36356018
Solution of the Hamiltonian problem for self-complementary graphs
Abstract A graph G is said to be highly constricted if there exists a nonempty subset S of vertices such that (i) G − S has more than | S | components, (ii) S induces the complete graph, and (iii) for every u ∈ S and v ∉ S , we have d G ( u ) > d G ( v ), where d G ( u ) denotes the degree of u in G . In this paper it is shown that a non-hamiltonian self-complementary graph G of order p is highly constricted, unless p = 4 N and G is a particular graph G ∗ (4N) . It is also proved that if G is a self-complementary graph of order p (≥8) and π its degree sequence, then G is pancyclic if π has a realization with a hamiltonian cycle, and G has a 2-factor if π has a realization with a 2-factor, unless p = 4 N and G = G ∗ (4N) .
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.
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.
37364536
On regular and strongly-regular self-complementary graphs
Abstract In this paper we solve 3 of the 6 problems of A. Kotzig on regular and strongly-regular self-complementary graphs, mentioned in “Graph Theory and Related Topics” edited by J.A. Bondy and U.S.R. Murty.
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.
14267213
Geometric segmentation of perspective images based on symmetry groups
Symmetry is an effective geometric cue to facilitate conventional segmentation techniques on images of man-made environment. Based on three fundamental principles that summarize the relations between symmetry and perspective imaging, namely, structure from symmetry, symmetry hypothesis testing, and global symmetry testing, we develop a prototype system which is able to automatically segment symmetric objects in space from single 2D perspective images. The result of such a segmentation is a hierarchy of geometric primitives, called symmetry cells and complexes, whose 3D structure and pose are fully recovered. Such a geometrically meaningful segmentation may greatly facilitate applications such as feature matching and robot navigation.
32211361
On Computing a Largest Empty Arbitrarily Oriented Rectangle
Given a set P of n points within a rectangle R, we present an O(n3) time algorithm for computing an arbitrarily oriented empty rectangle of largest area in R that is bounded by a point of P on each of its four sides. We assume that R is large enough to contain such a rectangle.
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.
5596998
Computing Refined Buneman Trees in Cubic Time
Reconstructing the evolutionary tree for a set of n species based on pairwise distances between the species is a fundamental problem in bioinformatics. Neighbor joining is a popular distance based tree reconstruction method. It always proposes fully resolved binary trees despite missing evidence in the underlying distance data. Distance based methods based on the theory of Buneman trees and refined Buneman trees avoid this problem by only proposing evolutionary trees whose edges satisfy a number of constraints. These trees might not be fully resolved but there is strong combinatorial evidence for each proposed edge. The currently best algorithm for computing the refined Buneman tree from a given distance measure has a running time of O(n 5) and a space consumption of O(n 4). In this paper, we present an algorithm with running time O(n 3) and space consumption O(n 2). The improved complexity of our algorithm makes the method of refined Buneman trees computational competitive to methods based on neighbor joining.