24660543
A note on the lower bounds of signed domination number of a graph
Abstract Let G = (V, E) be a graph. For a function f : V → {−1, 1}, the weight of f is w(f) = Σv ∈ V f(v). For a vertex v in V, we define f[v] = Σu∈N[v] f(u). A signed dominating function of G is a function f : V → {−1, 1} such that f[v] ⩾ 1 for all v ∈ V. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. A signed dominating function of a weight γs(G) we call a γs-function of G. In this paper, we study the signed domination problem of general graph, and obtain some lower bounds of the signed domination number of a graph, and show that these lower bounds are sharp, and extend a result in Dunbar et al. (1995).
3006898
A six-color theorem for the edge-face coloring of plane graphs
Abstract It was shown (Kronk and Mitchen, 1973) that the set of vertices, edges and faces of any normal map on the sphere can be colored with seven colors. In this paper we solve a somewhat different problem: the set of edges and faces of any plane graph with Δ ⩽ 3 can be colored by six colors.
12558561
Statistical Analysis of Generalized Processor Sharing Scheduling Discipline
In this paper, we consider the problem of providing statistical guarantees (for example, on the tail distribution of delay) under the Generalized Processor Sharing (GPS) scheduling discipline. This work is motivated by, and is an extension of, Parekh and Gallager's deterministic study of GPS scheduling discipline with leaky-bucket token controlled sessions [PG93a,b, Parekh92]. Using the exponentially bounded burstiness (E.B.B.) process model introduced in [YaSi93a] as a source traffic characterization, we establish results that extend the deterministic study of GPS: for a single GPS server in isolation, we present statistical bounds on the tail distributions of backlog and delay for each session. In the network setting, we show that networks belonging to a broad class of GPS assignments, the so-called Consistent Relative Session Treatment (CRST) GPS assignments, are stable in a stochastic sense. In particular, we establish simple bounds on the tail distribution of backlog and delay for each session in a Rate Proportional Processor Sharing (RPPS) GPS network with arbitrary topology.
14479142
WDM optical interconnects with recirculating buffering and limited range wavelength conversion
All-optical communication, in particular, wavelength-division-multiplexing (WDM) technique, has been proposed as a promising candidate to meet the ever-increasing demands on bandwidth from emerging bandwidth-intensive computing/networking applications. However, with current technology, the cost of optical communication, especially the cost of optical buffering and wavelength conversion, remains a major concern for such applications. In this paper, we study WDM optical interconnects that utilize low cost recirculating buffering and limited range wavelength conversion. We first consider the packet scheduling problem in this type of interconnect, and formalize the problem of maximizing throughput and minimizing packet delay as a matching problem in a bipartite graph. We give an optimal parallel algorithm for this problem that runs in O(Bk/sup 2/) time, compared to O((N+B)/sup 3/k/sup 3/) time if directly applied to existing matching algorithms for general bipartite graphs, where N is the number of input/output fibers of the interconnect, B is the number of fiber delay lines, and k is the number of wavelengths. We also consider efficient switching fabric designs for this type of interconnect. We distinguish between the switching fabric connecting the input fibers to the output fibers and the switching fabric connecting the input fibers to the delay lines and show that by adopting the idea of concentration, the cost of the latter can be reduced significantly in terms of the number of crosspoints.
1035628
Joint categorization of queries and clips for web-based video search
Building a video search engine on the Web is a very challenging problem. Compared with web page search, video search has its unique characteristics (such as high volume of data for each video, existence of multi-modal information including meta-data, visual content, audio, closed caption, etc). In this paper, we investigate some promising approaches to boosting the search relevance of a large scale video search engine on the Web. The contribution of our work is three-fold. (1) We developed a specialized video categorization framework which combines multiple classifiers based on different modalities. (2) By learning users' querying history and clicking log, we proposed an automatic query profile generation technique and applied the profile to query categorization. (3) A highly scalable system was developed, which integrates the online query categorization and offline video categorization. Naive Bayes with mixture of multinomials, Maximum Entropy, and Support Vector Machine categorization methods and the profile learn-ing technique were evaluated on a large scale set of video data on the Web. The evaluation of the developed system and user study has indicated that the joint categorization of queries and video data boosts the video search relevance and user search experience. The high efficiency of our approaches is also demonstrated by the good responsiveness of the system for the video search engine on the Web.
15502339
Optimal parallel scheduling algorithm for WDM optical interconnects with recirculating buffering
We study scheduling algorithms in WDM optical interconnects with recirculating buffering. The interconnect we consider has wavelength conversion capabilities. We focus on limited range wavelength conversion while considering full range wavelength conversion as a special case. We formalize the problem of maximizing throughput and minimizing packet delay in such an interconnect as a matching problem in a bipartite graph and give an optimal parallel algorithm that runs in O(Bk/sup 2/), as compared to O((N+B)/sup 3/k/sup 3/) time if directly applying other existing matching algorithms, where N is the number of input/output fibers, B is the number of fiber delay lines and k is the number of wavelengths per fiber.
17171833
What can be determined from a full and a weak perspective image?
This paper presents a first investigation on the structure from motion problem from the combination of full and weak perspective images. This problem arises in multiresolution object modeling where multiple zoomed-in or close-up views are combined with wider or distant reference views. The narrow field-of-view (FOV) images from the zoomed-in or closeup views can be approximated as weak perspective projection. Using a full perspective projection model for the narrow FOV images, although more accurate, actually leads to instabilities during the estimation process due to the non-linearities in the imaging model. The weak perspective approximation leads to more stable estimation algorithms, although at the cost of a small amount of modeling inaccuracy. Previous work in structure from motion focused either on two (or more) perspective images or on a set of weak perspective (more generally, affine) images. The main contribution of this paper is the study of the SFM problem for the much neglected case of one perspective and one (or more) weak perspective image. We show that in contrast to the case of a pair of weak perspective images, there is adequate information to recover Euclidean structure from a single perspective and a single weak perspective image. The epipolar geometry is simpler than with two perspective images leading to simpler and more stable estimation algorithms. Computer simulation shows that more stable results can be obtained with the technique presented in this paper than if two images are both considered to be full perspective.