6695356
On orbital regular graphs and frobenius graphs
A graph is called a Frobenius graph if it is a connected orbital graph of a Frobenius group. In this paper, we show first that almost all orbital regular graphs are Frobenius graphs. Then we give a description of Frobenius graphs in terms of a family of (usually smaller) Frobenius graphs which are Cayley graphs for elementary abelian groups. Finally, based on this description, we obtain a formula for calculating the edge-forwarding index of Frobenius graphs.
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.
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.
15246731
Constructions of Self-complementary Circulants with No Multiplicative Isomorphisms
The main topic of the paper is the question of the existence of self-complementary Cayley graphs Cay(G, S) with the property S??=G#\S for all ??Aut(G). We answer this question in the positive by constructing an infinite family of self-complementary circulants with this property. Moreover, we obtain a complete classification of primes p for which there exist self-complementary circulants of order p2with this property.
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.
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.
39036081
Tongue image matching using color content
This paper addresses the problem of color image matching in medical diagnosis. The color matching of tongue images in different color spaces with different metrics have been investigated and is reported in this article. Two new metrics namely, sorted metric and probabilistic combined metric, are proposed. Existing distance measurements in coordinate space do not satisfy the reflexivity axiom. That means, they are not the valid metrics. To overcome this limitation, the sorted metric in coordinate space is proposed in coordinate space. To improve the matching performance, a probabilistic combined metric is proposed based on the theory of combining classifier. These metrics are applied for the matching of tongue color images and the results are encouraging.
29013572
Semi-supervised Learning in Medical Image Database
This paper presents a novel graph-based algorithm for solving the semi-supervised learning problem. The graph-based algorithm makes use of the recent advances in stochastic graph sampling technqiue and a modeling of the labeling consistency in semi-supervised learning. The quality of the algorithm is empirically evaluated on a synthetic clustering problem. The semi-supervised clustering is also applied to the problem of symptoms classification in medical image database and shows promising results.
516020
Efficient Processing of Ordered XML Twig Pattern
Finding all the occurrences of a twig pattern in an XML database is a core operation for efficient evaluation of XML queries. Holistic twig join algorithm has showed its superiority over binary decompose based approach due to efficient reducing intermediate results. The existing holistic join algorithms, however, cannot deal with ordered twig queries. A straightforward approach that first matches the unordered twig queries and then prunes away the undesired answers is obviously not optimal in most cases. In this paper, we study a novel holistic-processing algorithm, called OrderedTJ, for ordered twig queries. We show that OrderedTJ can identify a large query class to guarantee the I/O optimality. Finally, our experiments show the effectiveness, scalability and efficiency of our proposed algorithm.
9373274
A heuristic for parallel machine scheduling with agreeable due dates to minimize the number of late jobs
Abstract Given a set of identical parallel machines and a set of jobs with different due dates and release times, we consider the problem of finding a schedule such that the number of late jobs is minimized, where the given due dates and release times are assumed to be agreeable. A heuristic algorithm is presented and a dynamic programming lower bounding procedure is developed. Computational experiments are performed to show the effectiveness of the heuristic.
3403058
Selectivity Estimation for Fuzzy String Predicates in Large Data Sets
Many database applications have the emerging need to support fuzzy queries that ask for strings that are similar to a given string, such as "name similar to smith" and "telephone number similar to 412-0964." Query optimization needs the selectivity of such a fuzzy predicate, i.e., the fraction of records in the database that satisfy the condition. In this paper, we study the problem of estimating selectivities of fuzzy string predicates. We develop a novel technique, called SEPIA, to solve the problem. It groups strings into clusters, builds a histogram structure for each cluster, and constructs a global histogram for the database. It is based on the following intuition: given a query string q, a preselected string p in a cluster, and a string s in the cluster, based on the proximity between q and p, and the proximity between p and s, we can obtain a probability distribution from a global histogram about the similarity between q and s. We give a full specification of the technique using the edit distance function. We study challenges in adopting this technique, including how to construct the histogram structures, how to use them to do selectivity estimation, and how to alleviate the effect of non-uniform errors in the estimation. We discuss how to extend the techniques to other similarity functions. Our extensive experiments on real data sets show that this technique can accurately estimate selectivities of fuzzy string predicates.