7849638
Edge-fault-tolerant edge-bipancyclicity of hypercubes
In this paper, we consider the problem embedding a cycle into the hypercube Q"n with existence of faulty edges and show that for any edge subset F of Q"n with |F|==4 and all edges in F are not incident with the same vertex. This result improves some known results.
15426263
Super connectivity of line graphs
The super connectivity κ' and the super edge-connectivity λ' are more refined network reliability indices than connectivity κ and edge-connectivity λ. This paper shows that for a connected graph G with order at least four rather than a star and its line graph L(G), κ'(L(G)) = λ'(G) if and only if G is not super-λ'. As a consequence, we obtain the result of Hellwig et al. [Note on the connectivity of line graphs, Inform. Process. Lett. 91 (2004) 7] that κ(L(G)) = λ'(G). Furthermore, the authors show that the line graph of a super-λ' graph is super-λ if the minimum degree is at least three.
7639532
Fault diameter of Cartesian product graphs
The (k-1)-fault diameter D"k(G) of a k-connected graph G is the maximum diameter of G-F for any F@?V(G) with |F|=1 for i=1,2.
872168
The super connectivity of shuffle-cubes
The shuffle-cube SQn, where n ≡ 2 (mod 4), a new variation of hypercubes proposed by Li et al. [T.-K. Li, J.J.M. Tan, L.-H. Hsu, T.-Y. Sung, The shuffle-cubes and their generalization, Inform. Process. Lett. 77 (2001) 35-41], is an n-regular n-connected graph. This paper determines that the super connectivity of SQn is 2n - 4 and the super edge-connectivity is 2n - 2 for n ≥ 6.
39336188
Local Strongly Arc-Connectivity in Regular Bipartite Digraphs
We show that for any vertex x of a d-regular bipartite digraph there are a vertex y, in the other class of the bipartition, and d (x, y)-paths and d (y, x)-paths such that all 2d of them are pairwise arc-disjoint. This result generalizes a theorem of Hamidoune and Las Vergnas for graphs.
26138426
2-diameter of de Bruijn graphs
Binary strings are used as vertex labels or components of vertex labels. We will abbreviate “the vertex with label X” as “vertex x.” The binarji direcred de Briiijn graph of dimension n , denoted B ( n ) , has 2 ” vertices which are labeled with the binary strings of length n . There is an arc from any vertex x, x2 xn to the vertices x2x3 x,O and x2x3 x,, 1. We say that the ith coordinate of ,Y is x, . Any .u, is equal toOor l , andZ, = 1 x i . The undirected binary de Bruijn graph UB( n ) is obtained from B( n) by deleting the orientation of the arcs and omitting multiple edges and loops. It is well known that UB( n ) is 2-connected and that its diameter (maximum of the distances between all pairs of vertices) is equal to n . Due to their bounded maximum degree equal to 4 and their low diameter, de Bruijn graphs have been proposed as a possible good interconnection network for a parallel architecture [ 11. They have also been shown to solve a wide class of problems [ 21. For a k-connected graph, Hsu [ 4 ] introduced the notion of the kdiameter as follows: Given any two vertices x and y , a k-container between x and y is a set of k vertex disjoint paths between xand y . The length ofa k-container is the length of the longest of the k paths. The kdistance d k ( x , y ) between x and y is the minimum of the lengths of all the k-containers. Then, the k-diameter of a graph G is the maximum of d k ( x , y) for all pairs of vertices x and y . General results on the k-diameters of k-regular kconnected graphs can be found in [ 41 or [ 51. Results for some particular classes ofgraphs and many open problems can also be found in [ 41. It was shown by Pradhan and Reddy [ 7 ] that the 2diameter of U B ( n ) is less than or equal to 2n. The 2diameter is also obviously at least n. The aim of this paper was to prove that it is exactly n. In other words, between any two vertices of UB( n ) , there exist two internally vertex disjoint paths of length at most n. This gives a good measure of the fault tolerance of the graph [ 61. Let us first introduce some notation and recall some properties of the de Bruijn digraph B( n ) : Given two vertices x and y , we will denote f i x , y ] as a shortest path P from x to y . The length of this path, denoted by I PIX, y ] 1, is the number of edges in the path and is also the distance d ( x , y ) from x to y . P [ x , y ] also represents the set of vertices of the path, including its extremities.
