F. BARAHONA. On cuts and matchings in planar graphs. Math. Programming, 60(1, Ser. A):53-68, 1993. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Semidefinite Relaxations for Max-Cut - Laurent (2001) (2 citations) (Correct)
....relaxation Q t (MET(G) involves a large number of semidefinite constraints; precise definitions are given in section 2. Let En : fij j 1 i j ng denote the edge set of the complete graph Kn and let E denote the projection from R En onto R E . Obviously, CUT(G) E(CUT(Kn ) and Barahona [4] shows that MET(G) E(MET(Kn ) In the linear description of MET(G) it suffices to consider the circuit inequalities (4) for chordless circuits [6] therefore, MET(Kn ) is defined by the 4 Gamma n 3 Delta triangle inequalities: x ij x ik x jk Gamma1; x ij Gamma x ik Gamma x jk ....
F. Barahona. On cuts and matchings in planar graphs. Mathematical Programming, 60:53--68, 1993.
A Cutting Plane Algorithm for Large Scale Semidefinite Relaxations - Helmberg (2001) (1 citation) (Correct)
.... of the cut polytope for graphs not contractible to K 5 (the complete graph on 5 nodes) 33, 2] In a pure polyhedral setting, enlarging the number of cycles in a graph (and therefore the number of separable odd cycle inequalities) by adding edges with weight 0 does not improve the relaxation [3]. This is not true in combination with the semide nite relaxation (SMC) as has been observed on many examples. 3 Primal convergence of the spectral bundle method We rst introduce some basic objects and concepts that we will need throughout the next two sections. For a 0 let W = fX 0 : hI; ....
F. Barahona. On cuts and matchings in planar graphs. Math. Programming, 60:53-68, 1993.
Connections Between Semidefinite Relaxations of the.. - Laurent, Poljak, Rendl (1995) (15 citations) (Correct)
....indexed by the edge set of the complete graph K n . Thus CUT Sigma1 (K n ) MET Sigma1 (K n ) and E(K n ) contain the same information as CUT Sigma1 n Thetan , MET Sigma1 n Thetan and E n Thetan . An explicit description of MET Sigma1 (G) by linear inequalities can be found in [Bar93]. Namely, MET Sigma1 (G) fx 2 E j Gamma1 x e 1 for e 2 E; x(F ) Gamma x(C n F ) 2 Gamma jCj for F C; C cycle ; jF j oddg: On the other hand, a parametric description of E(G) is known for some classes of graphs including series parallel and chordal graphs [GJSW84, L94, BJL] ....
F. Barahona. On cuts and matchings in planar graphs. Mathematical Programming 60:53--68, 1993.
One-Third-Integrality in the Max-Cut Problem - Laurent, Poljak (Correct)
....(1) are for C chordless cycle of G and the nonredundant inequalities (2) are for the edges e that do not belong to any triangle of G. In particular, the polytope S(K n ) coincides with the metric polytope MP n . In fact, in general, the polytope S(G) is the projection of MP n on the space R E [3]. More precisely, the following can be easily checked. One third integrality in the max cut problem 5 Lemma 2.1 Let G = V; E) be a graph and let e be an edge of K(V ) which does not belong to G. Let G e denote the graph obtained by adding the edge e to G. i) If x 2 MP(V ) then the ....
F. Barahona. On cuts and matchings in planar graphs. Mathematical Programming, 60:53--68, 1993.
Geometry of Semide - Nite Max-Cut Relaxations (Correct)
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F. BARAHONA. On cuts and matchings in planar graphs. Math. Programming, 60(1, Ser. A):53-68, 1993.
Unknown - Strengthenedsemidefiniteprogramming.. (Correct)
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F. BARAHONA. On cuts and matchings in planar graphs. Math. Programming, 60(1, Ser. A):53--68, 1993.
Postman Problems on Mixed Graphs - Mart (2003) (Correct)
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F. Barahona. On cuts and matchings in planar graphs. Math. Programming, 60(1, Ser. A):53--68, 1993. 151
Semidefinite Relaxations for Max-Cut - Laurent (2002) (2 citations) (Correct)
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F. Barahona, On cuts and matchings in planar graphs. Mathematical Programming, 60:53-68, 1993.
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