10017070
Upper bounds for f-domination number of graphs,
Abstract For an integer-valued function ƒ defined on the vertices of a graph G , the ƒ- domination number γ ƒ (G) of G is the smallest cardinality of a subset D ⊆ V ( G ) such that each x ∈ V ( G ) − D is adjacent to at least ƒ(x) vertices in D . When ƒ(x) = k for all x ∈ V(G), γ ƒ (G) is the k -domination number γ k ( G ). In this note, we give a tight upper bound for γ ƒ and an improvement of the upper bound for a special ƒ- domination number μ j , k of Stracke and Volkmann (1993). Some upper bounds for γ k are also obtained.
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.
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.
8997397
BoostMotion: Boosting a Discriminative Similarity Function for Motion Estimation
Motion estimation for applications where appearance undergoes complex changes is challenging due to lack of an appropriate similarity function. In this paper, we propose to learn a discriminative similarity function based on an annotated database that exemplifies the appearance variations. We invoke the LogitBoost algorithm to selectively combine weak learners into one strong similarity function. The weak learners based on local rectangle features are constructed as nonparametric 2D piecewise constant functions, using the feature responses from both images, to strengthen the modeling power and accommodate fast evaluation. Because the negatives possess a location parameter measuring their closeness to the positives, we present a locationsensitive cascade training procedure, which bootstraps negatives for later stages of the cascade from the regions closer to the positives. This allows viewing a large number of negatives and steering the training process to yield lower training and test errors. In experiments of estimating the motion for the endocardial wall of the left ventricle in echocardiography, we compare the learned similarity function with conventional ones and obtain improved performances. We also contrast the proposed method with a learning-based detection algorithm to demonstrate the importance of temporal information in motion estimation. Finally, we insert the learned similarity function into a simple contour tracking algorithm and find that it reduces drifting.
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.
7007263
The rich-club phenomenon in the Internet topology
We show that the Internet topology at the autonomous system (AS) level has a rich-club phenomenon. The rich nodes, which are a small number of nodes with large numbers of links, are very well connected to each other. The rich-club is a core tier that we measured using the rich-club connectivity and the node-node link distribution. We obtained this core tier without any heuristic assumption between the ASs. The rich-club phenomenon is a simple qualitative way to differentiate between power law topologies and provides a criterion for new network models. To show this, we compared the measured rich-club of the AS graph with networks obtained using the Baraba/spl acute/si-Albert (BA) scale-free network model, the Fitness BA model and the Inet-3.0 model.
135505
Image based regression using boosting method
We present a general algorithm of image based regression that is applicable to many vision problems. The proposed regressor that targets a multiple-output setting is learned using boosting method. We formulate a multiple-output regression problem in such a way that overfitting is decreased and an analytic solution is admitted. Because we represent the image via a set of highly redundant Haar-like features that can be evaluated very quickly and select relevant features through boosting to absorb the knowledge of the training data, during testing we require no storage of the training data and evaluate the regression function almost in no time. We also propose an efficient training algorithm that breaks the computational bottleneck in the greedy feature selection process. We validate the efficiency of the proposed regressor using three challenging tasks of age estimation, tumor detection, and endocardial wall localization and achieve the best performance with a dramatic speed, e.g., more than 1000 times faster than conventional data-driven techniques such as support vector regressor in the experiment of endocardial wall localization.
15698378
A Binary Decision Tree Implementation of a Boosted Strong Classifier
Viola and Jones [1] proposed the influential rapid object detection algorithm. They used AdaBoost to select from a large pool a set of simple features and constructed a strong classifier of the form {∑jαjhj(x) ≥ θ} where each hj(x) is a binary weak classifier based on a simple feature. In this paper, we construct, using statistical detection theory, a binary decision tree from the strong classifier of the above form. Each node of the decision tree is just a weak classifier and the knowledge of the coefficients αjis no longer needed. Also, the binary tree has a lot of early exits. As a result, we achieve an automatic speedup that always makes the rapid Viola and Jones algorithm rapider.