151575
Matroid tree graphs and interpolation theorems
Using the Hamiltonicity of matroid tree graphs we give a new proof for an interpolation theorem of Barefoot (1984) and other related results. From the proof we refine a general approach for dealing with interpolation problems of graphs.
34996713
Polynomial Time Solvability Of The Weighted Ring Arc-Loading Problem With Integer Splitting
In the Weighted Ring Arc-Loading Problem with Integer Splitting, we are given a set of communication requests each associated with a non-negative integer weight. The problem is to find a routing scheme such that the maximum load on arcs of the ring is minimized, subject to that the weight of each request may be split into two integral parts routed in two directions around the ring, where the load of an arc is the sum of parts routed through the arc. A pseudo-polynomial algorithm for this problem is implied by a result in [G. Wilfong and P. Winkler, Ring routing and wavelength translation, Proceedings of the 9th ACM-SIAM Symposium on Discrete Algorithms, San Fancisco, CA, 1998, 333-341]. By refining the rounding technique developed in the same paper, we prove that the problem can be solved in polynomial time.
38623555
Domination number and neighbourhood conditions
Abstract The domination number γ of a graph G is the minimum cardinality of a subset D of vertices of G such that each vertex outside D is adjacent to at least one vertex in D . For any subset A of the vertex set of G , let ∂ + ( A ) be the set of vertices not in A which are adjacent to at least one vertex in A . Let N (A) be the union of A and ∂ + ( A ), and d ( A ) be the sum of degrees of all the vertices of A . In this paper we prove the inequality 2q ⩽ (p−γ)(p−γ+2)−|∂ + (A)| (p−γ+1)+d( N (A)) , and characterize the extremal graphs for which the equality holds, where p and q are the numbers of vertices and edges of G , respectively. From this we then get an upper bound for γ which generalizes the known upper bound γ⩽p+1− 2q+1 . Let I ( A ) be the set of vertices adjacent to all vertices of A , and I (A) be the union of A and I ( A ). We prove that 2q ⩽ (p − γ − | I (A)| + 2)(p − γ + 4) + d( I (A)) − min {p − γ − | I (A)| + 2, |A|, |I(A)|, 3} , which implies an upper bound for γ as well.
20645165
Harper-type lower bounds and the bandwidths of the compositions of graphs
Abstract We give a general Harper-type lower bound for the bandwidth of a graph which is a common generalization of several known results. As applications we get a lower bound for the bandwidth of the composition of two graphs. By using this we determine the bandwidths of some composition graphs such as ( P r × P s )[ H ], ( P r × C s )[ H ] (2 r ≠ s ), ( C r × C s )[ H ] (6 ⩽ 2 r ⩽ s ), etc., for any graph H . Interestingly, the bandwidths of these graphs have nothing to do with the structure of H in general.
8520561
Bounding the bandwidths for graphs
Let G;H be nite graphs with jV(H)j>jV(G)j. The bandwidth of G with respect to H is dened to be BH(G) = minmaxuv2E(G)dH((u);(v)), with the minimum taken over all injections from V(G )t oV(H), where dH(x;y) is the distance in H between two vertices x;y 2 V(H). This number is involved with the VLSI design and optimization, especially when the \host" graph H is a path Pn or a cycle Cn of length n = jV(G)j. In these two cases, BH(G) is known to be the ordinary bandwidth B(G) and the cyclic bandwidth Bc(G), respectively, and the corresponding decision problem is NP-complete. So estimations of B(G), Bc(G) and in general BH(G) are needed, especially in determining the bandwidths of some specic graphs. In this paper, we rst propose a systematic method for obtaining lower bounds for the bandwidth BH(G). By using this method, we then get a number of lower bounds for B(G) and Bc(G )i n terms of some distance- and degree-related parameters. c 2000 Elsevier Science B.V. All rights reserved.
14537383
Constructing a Class of Symmetric Graphs
We find a natural construction of a large class of symmetric graphs from point- and block-transitive 1-designs. The graphs in this class can be characterized as G -symmetric graphs whose vertex sets admit a G -invariant partition B of block size at least 3 such that, for any two blocks B, C of B, either there is no edge between B and C, or there exists only one vertex in B not adjacent to any vertex inC . The special case where the quotient graph ?Bof ? relative to B is a complete graph occurs if and only if the 1-design needed in the construction is a G -doubly transitive and G -block-transitive 2-design, and in this case we give an explicit classification of ? when G is a doubly transitive projective group or an affine group containing the affine general group. Examples of such graphs include cross ratio graphs studied recently by Gardiner, Praeger and Zhou and some other graphs with vertices the (point, line)-flags of the projective or affine geometry.
1466117
Redundancy and Robustness of the AS-level Internet topology and its models
A comparison between the topological properties of the measured Internet topology, at the autonomous system level (AS graph), and the equivalent graphs generated by two different power law topology generators are presented. Only one of the synthetic generators reproduces the tier connectivity of the AS graph.
379157
From sample similarity to ensemble similarity: probabilistic distance measures in reproducing kernel Hilbert space
This paper addresses the problem of characterizing ensemble similarity from sample similarity in a principled manner. Using a reproducing kernel as a characterization of sample similarity, we suggest a probabilistic distance measure in the reproducing kernel Hilbert space (RKHS) as the ensemble similarity. Assuming normality in the RKHS, we derive analytic expressions for probabilistic distance measures that are commonly used in many applications, such as Chernoff distance (or the Bhattacharyya distance as its special case), Kullback-Leibler divergence, etc. Since the reproducing kernel implicitly embeds a nonlinear mapping, our approach presents a new way to study these distances whose feasibility and efficiency is demonstrated using experiments with synthetic and real examples. Further, we extend the ensemble similarity to the reproducing kernel for ensemble and study the ensemble similarity for more general data representations.
13254850
Profile guided management of code partitions for embedded systems
Researchers have proposed to divide embedded applications into code partitions and to download partitions on demand from a wireless code server to enable a diverse set of applications for very tightly constrained embedded systems. This paper describes a new approach for managing the request and storage of code partitions and we explore the benefits of our scheme.
10785532
Probabilistic recognition of human faces from video
Most present face recognition approaches recognize faces based on still images. We present a novel approach to recognize faces in video. In that scenario, the face gallery may consist of still images or may be derived from a videos. For evidence integration we use classical Bayesian propagation over time and compute the posterior distribution using sequential importance sampling. The probabilistic approach allows us to handle uncertainties in a systematic manner. Experimental results using videos collected by NIST/USF and CMU illustrate the effectiveness of this approach in both still-to-video and video-to-video scenarios with appropriate model choices.
13207643
Towards Modelling The Internet Topology - The Interactive Growth Model
The Internet topology at the Autonomous Systems level (AS graph) has a power-law degree distribution and a tier structure. In this paper, we introduce the Interactive Growth (IG) model based on the joint growth of new nodes and new links. This simple and dynamic model compares favorable with other Internet power-law topology generators because it not only closely resembles the degree distribution of the AS graph, but also accurately matches the hierarchical structure, which is measured by the recently reported rich-club phenomenon.