29793155
Finite symmetric graphs with two-arc transitive quotients
This paper forms part of a study of 2-arc transitivity for finite imprimitive symmetric graphs, namely for graphs Γ admitting an automorphism group G that is transitive on ordered pairs of adjacent vertices, and leaves invariant a nontrivial vertex partition B. Such a group G is also transitive on the ordered pairs of adjacent vertices of the quotient graph ΓB corresponding to B. If in addition G is transitive on the 2-arcs of Γ (that is, on vertex triples (α, β γ) such that α, β and β, γ are adjacent and α ≠ γ), then G is not in general transitive on the 2-arcs of ΓB, although it does have this property in the special case where B is the orbit set of a vertex-intransitive normal subgroup of G. On the other hand, G is sometimes transitive on the 2-arcs of ΓB even if it is not transitive on the 2-arcs of Γ. We study conditions under which G is transitive on the 2-arcs of ΓB. Our conditions relate to the structure of the bipartite graph induced on B ∪ C for adjacent blocks B, C of B and a graph structure induced on B. We obtain necessary and sufficient conditions for G to be transitive on the 2-arcs of one or both of Γ, ΓB, for certain families of imprimitive symmetric graphs.
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.
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.
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.
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.
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.
11541594
A network-centric approach to enhancing the interactivity of large-scale distributed virtual environments
In Distributed Virtual Environments (DVEs), where many simultaneous human users interact with each other in a shared, 3D virtual world, enhancing interactivity is of crucial importance, since the success of a DVE greatly depends on users' perceptions. In general, enhancing interactivity for large-scale DVEs with thousands of geographically distributed users faces various challenges such as large Internet latencies, high resource demands and high potential of security threats. In this paper, we propose a network-centric approach to enhance the interactivity of DVEs by directly minimizing the network latencies in client-server communications. We consider two key problems: the server placement problem and the client assignment problem. We have formulated these two problems and proved that they are both NP-hard. We then adapt and develop several degree-based server placement approaches and greedy client assignment algorithms. Extensive simulation studies using realistic models have shown that our approach is very effective in enhancing the interactivity of large-scale DVEs.
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.
61202442
Probabilistic identity characterization for face recognition
We present a general framework for characterizing the object identity in a single image or a group of images with each image containing a transformed version of the object, with applications to face recognition. In terms of the transformation, the group is made of either many still images or frames of a video sequence. The object identity is either discrete- or continuous-valued. This probabilistic framework integrates all the evidence of the set and handles the localization problem, illumination and pose variations through subspace identity encoding. Issues and challenges arising in this framework are addressed and efficient computational schemes are presented. Good face recognition results using the PIE database are reported.
5971410
Time-space consistency in large-scale distributed virtual environments
Maintaining a consistent view of the simulated world among different simulation nodes is a fundamental problem in large-scale distributed virtual environments (DVEs). In this paper, we characterize this problem by quantifying the time-space inconsistency in a DVE. To this end, a metric is defined to measure the time-space inconsistency in a DVE. One major advantage of the metric is that it may be estimated based on some characteristic parameters of a DVE, such as clock asynchrony, message transmission delay, the accuracy of the dead reckoning algorithm, the kinetics of the moving entity, and human factors. Thus the metric can be used to evaluate the time-space consistency property of a DVE without the actual execution of the DVE application, which is especially useful in the design stage of a DVE. Our work also clearly shows how the characteristic parameters of a DVE are interrelated in deciding the time-space inconsistency, so that we may fine-tune the DVE to make it as consistent as possible. To verify the effectiveness of the metric, a Ping-Pong game is developed. Experimental results show that the metric is effective in evaluating the time-space consistency property of the game.
14594677
Techniques and tools for dynamic optimization
Traditional code optimizers have produced significant performance improvements over the past forty years. While promising avenues of research still exist, traditional static and profiling techniques have reached the point of diminishing returns. The main problem is that these approaches have only a limited view of the program and have difficulty taking advantage of the actual run-time behavior of a program. We are addressing this problem through the development of a dynamic optimization system suited for aggressive optimization - using the full power of the most beneficial optimizations. We have designed our optimizer to operate using a software dynamic translation (SDT) execution system. Difficult challenges in this research include reducing SDT overhead and determining what optimizations to apply and where in the code to apply them. Another challenge is having the necessary tools to ensure the reliability of software that is dynamically optimized. In this paper, we describe our efforts in reducing overhead in SDT and efficient techniques for instrumenting the application code. We also describe our approach to determine what and where an optimization should be applied. We discuss other fundamental issues in developing a dynamic optimizer and finally present a basic debugger for SDT systems