We apply theta body relaxations to the Ki-cover problem and show polynomial time solvability for certain classes of graphs. In particular, we give an effective relaxation where all Kip-hole facets are valid, and study its relation to an open question of Conforti et al. For the triangle free problem, we show for Kn that the theta body relaxations do not converge by (n−2)/4 steps; we also prove f...

We build on the work of Andelman & Mansour and Azar, Birnbaum, Karlin, Mathieu & Thach Nguyen to show that the fullinformation (i.e., offline) budgeted-allocation problem can be approximated to within 4/3: we conduct a rounding of the natural LP relaxation, for which our algorithm matches the known lower-bound on the integrality gap.

LP relaxation One way to deal with this is to relax the integrality constraints and allow xe ∈ [0, 1] to get a linear program, which can be solved in polynomial-time. However, this gives rise to fractional matchings. Characteristic vectors of matchings in G can be seen as points in R where m = |E|. The convex hull of all the matchings forms a polytope called the matching polytope M. However, th...

A defining stylized fact associated with exchange-rate-based stabilization programs is that their initial phase is characterized by several years of continuous expansion in private consumption and a gradual appreciation of the real exchange rate. This paper shows that a large class of standard optimizing models is unable to account for this empirical regularity. In particular, models in this cl...

A new method Is described for calculating bounds for a special class of 0-1 Integer programning problems. This met lod includes features of both Lagrangean and surrogate relaxation approaches. Certain binary knapsack calculations carried out in appropriate combinations together with an additivity principle provide the basis for computing the bounds.

We consider the problem to decompose a binary matrix into a small number of binary matrices whose 1-entries form a rectangle. We show that the linear relaxation of this problem has an optimal integral solution corresponding to a well known geometric result on the decomposition of rectilinear polygons. MSC: 90C27, 90C46

We propose a novel extended formulation for the line planning problem in public transport. It is based on a new concept of frequency configurations that account for all possible options to provide a required transportation capacity on an infrastructure edge. We show that this model yields a strong LP relaxation. It implies, in particular, general classes of facet defining inequalities for the s...

McCormick (Math Prog 10(1):147–175, 1976) provides the framework for convex/concave relaxations of factorable functions, via rules for the product of functions and compositions of the form F◦ f , where F is a univariate function. Herein, the composition theorem is generalized to allowmultivariate outer functions F , and theory for the propagation of subgradients is presented. The generalization...

The sensitivity of continuous-wave, non-linear EPR signals to spin–lattice (T1) relaxation has been investigated. The aim was to identify those spectral displays that are most appropriate to obtain structural and dynamic information from spin-label EPR experiments that involve detection of T1-relaxation enhancements. This has been achieved by solving the Bloch equations for the various harmonic...

We develop an algorithm for the linear ordering problem, which has a large number of applications such as triangulation of input-output matrices, minimizing total weighted completion time in one-machine scheduling, and aggregation of individual preferences. The algorithm is based on the Lagrangian relaxation of a binary integer linear programming formulation of the problem. Since the number of ...