19946044
On edge-Hamiltonian property of Cayley graphs
Abstract Let G be a group generated by X . A Cayley graph over G is defined as a graph G ( X ) whose vertex set is G and whose edge set consists of all unordered pairs [ a,b ] with a , b ϵ G and a -1 b ϵ X ∩ X -1 , where X -1 denotes the set { x -1 ∣ x ϵ X }. When X is a minimal generating set or each element of X is of even order, it can be shown that G ( X ) is Hamiltonian if it is edge-Hamiltonian. Hence every Cayley graph of order a power of 2 is edge-Hamiltonian.
18457324
On the higher-order edge toughness of a graph
For an integer c, 1?c??V(G)??1, we define the cth-order edge toughness of a graph G as tc(G)=min|X|?(G?X)?cX?E(G) & ?(G?X)>c The objective of this paper is to study this generalized concept of edge toughness. Besides giving the of the cth-order edge toughness ?c(G) of a graph G, we prove that `?c(G)?k if and only if G has k edge-disjoint spanning forests with exactly c components?. We also study the `balancity? of a graph G of order p and size q, which is defined as the smallest positive integer c such that ?c(G) = p/(p?c).
20337056
On 2-extendable abelian Cayley graphs
Abstract A graph G is 2-extendable if any two independent edges of G are contained in a perfect matching of G. A Cayley graph of even order over an abelian group is 2-extendable if and only if it is not isomorphic to any of the following circulant graphs: 1. (I) Z2n(1, 2n - 1), n ⩾ 3; 2. (II) Z2n(1, 2, 2n - 1, 2n - 2), n ⩾ 3; 3. (III) Z4n(1, 4n - 1, 2n), n ⩾ 2; 4. (IV) Z4n + 2(2,4n,2n + 1), n ⩾ 1; and 5. (V) Z4n +2(1,4n + 1, 2n, 2n + 2), n ⩾ 1.
27714693
Efficient Parallel Processing for K-Nearest-Neighbor Search in Spatial Databases
Even though the problem of k nearest neighbor (kNN) query is well-studied in serial environment, there is little prior work on parallel kNN search processing in parallel one. In this paper, we present the first Best-First based Parallel kNN (BFPkNN) query algorithm in a multi-disk setting, for efficient handling of kNN retrieval with arbitrary values of k by parallelization. The core of our method is to access more entries from multiple disks simultaneously and enable several effective pruning heuristics to discard non-qualifying entries. Extensive experiments with real and synthetic datasets confirm that BFPkNN significantly outperforms its competitors in both efficiency and scalability.
61166019
Footprints of information foragers: behaviour semantics of visual exploration
Social navigation exploits the knowledge and experience of peer users of information resources. A wide variety of visual-spatial approaches become increasingly popular as a means to optimize information access as well as to foster and sustain a virtual community among geographically distributed users. An information landscape is among the most appealing design options of representing and communicating the essence of distributed information resources to users. A fundamental and challenging issue is how an information landscape can be designed such that it will not only preserve the essence of the underlying information structure, but also accommodate the diversity of individual users. The majority of research in social navigation has been focusing on how to extract useful information from what is in common between users' profiles, their interests and preferences. In this article, we explore the role of modelling sequential behaviour patterns of Users in augmenting social navigation in thematic landscapes. In particular, we compare and analyse the trails of individual users in thematic spaces along with their cognitive ability measures. We are interested in whether such trails can provide useful guidance for social navigation if they are embedded in a visual-spatial environment. Furthermore, we are interested in whether such information can help users to learn from each other, for example, from the ones who have been successful in retrieving documents. In this article, we first describe how users' trails in sessions of an experimental study of visual information retrieval can be characterized by Hidden Markov Models. Trails of users with the most successful retrieval performance are used to estimate parameters of such models. Optimal virtual trails generated from the models are visualized and animated as if they were actual trails of individual users in order to highlight behavioural patterns that may foster social navigation. The findings of the research will provide direct input to the design of social navigation systems as well as to enrich theories of social navigation in a wider context. These findings will lead to the further development and consolidation of a tightly coupled paradigm of spatial, semantic and social navigation.
8200860
Digital imagery for significant cultural and historical materials
Digital imagery for significant cultural and historical materials is an emerging research field that bridges people, culture, and technologies. In this paper, we first discuss the great importance of this field. Then we focus on its four interrelated subareas: (1) creation and preservation, (2) retrieval, (3) presentation and usability, and (4) applications and use. We propose several mechanisms to encourage collaboration and argue that the field has high potential impact on our digital society. Finally, we make specific recommendations on what to pursue in this field.
16940810
Vertex and Tree Arboricities of Graphs
This paper studies the following variations of arboricity of graphs. The vertex (respectively, tree) arboricity of a graph G is the minimum number va(G) (respectively, ta(G)) of subsets into which the vertices of G can be partitioned so that each subset induces a forest (respectively, tree). This paper studies the vertex and the tree arboricities on various classes of graphs for exact values, algorithms, bounds, hamiltonicity and NP-completeness. The graphs investigated in this paper include block-cactus graphs, series-parallel graphs, cographs and planar graphs.
204988011
A class of additive multiplicative graph functions
For a fixed graph G, the capacity function for G, Po, is defined by Pc(H)= lim,__,®[yo(H')] TM, where y6(H) is the maximum number of disjoint G's in H. In [2], Hsu proved that Pr2 can be viewed as a lower bound for multiplicative increasing graph functions. But it was not known whether Pr2 is multiplicative or not. In this paper, we prove that Pc is multiplicative and additive for some graphs G which include K2. Some properties of Pc are also discussed in this paper.