Skip to main content
SpringerLink
Log in

Some properties of cliques in 0–1 mixed integer programs

  • Published:
Top Aims and scope Submit manuscript

Summary

In this note we present new properties of cliques induced constraints straintsX(C +r )-X(C -r ) ≤ 1 - |C -r | for λ εS, whereS is the set of cliques that are implied by 0–1 mixed integer programs. These properties allow to further fixing of 0–1 variables, to detect instance's infeasibility and to imply new cliques.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Brearley, A.L., G. Mitra and H.P. Williams (1975). Analysis of mathematical programming problems prior to applying the simplex algorithms,Mathematical Programming 8, 54–83.

    Article  Google Scholar 

  • Crowder, H., E.L. Johnson and M.W. Padberg (1983). Solving large-scale programming problems,Operations Research 31, 803–834.

    Google Scholar 

  • Dietrich, B.L., L.F. Escudero and F. Chance (1993). Efficient reformulation for 0–1 programs, methods and computational results,Discrete Applied Mathematics 42, 147–175.

    Article  Google Scholar 

  • Dietrich, B.L., L.F. Escudero, A. Garín and G. Pérez (1993).O(n) procedures for identifying maximal cliques and non-dominated extensions of consecutime minimal covers and alternates,TOP 1, 139–160.

    Article  Google Scholar 

  • Guignard, M. and K. Spielberg (1981). Logical reduction methods in zero-one programming (minimal preferred variables).Operations Research 29, 49–74.

    Article  Google Scholar 

  • Hoffman, K.L. and M.W. Padberg (1984). LP-based combinatorial problem solving,Annals of Operations Research 4, 145–194.

    Article  Google Scholar 

  • Hoffman, K.L. and M.W. Padberg (1984). Improving LP representations of zero-one linear programs for branch-and-cut,ORSA Journal on Computing 3, 421–434.

    Google Scholar 

  • Johnson, E.L. and M.W. Padberg (1992). Degree-two inequalities, clique facets and biperfect graphs.Annals of Discrete Mathematics 16, 169–187.

    Google Scholar 

  • Nemhauser, G.L., M.W.P. Savelsbergh and G.C. Sigismondi (1994). MINTO, a Mixed INTeger Optimizer,Operational Research Letters 15, 47–58.

    Article  Google Scholar 

  • Nemhauser, G.L., and L.A. Wolsey (1988).Integer and combinatorial optimization, John Wiley, N.Y.

    Google Scholar 

  • Padberg, M.W. (1973). On the facial structure of set packing polyhedra,Mathematical Programming 5, 199–215.

    Article  Google Scholar 

  • Padberg, M.W. and G. Rinaldi (1991). A branch-and-cut algorithm for the resolution of large scale symmetric travelling salesman problems,SIAM Review 33, 60–100.

    Article  Google Scholar 

  • Savelsbergh, M.W.P. (1994). Preprocessing and probing techniques for mixed integer programming problems.ORSA Journal on Computing 6, 445–454.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Iberdrola Ingeniería y Consultoría, and Dpto. de Estadística e I.O., Universidad Complutense, Madrid, Spain

    L. F. Escudero

  2. Dpto. Economía Aplicada III Fac. CC.EE. y Empresariales, Universidad del País Vasco, Bilbao, Spain

    A. Garín

  3. Dpto. Matemática Aplicada, Estadística e I.O. Fac. de Ciencias, Universidad del País Vasco, Bilbao, Spain

    G. Pérez

Authors
  1. L. F. Escudero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Garín
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Pérez
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Escudero, L.F., Garín, A. & Pérez, G. Some properties of cliques in 0–1 mixed integer programs. Top 4, 215–223 (1996). https://doi.org/10.1007/BF02568509

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02568509

Keywords

Search

Navigation