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.
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.
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.
8083367
On Some Three-Color Ramsey Numbers
Abstract. In this paper we study three-color Ramsey numbers. Let Ki,j denote a complete i by j bipartite graph. We shall show that (i) for any connected graphs G1, G2 and G3, if r(G1, G2)≥s(G3), then r(G1, G2, G3)≥(r(G1, G2)−1)(χ(G3)−1)+s(G3), where s(G3) is the chromatic surplus of G3; (ii) (k+m−2)(n−1)+1≤r(K1,k, K1,m, Kn)≤ (k+m−1)(n−1)+1, and if k or m is odd, the second inequality becomes an equality; (iii) for any fixed m≥k≥2, there is a constant c such that r(Kk,m, Kk,m, Kn)≤c(n/logn), and r(C2m, C2m, Kn)≤c(n/logn)m/(m−1) for sufficiently large n.
5262698
An integrated algorithm of incremental and robust PCA
Principal component analysis (PCA) is a well-established technique in image processing and pattern recognition. Incremental PCA and robust PCA are two interesting problems with numerous potential applications. However, these two issues have only been separately addressed in the previous studies. In this paper, we present a novel algorithm for incremental and robust PCA by seamlessly integrating the two issues together. The proposed algorithm has the advantages of both incremental PCA and robust PCA. Moreover, unlike most M-estimation based robust algorithms, it is computational efficient. Experimental results on dynamic background modelling are provided to show the performance of the algorithm with a comparison to the conventional batch-mode and nonrobust algorithms.
5886737
Using KCCA for Japanese–English cross-language information retrieval and document classification
Kernel Canonical Correlation Analysis (KCCA) is a method of correlating linear relationship between two variables in a kernel defined feature space. A machine learning algorithm based on KCCA is studied for cross-language information retrieval. We apply the algorithm in Japanese–English cross-language information retrieval. The results are quite encouraging and are significantly better than those obtained by other state of the art methods. Computational complexity is an important issue when applying KCCA to large dataset as in information retrieval. We experimentally evaluate several methods to alleviate the problem of applying KCCA to large datasets. We also investigate cross-language document classification using KCCA as well as other methods. Our results show that it is feasible to use a classifier learned in one language to classify the documents in other languages.
206964202
Asymptotic Upper Bounds for Ramsey Functions
Abstract. We show that for any graph G with N vertices and average degree d, if the average degree of any neighborhood induced subgraph is at most a, then the independence number of G is at least Nfa+1(d), where fa+1(d)=∫01(((1−t)1/(a+1))/(a+1+(d−a−1)t))dt. Based on this result, we prove that for any fixed k and l, there holds r(Kk+l,Kn)≤ (l+o(1))nk/(logn)k−1. In particular, r(Kk, Kn)≤(1+o(1))nk−1/(log n)k−2.
12780409
Discovering Temporal Patterns in Multiple Granularities
Many events repeat themselves as the time goes by. For example, an institute pays its employees on the first day of every month. However, events may not repeat with a constant span of time. In the payday example here, the span of time between each two consecutive paydays ranges between 28 and 31 days. As a result, regularity, or temporal pattern, has to be captured with a use of granularities (such as day, week, month, and year), oftentimes multiple granularities. This paper defines the above patterns, and proposes a number of pattern discovery algorithms. To focus on the basics, the paper assumes that a list of events with their timestamps is given, and the algorithms try to find patterns for the events. All of the algorithms repeat two possibly interleaving steps, with the first step generating possible (called candidate) patterns, and the second step verifying if candidate patterns satisfy some user-given requirements. The algorithms use pruning techniques to reduce the number of candidate patterns, and adopt a data structure to efficiently implement the second step. Experiments show that the pruning techniques and the data structure are quite effective.