We present a method for finding exact solutions of Max-Cut, the problem of finding a cut of maximum weight in a weighted graph. We use a Branch-and-Bound setting, that applies a dynamic version of the bundle method as bounding procedure. This approach uses Lagrangian duality to obtain a “nearly optimal” solution of the basic semidefinite Max-Cut relaxation, strengthened by triangle inequalities...

The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of graph cuts include community detection and computer vision. However, cut problems were originally proposed for static graphs, an assumption that does not hold ...

We describe an annealing procedure that computes the normalized N-cut of a weighted graph G. The first phase transition computes the solution of the approximate normalized 2-cut problem, while the low temperature solution computes the normalized N-cut. The intermediate solutions provide a sequence of refinements of the 2-cut that can be used to split the data to K clusters with 2 </= K </= N. T...

We propose a fixed-parameter tractable algorithm for the Max-Cut problem on embedded 1-planar graphs parametrized by the crossing number k of the given embedding. A graph is called 1-planar if it can be drawn in the plane with at most one crossing per edge. Our algorithm recursively reduces a 1-planar graph to at most 3 planar graphs, using edge removal and node contraction. The Max-Cut problem...

We introduce a generalized cake-cutting problem in which we seek to divide multiple cakes so that two players may get their most-preferred piece selections: a choice of one piece from each cake, allowing for the possibility of linked preferences over the cakes. For two players, we show that disjoint envy-free piece selections may not exist for two cakes cut into two pieces each, and they may no...

We propose two new dependent randomized rounding algorithms for approximating the global maximum of a quadratic program subject to linear as well as boolean constraints. We show that the rst of these methods based on the multivariate normal distribution, provides (a) a 0.878 approximation algorithm for s ?t max-cut problems, (b) a 0.878 approximation algorithm for the max-cut problem that has t...

In this paper, design issues for the authoring system of SMIL-based multimedia presentations are discussed and the solutions to these issues are presented. The proposed authoring system accepts the SMIL file as the input and provides useful editing functions, such as clear, cut, copy, and paste. The editing result of the presentation is finally saved in the SMIL format. For the input of a SMIL ...

In this paper we present a mathematical programming approach to tighten a Big-M formulation (PM ) of a Mixed Integer Problem with Logical Implications (P ). If M0 is a valid vector (the optimal solutions of P belong to the feasible solutions set of PM0) our procedures find a valid vector M such that M ≤ M0. As a consequence, the upper bounds generated by using the linear relaxations of PM are s...

In this paper we consider the multiple knapsack problem which is deened as follows: given a set N of items with weights f i , i 2 N, a set M of knapsacks with capacities F k , k 2 M, and a proot function c ik ; i 2 N; k 2 M; nd an assignment of a subset of the set of items to the set of knapsacks that yields maximum proot (or minimum cost). With every instance of this problem we associate a pol...

DuctTake is a system designed to enable practical compositing of multiple takes of a scene into a single video. Current industry solutions are based around object segmentation, a hard problem that requires extensive manual input and cleanup, making compositing an expensive part of the film-making process. Our method instead composites shots together by finding optimal spatiotemporal seams using...