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.
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.
22734385
On cubic Cayley graphs of finite simple groups
For a finite group G, a Cayley graph Cay(G,S) is said to be normal if the group GR of right translations on G is a normal subgroup of the full automorphism group of Cay(G,S). In this paper, we prove that, for most finite simple groups G, connected cubic Cayley graphs of G are all normal. Then we apply this result to study a problem related to isomorphisms of Cayley graphs, and a problem regarding graphical regular representations of finite simple groups. The proof of the main result depends on the classification of finite simple groups.
35890566
On Isomorphisms of Minimal Cayley Graphs and Digraphs
Abstract. A Cayley graph or digraph Cay(G,S) is called a CI-graph of G if, for any T⊂G, Cay(G,S)≅Cay(G,T) if and only if Sσ=T for some σ∈Aut(G). The aim of this paper is to characterize finite abelian groups for which all minimal Cayley graphs and digraphs are CI-graphs.
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.
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.
19930573
Learning Pathological Characteristics from User's Relevance Feedback for Content-Based Mammogram Retrieval
Content-based image retrieval (CBIR) has been proposed to address the problem of image retrieval from medical image databases. Relevance feedback, explaining the user's query concept, can be used to bridge the semantic gap and improve the performance of CBIR systems. This paper proposes a learning method for relevance feedback, which utilizes probabilistic model to generalize the 2-class problem and provide an estimate of probability of class membership. To build the probabilistic model, support vector machine (SVM) is applied to classify the mammograms, and then scale them to the probability of class membership. Experimental results show that the proposed learning method can effectively improve the average precision rate from 40% to 62% through five iterations of relevance feedback rounds
2028079
Strong uniqueness of the restricted Chebyshev center with respect to an RS-set in a Banach space
Let G be a strict RS-set (resp. an RS-set) in X and let F be a bounded (resp. totally bounded) subset of X satisfying rG (F) < rx (F), where rG (F) is the restricted Chebyshev radius of F with respect to G. It is shown that the restricted Chebyshev center of F with respect to G is strongly unique in the case when X is a real Banach space, and that, under some additional convexity assumptions, the restricted Chebyshev center of F with respect to G is strongly unique of order α ≥ 2 in the case when X is a complex Banach space.
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.
10617810
Integrated Requirement Selection and Scheduling for the Release Planning of a Software Product
This paper investigates two integer linear programming models that integrate requirement scheduling into software release planning. The first model can schedule the development of the requirements for the new release exactly in time so that the project span is minimized and the resource and precedence constraints are satisfied. The second model is for combined requirement selection and scheduling, which can not only maximize revenues but also calculates an on-time-delivery project schedule simultaneously. Two simulations are presented to examine the influence of precedence constraints and compare the differences of the traditional prioritization models and the two new ones. The simulation results suggest that requirement dependency can significantly influence the project plan and the combined model for requirement selection and scheduling is better in the sense of efficiency and on-time delivery.
2275351
On best uniform restricted range approximation in complex-valued continuous function spaces
We investigate the problem of best restricted range approximation of complex-valued continuous functions for a very general system of restrictions. Our results, including the characterizations, uniqueness and strong uniqueness, extend all recent results due to Smirnovs.