45427128
Alternating eulerian trails with prescribed degrees in two edge-colored complete graphs
Let K"n be the complete graph with vertex set {v"1, v"2, ..., v"n} and let g=(g"1, ..., g"n) be a sequence of positive integers. Color each edge of this K"n red or blue. In this paper necessary and sufficient conditions are given which guarantee the existence of a connected spanning subgraph F in K"n (as colored) with both red degree and blue degree in F at vertex v"1 equal to g"i. When each g"i = 1 this answers a question of Erdos proved in this special case in [1].
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.
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.
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) .
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.
7179412
Considering Priority in Overlay Multicast Protocols Under Heterogeneous Environments
Hosts participating in overlay multicast applications have a wide range of heterogeneity in bandwidth and participation characteristics. In this paper, we highlight and show the need to systematically consider prioritization as a key criterion in the design of protocols for overlay multicast. We identify trade-offs in the design of prioritization heuristics in two important contexts. The first part of the paper considers prioritization strategies in the context of heterogeneity in node outgoing bandwidth and node stay time durations, and a lack of correlation between the two dimensions. The second part of the paper considers bandwidth allocation and prioritization policies with multi-tree data delivery in environments with heterogeneity in outgoing bandwidth and a certain degree of altruistic behavior. We conduct a systematic study of the trade-offs using both real trace data, and sensitivity studies using synthetic workloads. To the best of our knowledge, this is the first work to identify and study these trade-offs, and to demonstrate the potential benefits of the resulting prioritization heuristics.
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.
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.
8131766
Segmentation of a piece-wise planar scene from perspective images
We study and compare two novel embedding methods for segmenting feature points of piece-wise planar structures from two (uncalibrated) perspective images. We show that a set of different homographies can be embedded in different ways to a higher-dimensional real or complex space, so that each homography corresponds to either a complex bilinear form or a real quadratic form. Each embedding reveals different algebraic properties and relations of homographies. We give a closed-form segmentation solution for each case by utilizing these properties based on subspace-segmentation methods. These theoretical results show that one can intrinsically segment a piece-wise planar scene from 2-D images without explicitly performing any 3-D reconstruction. The resulting segmentation may make subsequent 3-D reconstruction much better-conditioned. We demonstrate the proposed methods with some convincing experimental results.
62583987
Enabling Confidentiality of Data Delivery in an Overlay Broadcasting System
In this paper, we present an extensive study of key dissemination schemes in an overlay multicast context, and the first to involve actual implementation, real traces, and performance in Internet environments. Given that rekey traffic has stronger resilience requirements and is burstier than data traffic, we consider whether data and keys must be distributed using the same overlay or using two separate dissemination structures. Our key findings are: (i) a coupled architecture is effective in achieving resilient key dissemination. Using TCP in each hop of the dissemination structure (an opportunity unique to overlays) is effective in achieving resiliency in end-to-end key delivery. The performance can be further enhanced if convergence properties of overlays are considered; and (ii) a coupled architecture optimized for data delivery has high overheads, while a coupled architecture optimized for key delivery may not honor access bandwidth constraints of nodes. Distributing data and keys using separate overlays achieves low overhead for key dissemination while honoring access bandwidth constraints of nodes.