In this paper, we present an analysis of the strength of sparse cutting-planes for mixed integer linear programs (MILP) with sparse formulations. We examine three kinds of problems: packing problems, covering problems, and more general MILPs with the only assumption that the objective function is non-negative. Given a MILP instance of one of these three types, assume that we decide on the suppo...

In this paper, we present an analysis of the strength of sparse cutting-planes for mixed integer linear programs (MILP) with sparse formulations. We examine three kinds of problems: packing problems, covering problems, and more general MILPs with the only assumption that the objective function is non-negative. Given a MILP instance of one of these three types, assume that we decide on the suppo...

Motivated by a VLSI masking problem, we explore partitions of an orthogonal polygon of n vertices into isothetic rectangles that maximize the shortest rectangle side over all rectangles. Thus no rectangle is “thin”; all rectangles are “fat.” We show that such partitions have a rich structure, more complex than what one might at first expect. For example, for partitions all “cuts” of which are a...

This paper describes an optimal method of inserting new frames or recovering missing frames in a video sequence. The method is based on an optimization scheme using graph-cuts that finds the ‘optimal’ frames to be inserted in between two given frames. The core problem is a typical visual correspondence problem between pixels in two or more frames and having formulated the appropriate energy, gr...

The problem of cutting a convex polygon P out of a planar piece of material Q (P is already drawn on Q) with minimum total cutting cost is a well studied problem in computational geometry that has been studied with several variations such as P and Q are convex or non-convex polygons, Q is a circle, and the cuts are line cuts or ray cuts. In this paper, we address this problem without the restri...

In this paper we propose practical strategies for generating split cuts, by considering integer linear combinations of the rows of the optimal simplex tableau, and deriving the corresponding Gomory mixed-integer cuts; potentially, we can generate a huge number of cuts. A key idea is to select subsets of variables, and cut deeply in the space of these variables. We show that variables with small...

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Di erent optimal structures: minimum cuts, minimum spanning forests and shortest-path forests, have been used as the basis for powerful image segmentation procedures. The well-known notion of watershed also falls into this category. In this paper, we present some new results about the links which exist between these di erent approaches. Especially, we show that min-cuts coincide with watersheds...

We propose the bound-optimal cutting plane method. It is a new paradigm for cutting plane generation in Mixed Integer Programming allowing for the simultaneous generation of k cuts which, when added to the current Linear Programming relaxation, yield the largest bound improvement. By Linear Programming duality arguments and standard linearization techniques we show that, for a large family of c...

In the multilevel generalized assignment problem (MGAP) agents can perform tasks at more than one efficiency level. Important manufacturing problems, such as lot sizing, can be easily formulated as MGAPs; however, the large number of variables in the related 01 integer program makes it hard to find optimal solutions to these problems, even when using powerful commercial optimization packages. T...