This paper presents some strong valid inequalities for the Maximum Common Induced Subgraph Problem (MCIS) and the proofs that the inequalities are facet-defining under certain conditions. TheMCIS is an NP-hard problem and, therefore, no polynomial time algorithm is known to solve it. In this context, the study of its polytope can help in the development of more efficient branch-and-bound and br...

It is proved that there exist encoding schemes which are arbitrarily as efficient as the binary encoding (in terms of compactness and arithmetic operations), with respect to which Khachiyan's algorithm for Linear Programming is exponential. This constitutes an objection to the standard translation of problems into languages via the binary encoding. When we speak about the complexity of a proble...

Let TP f(x) = ∫ e K(y)f(x − y) dy, where K(y) is a smooth Calderón–Zygmund kernel on R, and P be a polynomial. We show that there is a sparse bound for the bilinear form 〈TP f, g〉. This in turn easily implies Ap inequalities. The method of proof is applied in a random discrete setting, yielding the first weighted inequalities for operators defined on sparse sets of integers.

Let x1 and xk be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree k. We shall establish sharp inequalities of the form x1 < A, xk > B, which are uniform in all the parameters involved. Together with inequalities in the opposite direction, recently obtained by the author, this locates the extreme zeros of classical orthogonal polynomials with the relative precision,...

We extend the work of Letchford [Letchford, A. N. 2000. Separating a superclass of comb inequalities in planar graphs. Math. Oper. Res. 25 443–454] by introducing a new class of valid inequalities for the traveling salesman problem, called the generalized domino-parity (GDP) constraints. Just as Letchford’s domino-parity constraints generalize comb inequalities, GDP constraints generalize the m...