1942335
On restricted edge-connectivity of graphs
This paper considers the concept of restricted edge-connectivity, and relates that to the edge-degree of a connected graph. The author gives some necessary conditions for a graph whose restricted edge-connectivity is smaller than its minimum edge-degree, then uses these conditions to show some large classes of graphs, such as all connected edge-transitive graphs except a star, and all connected vertex-transitive graphs with odd order or without triangles, have equality of the restricted edge-connectivity and the minimun edge-degree.
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.
10735574
Forwarding indices of folded n-cubes
For a given connected graph G of order n, a routing R is a set of n(n - 1) elementary paths specified for every ordered pair of vertices in G. The vertex (resp. edge) forwarding index of a graph is the maximum number of paths of R passing through any vertex (resp. edge) in the graph. In this paper, the authors determine the vertex and the edge forwarding indices of a folded n-cube as (n-1)2n-1 +1-((n+l)/2) (n ⌊n+1/2⌋) and 2n-(n,⌊n+1/2⌋),respectively.
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.
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.
17341019
Automatically detecting criminal identity deception: an adaptive detection algorithm
Identity deception, specifically identity concealment, is a serious problem encountered in the law enforcement and intelligence communities. In this paper, the authors discuss techniques that can automatically detect identity deception. Most of the existing techniques are experimental and cannot be easily applied to real applications because of problems such as missing values and large data size. The authors propose an adaptive detection algorithm that adapts well to incomplete identities with missing values and to large datasets containing millions of records. The authors describe three experiments to show that the algorithm is significantly more efficient than the existing record comparison algorithm with little loss in accuracy. It can identify deception having incomplete identities with high precision. In addition, it demonstrates excellent efficiency and scalability for large databases. A case study conducted in another law enforcement agency shows that the authors' algorithm is useful in detecting both intentional deception and unintentional data errors
5147011
Wide Diameters of Cartesian Product Graphs and Digraphs
In graph theory and study of fault tolerance and transmission delay of networks, connectivity and diameter of a graph are two very important parameters and have been deeply studied by many authors. Wide diameter combining connectivity with diameter is a more important parameter to measure fault tolerance and efficiency of parallel processing computer networks and has received much attention in the recent years. Diameter with width k of a graph G is defined as the minimum integer d for which between any two distinct vertices in G there exist at least k internally disjoint paths of length at most d. In the present paper, the tight upper bounds of wide diameter of the Cartesian product graphs are obtained. Some known results can be deduced or improved from ours.
11486473
Circumference of Graphs with Bounded Degree
Karger, Motwani, and Ramkumar Algorithmica, 18 (1997), pp. 82--98] have shown that there is no constant approximation algorithm to find a longest cycle in a Hamiltonian graph, and they conjectured that this is the case even for graphs with bounded degree. On the other hand, Feder, Motwani, and Subi [SIAM J. Comput., 31 (2002), pp. 1596--1607] have shown that there is a polynomial time algorithm for finding a cycle of length $n^{\log_32}$ in a 3-connected cubic n-vertex graph. In this paper, we show that if G is a 3-connected n-vertex graph with maximum degree at most d, then one can find, in O(n3) time, a cycle in G of length at least $\Omega(n^{\log_b2})$, where $b=2(d-1)^2+1$.
7874615
A generic framework for monitoring continuous spatial queries over moving objects
This paper proposes a generic framework for monitoring continuous spatial queries over moving objects. The framework distinguishes itself from existing work by being the first to address the location update issue and to provide a common interface for monitoring mixed types of queries. Based on the notion of safe region, the client location update strategy is developed based on the queries being monitored. Thus, it significantly reduces the wireless communication and query reevaluation costs required to maintain the up-to-date query results. We propose algorithms for query evaluation/reevaluation and for safe region computation in this framework. Enhancements are also proposed to take advantage of two practical mobility assumptions: maximum speed and steady movement. The experimental results show that our framework substantially outperforms the traditional periodic monitoring scheme in terms of monitoring accuracy and CPU time while achieving a close-to-optimal wireless communication cost. The framework also can scale up to a large monitoring system and is robust under various object mobility patterns.
21098955
Topological Peeling and Implementation
We present a new approach, called topological peeling, and its implementation for traversing a portion AR of the arrangement formed by n lines within a convex region R on the plane. Topological peeling visits the cells of AR in a fashion of propagating a "wave" of a special shape (called a double-wriggle curve) starting at a single source point. This special traversal fashion enables us to solve several problems (e.g., computing shortest paths) on planar arrangements to which previously best known arrangement traversal techniques such as topological sweep and topological walkm ay not be directly applicable. Our topological peeling algorithm takes O(K + n log(n + r)) time and O(n + r) space, where K is the number of cells in AR and r is the number of boundary vertices of R. Comparing with topological walk, topological peeling uses a simpler and more efficient way to sweep different types of lines, and relies heavily on exploring small local structures, rather than a much larger global structure. Experiments show that, on average, topological peeling outperforms topological walkb y 10 - 15% in execution time.