19994829
Finite Abelian Groups with the m-DCI Property
10480954
Isomorphisms of Finite Cayley Digraphs of Bounded Valency
LetGbe a finite group,Sa subset ofG\{1}, and let Cay(G,S) denote the Cayley digraph ofGwith respect toS. If, for all subsetsS,TofG\{1} of size at mostm, Cay(G,S)?Cay(G,T) implies thatS?=Tfor some??Aut(G), thenGis called anm-DCI-group. In this paper, we prove that, form?2, allm-DCI-groups are of the formU×V, where (|U|, |V|)=1,Uis abelian andVbelongs to an explicitly determined list of groups. Moreover Sylow subgroups of such groups satisfy some very restrictive conditions.
23350440
On Isomorphisms of Connected Cayley Graphs, II
A Cayley graph or digraph Cay(G, S) of a finite groupGis called aCI-graphofGif, for anyT?G, Cay(G, S)?Cay(G, T) if and only ifS?=Tfor some??Aut(G). We study the problem of determining which Cayley graphs and digraphs for a given group are CI-graphs. A finite groupGis called aconnected m-DCI-group(orconnected m-CI-group) if all connected Cayley digraphs (or connected Cayley graphs, respectively) ofGof (out)-valency at most m are CI-graphs. For a groupG, letp(G) be the smallest prime divisor of |G|. It was previously shown that all finite groupsGare connected (p(G)?1)-DCI-groups and all finite groupsGare connected 2(p(G)?1)-CI-groups. In this paper, for every primep, we construct infinitely many finite groupsGsuch thatp(G)=pandGis neither a connectedp-DCI-group nor a connected 2p-CI-group, which provides solutions for several open problems in this area.
27555290
Constructing Homogeneous Factorisations of Complete Graphs and Digraphs
Abstract. A homogeneous factorisation of a complete graph Kn is a partition of the edge set that is invariant under a subgroup G of Sn such that G is transitive on the parts of the partition and induces a vertex-transitive automorphism group on the graph corresponding to each part. A product construction is given for such factorisations.
206571122
On Half-Transitive Metacirculant Graphs of Prime-Power Order
In this paper, infinitely many graphs of large valency which are half-transitive (that is vertex- and edge-transitive but not arc-transitive) are constructed, and a complete classification is given of half-transitive metacirculant graphs of order a p-power and valency less than 2p, where p is a prime. In particular, it is shown that, for any odd prime p, integers n?3 and k?2 such that k divides p?1, there are exactly (pn?2?1)/2+pn?3?1 nonisomorphic connected half-transitive metacirculants of order pn and valency 2k.
16649809
Relative difference sets fixed by inversion and Cayley graphs
Using graph theoretical technique, we present a construction of a (30, 2, 29, 14)-relative difference set fixed by inversion in the smallest finite simple group--the alternating group A5. To our knowledge this is the first example known of relative difference sets in the finite simple groups with a non-trivial forbidden subgroup. A connection is then established between some relative difference sets fixed by inversion and certain antipodal distance-regular Cayley graphs. With the connection, several families of antipodal distance-regular Cayley graphs which are coverings of complete graphs are presented.
222927
Regularized color clustering in medical image database
A regularized color clustering algorithm is proposed to solve the color clustering problem in medical image database. By incorporating both measures of cluster separability and cluster compactness, regularized color clustering allows the automatic extraction of significant color groups with varying populations. Experimental results in different color spaces show that the regularized color clustering gives superior results in extracting significant distinct/abnormal color clusters without significant increases in cluster compactness. Furthermore, results of color clustering in different color spaces show that the LUV color space is more suitable for color clustering. Methods for selecting the regularization constants have also been suggested.
15577452
New Complexity Results for Some Linear Counting Problems Using Minimal Solutions to Linear Diophantine Equations
The linear reachability problem is to decide whether there is an execution path in a given finite state transition system such that the counts of labels on the path satisfy a given linear constraint. Using results on minimal solutions (in nonnegative integers) for linear Diophantine systems, we obtain new complexity results for the problem, as well as for other linear counting problems of finite state transition systems and timed automata. In contrast to previously known results, the complexity bounds obtained in this paper are polynomial in the size of the transition system in consideration, when the linear constraint is fixed.
139092767
An Improved Prefix Labeling Scheme: A Binary String Approach for Dynamic Ordered XML
A number of labeling schemes have been designed to facilitate the query of XML, based on which the ancestor-descendant relationship between any two nodes can be determined quickly. Another important feature of XML is that the elements in XML are intrinsically ordered. However the label update cost is high based on the present labeling schemes. They have to re-label the existing nodes or re-calculate some values when inserting an order-sensitive element. Thus it is important to design a scheme that supports order-sensitive queries, yet it has low label update cost. In this paper, we design a binary string prefix scheme which supports order-sensitive update without any re-labeling or re-calculation. Theoretical analysis and experimental results also show that this scheme is compact compared to the existing dynamic labeling schemes, and it provides efficient support to both ordered and un-ordered queries.
3813961
Using MMQ Model for Performance Simulation of Storage Area Network
The infrastructures of SANs are complex, and the implementations/designs of SANs are varied. So finding a proper modeling method to analysis and simulate SAN performance in a systemic/consistent way is very important for the work efficiency of SAN designers and performance tuners. This paper proposes a methodology of using a multi-tier multiserver queue (MMQ) network system to model a SAN system, which can be generalized to different SAN instances neatly, and be used for both performance analysis and simulation. Besides the main idea and high-level MMQ model, the application of this method is illustrated by constructing a software simulator, which is also designed and implemented in a systemic and reusable style. The simulation validation shows that maximum error range is less than 10%. So we can consider this method a sound solution for the quick performance design comparison and analysis of SAN.
15126663
Semi-fragile watermarking scheme for authentication of JPEG images
With the increasing popularity of JPEG images, a need arises to devise effective watermarking techniques which consider JPEG compression as an acceptable manipulation. In this paper, we present a semi-fragile watermarking scheme which embeds a watermark in the quantized DCT domain. It is tolerant to JPEG compression to a pre-determined lowest quality factor, but is sensitive to all other malicious attacks, either in spatial or transform domains. Feature codes are extracted based on the relative sign and magnitudes of coefficients, and these are invariant due to an important property of JPEG compression. The employment of a nine-neighborhood mechanism ensures that non-deterministic block-wise dependence is achieved. Analysis and experimental results are provided to support the effectiveness of the scheme.