36507
Ranking definitions with supervised learning methods
This paper is concerned with the problem of definition search. Specifically, given a term, we are to retrieve definitional excerpts of the term and rank the extracted excerpts according to their likelihood of being good definitions. This is in contrast to the traditional approaches of either generating a single combined definition or simply outputting all retrieved definitions. Definition ranking is essential for the task. Methods for performing definition ranking are proposed in this paper, which formalize the problem as either classification or ordinal regression. A specification for judging the goodness of a definition is given. We employ SVM as the classification model and Ranking SVM as the ordinal regression model respectively, such that they rank definition candidates according to their likelihood of being good definitions. Features for constructing the SVM and Ranking SVM models are defined. An enterprise search system based on this method has been developed and has been put into practical use. Experimental results indicate that the use of SVM and Ranking SVM can significantly outperform the baseline methods of using heuristic rules or employing the conventional information retrieval method of Okapi. This is true both when the answers are paragraphs and when they are sentences. Experimental results also show that SVM or Ranking SVM models trained in one domain can be adapted to another domain, indicating that generic models for definition ranking can be constructed.
7149198
A fault-tolerant approach to secure information retrieval
Several private information retrieval (PIR) schemes were proposed to protect users' privacy when sensitive information stored in database servers is retrieved. However, existing PIR schemes assume that any attack to the servers does not change the information stored and any computational results. We present a novel fault-tolerant PIR scheme (called FT-PIR) that protects users' privacy and at the same time ensures service availability in the presence of malicious server faults. Our scheme neither relies on any unproven cryptographic assumptions nor the availability of tamper-proof hardware. A probabilistic verification function is introduced into the scheme to detect corrupted results. Unlike previous PIR research that attempted mainly to demonstrate the theoretical feasibility of PIR, we have actually implemented both a PIR scheme and our FT-PIR scheme in a distributed database environment. The experimental and analytical results show that only modest performance overhead is introduced by FT-PIR while comparing with PIR in the fault-free cases. The FT-PIR scheme tolerates a variety of server faults effectively. In certain fail-stop fault scenarios, FT-PIR performs even better than PIR. It was observed that 35.82% less processing time was actually needed for FT-PIR to tolerate one server fault.
9706723
Efficient Job Scheduling Algorithms with Multi-Type Contentions
In this paper, we consider an interesting generalization of the classic job scheduling problem in which each job needs to compete not only for machines but also for other types of resources. The contentions among jobs for machines and for resources could interfere with each other, which complicates the problem dramatically. We present a family of approximation algorithms for solving several variants of the problem by using a generic algorithmic framework. Our algorithms achieve a constant approximation ratio (i.e., 3) when there is only one type of resources or certain dependency relation exists among multiple types of resources. When the r resources are unrelated, the approximation ratio of our algorithm becomes k+2, where k≤ r is a constant depending on the problem instance. As an application, we also show that our techniques can be easily applied to optical burst switching (OBS) networks to design more efficient wavelength scheduling algorithms.
41027997
Graph bandwidth of weighted caterpillars
Graph bandwidth minimization (GBM) is a classical and challenging problem in graph algorithms and combinatorial optimization. Most of existing researches on this problem have focused on unweighted graphs. In this paper, we study the bandwidth minimization problem of weighted caterpillars, and propose several algorithms for solving various types of caterpillars and general graphs. More specifically, we show that the GBM problem on caterpillars with hair-length at most 2 and the GBM problem on star-shape caterpillars are NP-complete, and give a lower bound of the graph bandwidth for general weighted graphs. For caterpillars with hair-length at most 1, we present an O(n log n log(nwmax))-time algorithm to compute an optimal bandwidth layout, where n is the total number of vertices in the graph and wmax is the maximum wedge weight. For caterpillars with hair-length at most k, we give a k-approximation algorithm. For arbitrary caterpillars and general graphs, we give a heuristic algorithm and some experimental results. Experiments show that the solutions obtained by our heuristic algorithm are roughly within a factor of clog(n) of the lower bound for a small number c, which is consistent with the inapproximability results of this problem (i.e., no constant approximation for the GBM problem unless P = NP).
757091
Efficient Job Scheduling Algorithms with Multi-type Contentions
In this paper, we consider an interesting generalization of the classic job scheduling problem in which each job needs to compete for not only machines but also other types of resources The contentions among jobs for machines and resources could interfere with each other, which complicates the problem dramatically We present a family of approximation algorithms for solving several variants of the problem by using a generic algorithmic framework Our algorithms achieve a constant approximation ratio (i.e., 3) if there is only one type of resources or certain dependency relation exists among multiple types of resources For the case that r unrelated resources are given, the approximation ratio of our algorithm becomes k + 2, where k ≤ r is a constant depending on the problem instance As an application, we also show that our techniques can be easily applied to optical burst switching (OBS) networks for deriving more efficient wavelength scheduling algorithms.