12535527
Fault-tolerant cycle embedding in hypercube with mixed link and node failures
17836895
Binomial-Tree Fault Tolerant Routing in Dual-Cubes with Large Number of Faulty Nodes
A dual-cube DC(m) has m + 1 links per node where m is the degree of a cluster (m-cube), and one extra link is used for connection between clusters. The dual-cube mitigates the problem of increasing number of links in the large-scale hypercube network while keeps most of the topological properties of the hypercube network. In this paper, we propose efficient algorithms for finding a nonfaulty routing path between any two nonfaulty nodes in the dual-cube with a large number of faulty nodes. A node v ∈ DC(m) is called k-safe if v has at least k nonfaulty neighbors. The DC(m) is called k-safe if every node in DC(m) is k-safe. The first algorithm presented in this paper is an off-line algorithm that uses global information of faulty status. It finds a nonfaulty path of length at most d(s,t) + O(k2) in O(|F| + m) time for any two nonfaulty nodes s and t in the k-safe DC(m) with number of faulty nodes |F| < 2k(m + 1 – k), where 0≤ k ≤ m/2. The second algorithm is an online algorithm that uses local information only. It can find a fault-free path with high probability in an arbitrarily faulty dual-cube with unbounded number of faulty nodes.
18839021
Adaptive-Subcube Fault Tolerant Routing in Dual-Cube with Very Large Number of Faulty Nodes
The dual-cube is a newly proposed interconnection network for linking a large amount of nodes with low node degree. It uses low-dimensional hypercubes as building blocks and keeps the main desired properties of the hypercubes. In this paper, we give an efficient algorithm for fault tolerant routing in dual-cube networks with a large number of faulty nodes. Our algorithm uses the adaptive-subcube technique to select a suitable dimension to route a node. This technique not only increases the routing speed but also shortens the path and improves the successful routing rate. The experimental results show that, with high percentages of node failures, the algorithm can build routing paths with a very high probability. Our simulation results show that when a dual-cube with 32,768 nodes contains up to 20 percent faulty nodes, the success rate of constructing a faultfree path between any two nonfaulty nodes is 99.5 percent with a 4-subcube.
7971918
An Efficient Algorithm for Fault Tolerant Routing Based on Adaptive Binomial-Tree Technique in Hypercubes
We propose an efficient fault-tolerant routing algorithm for hypercube networks with a very large number of faulty nodes. The algorithm is distributed and local-information-based in the sense that each node in the network knows only its neighbors’ status and no global information of the network is required by the algorithm. For any two given nonfaulty nodes in a hypercube network that may contain a large fraction of faulty nodes, the algorithm can find a fault-free path of nearly optimal length with very high probability. The algorithm uses the adaptive binomial-tree to select a suitable dimension to route a node. We perform empirical analysis of our algorithm through simulations under a uniform node failure distribution and a clustered node failure distribution. The experimental results show that the algorithm successfully finds a fault-free path of nearly optimal length with the probability larger than 90 percent in a hypercube network that may contain up to 50 percent faulty nodes.
34644814
The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers
Let k ≥ 5 be a fixed integer and let m = ⌊(k − 1)/2⌋. It is shown that the independence number of a Ck-free graph is at least c1[∑ d(v)1/(m − 1)](m − 1)/m and that, for odd k, the Ramsey number r(Ck, Kn) is at most c2(nm + 1/log n)1/m, where c1 = c1(m) > 0 and c2 = c2(m) > 0.
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).
16207650
Term Disambiguation in Natural Language Query for XML
Converting a natural language query sentence into a formal database query is a major challenge. We have constructed NaLIX, a natural language interface for querying XML data. Through our experience with NaLIX, we find that failures in natural language query understanding can often be dealt with as ambiguities in term meanings. These failures are typically the result of either the user's poor knowledge of the database schema or the system's lack of linguistic coverage. With automatic term expansion techniques and appropriate interactive feedback, we are able to resolve these ambiguities. In this paper, we describe our approach and present results demonstrating its effectiveness.
17592729
On the Lower Bound of Reconstruction Error for Spectral Filtering Based Privacy Preserving Data Mining
Additive Randomization has been a primary tool to hide sensitive private information during privacy preserving data mining. The previous work based on Spectral Filtering empirically showed that individual data can be separated from the perturbed one and as a result privacy can be seriously compromised. Our previous work initiated the theoretical study on how the estimation error varies with the noise and gave an upper bound for the Frobenius norm of reconstruction error using matrix perturbation theory. In this paper, we propose one Singular Value Decomposition (SVD) based reconstruction method and derive a lower bound for the reconstruction error. We then prove the equivalence between the Spectral Filtering based approach and the proposed SVD approach and as a result the achieved lower bound can also be considered as the lower bound of the Spectral Filtering based approach.
15872257
Independent component analysis of complex-valued functional magnetic resonance imaging data by complex nonlinearities
Independent component analysis (ICA) for separating complex-valued sources is needed for convolutive source-separation in the frequency domain, or for performing source separation on complex-valued data. Functional magnetic resonance imaging (fMRI) is a technique that produces complex-valued data; however the vast majority of fMRI analyses utilize only magnitude images due in large part to the difficulty of developing a temporal phase model. We have successfully applied ICA to complex fMRI data but there is a need to further optimize the complex ICA. We recently proposed a number of complex nonlinear functions for ICA of complex valued data. We apply two of these functions to fMRI data and examine the properties of these nonlinearities and their efficiency in generating the higher order statistics needed for ICA. We show that the complex infomax using these efficient nonlinearities demonstrates superior performance compared to analysis of the magnitude data with either ICA or linear regression. Complex ICA thus provides a potentially powerful method for the analysis of fMRI data.