In the context of branch-and-bound (B&B) for integer programming (IP) problems, a direction along which the polyhedron of the IP has minimum width is termed a thin direction. We demonstrate that a thin direction need not always be a good direction to branch on for solving the problem efficiently. Further, the integer width, which is the number of B&B nodes created when branching on the directio...

In this paper, we consider the two-dimensional rectangular strip packing problem, in the case where there is a perfect packing; that is, there is no wasted space. One can think of the problem as a jigsaw puzzle with oriented rectangular pieces. Although this comprises a quite special case for strip packing, we have found it useful as a subroutine in related work. We demonstrate a simple pruning...

Let V be a smooth complex projective 3-fold of general type with χ(ωV ) ≥ 0. We prove that the m-canonical map Φ|mKV | is birational onto its image for all m ≥ 14. Known examples show that the numerical bound r3 = 14 is optimal.

We describe three combinatorial branch-and-bound solvers for the maximum weight independent set problem. All use weighted clique covers to generate upper bounds, and all branch according to the method of Balas and Yu (1986). One extends and speeds up the method of Babel (1994). A second one employs a modified method from Balas and Yu (1986) to produce clique covers that share structural similar...

A fundamental challenge associated with research or new product development projects is identifying that innovative activity that will deliver success. In such projects, it is typically the case that innovative breakthroughs can be achieved by any of several possible alternative technologies, some of which may fail due to the technological risks involved. In some cases, the project payoff is ob...

State-of-the-art solvers for Constraint Satisfaction Problems (CSP), Mixed Integer Programs (MIP), and satisfiability problems (SAT) are usually based on a branch-and-bound algorithm. The question how to split a problem into subproblems (branching) is in the core of any branch-and-bound algorithm. Branching on individual variables is very common in CSP, MIP, and SAT. The rules, however, which v...

Metric constraints are known to be highly discriminative for many objects, but if training is limited to data captured from a particular 3-D sensor the quantity of training data may be severly limited. In this paper, we show how a crucial aspect of 3-D information–object and feature absolute size–can be added to models learned from commonly available online imagery, without use of any 3-D sensi...

We propose two exact approaches for non-convex quadratic integer minimization subject to linear constraints where lower bounds are computed by considering ellipsoidal relaxations of the feasible set. In the first approach, we intersect the ellipsoids with the feasible linear subspace. In the second approach we penalize exactly the linear constraints. We investigate the connection between both a...

This article begins with a review of previously proposed integer formulations for the maximum diversity problem (MDP). This problem consists of selecting a subset of elements from a larger set in such a way that the sum of the distances between the chosen elements is maximized. We propose a branch and bound algorithm and develop several upper bounds on the objective function values of partial s...