network matrix

A Row-wise Algorithm for Graph Realization

  • Rolf van der Hulst
  • Matthias Walter
    • Categories (Mixed) Integer Linear Programming, Graphs and Matroids, Network Optimization Tags , , , , ,

    Given a \(\{0,1\}\)-matrix \(M\), the graph realization problem for \(M\) asks if there exists a spanning forest such that the columns of \(M\) are incidence vectors of paths in the forest. The problem is closely related to the recognition of network matrices, which are a large subclass of totally unimodular matrices and have many applications … Read more

    An exact approach to the problem of extracting an embedded network matrix

  • Cid C. de Souza
  • Martine LabbĂ©
  • R. M. V. Figueiredo
    • Categories Branch and Cut Algorithms, Network Optimization, Polyhedra Tags , , ,

    We study the problem of detecting a maximum embedded network submatrix in a {-1,0,+1}-matrix. Our aim is to solve the problem to optimality. We introduce a 0-1 integer linear formulation for this problem based on its representation over a signed graph. A polyhedral study is presented and a branch-and-cut algorithm is described for finding an … Read more