33854423
Cycles in self-complementary graphs
Abstract Let G be a self-complementary graph of order p ≥ 8. It is shown that for every integer l , 3 ≤ l ≤ p − 2, G has an l -cycle. Further, if G is hamiltonian, then G is pancyclic.
205492674
Spectra and energies of iterated line graphs of regular graphs
If G is a graph and L(G)=L1(G) its line graph, then Lk(G), k=2,3,…, defined recursively via Lk(G)=L(Lk−1(G)), are the iterated line graphs of G. If G is a regular graph of degree r, r≥3, then all negative eigenvalues of its iterated line graphs are equal to minus 2. The energy E(G) of a graph G is the sum of absolute values of the eigenvalues of G. If G is a regular graph of order n and of degree r≥3, then for each k≥2, E(Lk(G)) depends solely on n and r. In particular, E(L2(G))=2nr(r−2). This result enables a systematic construction of pairs of non-cospectral connected graphs of the same order, having equal energies.
1697925
The Impact of Heterogeneous Bandwidth Constraints on DHT-Based Multicast Protocols
In this paper, we consider support for bandwidth-demanding applications such as video broadcasting using DHTs. Our investigations focus on the impact of heterogeneity in the outgoing bandwidth capabilities of nodes on Scribe, a representative and relatively mature DHT-based multicast protocol. We expose important issues that arise due to the mismatch between the ID space that underlies the DHT and the outgoing bandwidth constraints on nodes.
383922
Early Experience with an Internet Broadcast System Based on Overlay Multicast
In this paper, we report on experience in building and deploying an operational Internet broadcast system based on Overlay Multicast. In over a year, the system has been providing a cost-effective alternative for Internet broadcast, used by over 4000 users spread across multiple continents in home, academic and commercial environments. Technical conferences and special interest groups are the early adopters. Our experience confirms that Overlay Multicast can be easily deployed and can provide reasonably good application performance. The experience has led us to identify first-order issues that are guiding our future efforts and are of importance to any Overlay Multicast protocol or system. Our key contributions are (i) enabling a real Overlay Multicast application and strengthening the case for overlays as a viable architecture for enabling group communication applications on the Internet, (ii) the details in engineering and operating a fully functional streaming system, addressing a wide range of real-world issues that are not typically considered in protocol design studies, and (iii) the data, analysis methodology, and experience that we are able to report given our unique standpoint.
11142529
Segmentation of hybrid motions via hybrid quadratic surface analysis
In this paper, we investigate the mathematical problem underlying segmentation of hybrid motions: given a series of tracked feature correspondences between two (perspective) images, we seek to segment and estimate multiple motions, possibly of different types (e.g., affine, epipolar, and homography). In order to accomplish this task, we cast the problem into a more general mathematical framework of segmenting data samples drawn from a mixture of linear subspaces and quadratic surfaces. The result is a novel algorithm called hybrid quadratic surface analysis (HQSA). HQSA uses both the derivatives and Hessians of fitting polynomials for the data to separate linear data samples from quadratic data samples. These derivatives and Hessians also lead to important necessary conditions, based on the so-called mutual contraction subspace, to separate data samples on different quadratic surfaces. The algebraic solution we derive is non-iterative and numerically stable. It tolerates moderate noise and can be used in conjunction with outlier removal techniques. We show how to solve the hybrid motion segmentation problem using HQSA, and demonstrate its performance on simulated data with noise and on real perspective images.
17940922
Symmetry-based 3-D reconstruction from perspective images
Symmetry is an important geometric cue for 3-D reconstruction from perspective images. In this paper, we introduce a unified theoretical framework for extracting poses and structures of 2-D symmetric patterns in space from calibrated images. The framework uniformly encompasses all three fundamental types of symmetry, i.e., reflective, rotational, and translational, based on a systematic study of the homography groups in image induced by the symmetry groups in space. We claim that if a planar object admits rich enough symmetry, no 3-D geometric information is lost through perspective imaging. Based on two fundamental principles that utilize common spatial relations among symmetric objects, we have developed a prototype system which can automatically extract and segment multiple 2-D symmetric patterns present in a single perspective image. The result of such a segmentation is a hierarchy of new geometric primitives, called symmetry cells and complexes, whose 3-D structures and poses are fully recovered. Finally, we propose a new symmetry-based matching technique, which can effectively establish correspondences among the extracted symmetry cells across multiple images. We demonstrate the application of the proposed algorithms on image segmentation, matching, and 3-D reconstruction with extensive experimental results. The algorithms and systems are more accurate and easier to implement than existing point-or line-based methods.
9742261
Portable and Efficient Parallel Computing Using the BSP Model
The Bulk-Synchronous Parallel (BSP) model was proposed by Valiant as a standard interface between parallel software and hardware. In theory, the BSP model has been shown to allow the asymptotically optimal execution of architecture independent software on a variety of architectures. Our goal in this work is to experimentally examine the practical use of the BSP model on current parallel architectures. We describe the design and implementation of the Green BSP Library, a small library of functions that implement the BSP model, and of several applications that were written for this library. We then discuss the performance of the library and application programs on several parallel architectures. Our results are positive in that we demonstrate efficiency and portability over a range of parallel architectures and show that the BSP cost model is useful for predicting performance trends and estimating execution times.