv atal [10] and by Gr otschel and Padberg [20, 21] for the TSP. Comb inequalities are de ned as follows; see Figure 3 for an illustration. We are given a handle set H V and t 3, t odd, tooth sets T 1 ; T t V such that T i H 6= and T i n H 6= hold for any i = 1; t. The comb inequality associated with H; T 1 ; T ....

M. Grotschel, M. Padberg (1979). On the symmetric traveling salesman problem I: Inequalities. Math. Program. 16, 265-280.

....s, of disjoint vertex sets T 1 ; T s , called teeth, each having one vertex in common with the handle H. The comb inequality is written as x(E(H) s X j=1 x(E(T j ) jHj s X j=1 (jT j j Gamma 1) Gamma 1 2 (s 1) 15) Chv atal s comb inequalities were generalized by Grotschel and Padberg (1979) who introduced structures where each tooth can have more than one vertex in common with the handle. The clique tree inequalities, introduced by Grotschel and Pulleyblank (1986) are further generalization of comb inequalities in the sense that clique trees contain multiple handles, which are ....

M. Gr otschel and M.W. Padberg (1979) "On the symmetric traveling salesman problem I: inequalities", Mathematical Programming 16 265--280.

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