A linear integer minimization problem (IP) has the modiied integer roundup property (MIRUP) if the optimal value of any instance of IP is not greater than the optimal value of the corresponding LP relaxation problem rounded up plus one. The aim of this paper is to investigate numerically whether the MIRUP holds for the one-dimensional cutting stock problem. The computational experiments carried...

We propose heuristic and exact algorithms for the (periodic and non-periodic) train timetabling problem on a corridor that are based on the solution of the LP relaxation of an ILP formulation in which each variable corresponds to a full timetable for a train. This is in contrast with previous approaches to the same problem, which were based on ILP formulations in which each variable is associat...

We demonstrate that ` rounds of the Sherali-Adams hierarchy and 2` rounds of the Lovász-Schrijver hierarchy suffice to reduce the integrality gap of a natural LP relaxation for Directed Steiner Tree in `-layered graphs from Ω( √ k) to O(` · log k) where k is the number of terminals. This is an improvement over Rothvoss’ result that 2` rounds of the considerably stronger Lasserre SDP hierarchy r...

Semi-metric labeling is a special case of energy minimization for pairwise Markov random fields. The energy function consists of arbitrary unary potentials, and pairwise potentials that are proportional to a given semi-metric distance function over the label set. Popular methods for solving semi-metric labeling include (i) move-making algorithms, which iteratively solve a minimum st-cut problem...

Metric labeling is a special case of energy minimization for pairwise Markov random fields. The energy function consists of arbitrary unary potentials, and pairwise potentials that are proportional to a given metric distance function over the label set. Popular methods for solving metric labeling include (i) move-making algorithms, which iteratively solve a minimum st-cut problem; and (ii) the ...

The global routing problem is becoming more and more important in the design of today's integrated circuits. A small chip may contain up to millions of components and wires. Although global routing can be formulated as an integer linear programming problem, it is hard to solve directly using currently available solvers. We discuss a relaxation of the problem to a linear programming (LP) formula...

An important subclass of the min-sum labeling problem (also known as discrete energy minimization or valued constraint satisfaction) is the pairwise min-sum problem with arbitrary unary costs and attractive Potts pairwise costs (also known as the uniform metric labeling problem). In analogy with our recent result, we show that solving the LP relaxation of the Potts min-sum problem is not signif...

Gomory mixed-integer (GMI) cuts are among the most effective cutting planes for general mixed-integer programs (MIP). They are traditionally generated from an optimal basis of a linear programming (LP) relaxation of a MIP. In this paper we propose a heuristic to generate useful GMI cuts from additional bases of the initial LP relaxation. The cuts we generate have rank one, i.e., they do not use...

We describe a model for multi-target tracking based on associating collections of candidate detections across frames of a video. In order to model pairwise interactions between different tracks, such as suppression of overlapping tracks and contextual cues about co-occurence of different objects, we augment a standard min-cost flow objective with quadratic terms between detection variables. We ...

This paper investigates the Steiner Tree Problem with Delays (STPD), a variation of the classical Steiner Tree problem that arises in multicast routing. We present a polynomial-size formulation for this challenging NP-hard problem. The LP relaxation of this formulation is enhanced through the derivation of new lifted Miller-Tucker-Zemlin subtour elimination constraints. Furthermore, we present ...