• Publications
  • Influence
The boolean quadric polytope: Some characteristics, facets and relatives
  • M. Padberg
  • Mathematics, Computer Science
  • Math. Program.
  • 1 August 1989
TLDR
We study unconstrained quadratic zero–one programming problems havingn variables from a polyhedral point of view by considering the Boolean quadric polytope QPn inn(n+1)/2 dimensions that results from the linearization of the quadRatic form. Expand
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  • 64
On the facial structure of set packing polyhedra
  • M. Padberg
  • Mathematics, Computer Science
  • Math. Program.
  • 1 December 1973
TLDR
In this paper we address ourselves to identifying facets of the set packing polyhedron, i.e., of the convex hull of integer solutions to the set covering problem with equality constraints and/or constraints of the form "⩽". Expand
  • 598
  • 48
A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems
TLDR
An algorithm is described for solving large-scale instances of the Symmetric Traveling Salesman Problem (STSP) to optimality by exploiting a subset of the system of linear inequalities defining the convex hull of the incidence vectors. Expand
  • 988
  • 38
  • PDF
Set Partitioning: A survey
This paper discusses the set partitioning or equality-constrained set covering problem. It is a survey of theoretical results and solution methods for this problem, and while we have tried not toExpand
  • 442
  • 37
Solving airline crew scheduling problems by branch-and-cut
The crew scheduling problem is one that has been studied almost continually for the past 40 years but all prior approaches have always approximated the problem of finding an optimal schedule for evenExpand
  • 554
  • 34
Odd Minimum Cut-Sets and b-Matchings
TLDR
We show that the determination of a minimum cut-set of odd cardinality in a graph with even and odd vertices can be dealt with by a minor modification of the polynomially bounded algorithm of Gomory and Hu for multi-terminal networks. Expand
  • 407
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Solving Large-Scale Zero-One Linear Programming Problems
TLDR
A combination of problem preprocessing, cutting planes, and clever branch-and-bound techniques permit the optimization of sparse large-scale zero-one linear programming problems, even those with no apparent special structure, in reasonable computation times. Expand
  • 650
  • 30
Valid Linear Inequalities for Fixed Charge Problems
TLDR
In this paper, we propose to study mixed problems from a mathematical point of view that is similar in spirit to recent research on purely combinatorial problems that has investigated systems of defining linear inequalities or facets of the underlying polytope. Expand
  • 252
  • 19
On the Set-Covering Problem
TLDR
This paper establishes some useful properties of the equality-constrained set-covering problem P and the associated linear program P′. Expand
  • 191
  • 19
Facet identification for the symmetric traveling salesman polytope
TLDR
We give exact procedures for the identification of facet inducing inequalities for the symmetric traveling salesman polytope, based on the Gomory—Hu and Padberg—Rao algorithms. Expand
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