We consider the problem of finding a maximum k-regular induced subgraph of a graph G. Theoretical results are established to compare upper bounds obtained from different techniques, including bounds from quadratic programming, Lagrangian relaxation and integer programming. This general problem includes well-known subproblems as particular cases of k. In this paper we focus on two particular cases. The case k = 1 which is the maximal cardinality strong-matching and the case of finding the maximal cardinality family of induced cycles (k = 2). For each one of the two cases, combinatorial algorithms are presented to solve the problem when graphs have particular structures and polyhedral descriptions of the convex hull of the corresponding feasible set are given. Computational tests are reported to compare the different upper bounds with the optimal values for different values of k, and to test the effectiveness of the inequalities introduced.
Volume carving is a well-known technique for reconstructing a 3D scene from a set of 2D images, using features detected in individual cameras, and camera parameters. Spatial calibration of the cameras is well understood, but the resulting carved volume is very sensitive to temporal offsets between the cameras. Automatic synchronization between the cameras is therefore desirable. In this paper, we present a highly efficient implementation of volume carving and synchronization on a heterogeneous system fitted with commodity GPUs using an improved version of the algorithm in [1].An online, real-time synchronization system is described and evaluated on surveillance video of an indoor scene. Improvements to the state of the art CPU-based algorithms are described.978-1-4799-0703-8/13/$31.00 ©2013 IEEE
A matrix of the form A = BBT where B is nonnegative is called completely positive (CP). Berman and Xu (2005) investigated a subclass of CP-matrices, called f0, 1g-completely positive matrices. We introduce a related concept and show connections between the two notions. An important relation to the so-called cut cone is established. Some results are shown for f0, 1g-completely positive matrices with given graphs, and for {0,1}-completely positive matrices constructed from the classes of (0, 1)-matrices with fixed row and column sums.
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