247296
On Finite s-Transitive Graphs of Odd Order
It is shown that, for a positive integer s, there exists an s-transitive graph of odd order if and only if s?3 and that, for s=2 or 3, an s-transitive graph of odd order is a normal cover of a graph for which there is an automorphism group that is almost simple and s-transitive.
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.
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.
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.
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.
35216739
Image Smoothing Using Parametric Relaxation
Abstract A new image-smoothing algorithm which smooths the image while preserving discontinuities is developed. The method poses the smoothing problem as an estimation problem of the maximum a posteriori probability of a pixel having a certain gray level. A prior probability density function is assigned to each pixel from the raw data, which is an estimate of the gray-level uncertainty. The algorithm is an application of the random measure field in image processing. Contextual information from neighbors is used in refining the probability distribution of each pixel, which is a continuous version of the relaxation algorithm. The way of parametrizing the probability functions enables the derivation of an efficient iterative formula for updating the gray-level values.
561187
Bilateral negotiation decisions with uncertain dynamic outside options
Negotiation is an important phase of e-contracting. E-contracting requires a proper negotiation model to effectively support negotiation decisions or automate the negotiation process. When an entity negotiates with a potential contractor, there may be some alternatives that exist simultaneously with the potential contractor, and/or some may present themselves in the future. We present a model for bilateral contract negotiations that considers the uncertain and dynamic outside options. Outside options affect the negotiation strategies via their impact on the reservation price. The model is composed of three modules, single-threaded negotiations, synchronized multi-threaded negotiations, and dynamic multi-threaded negotiations. These three models embody increased sophistication and complexity. The single-threaded negotiation model provides negotiation strategies without specifically considering outside options. The model of synchronized multi-threaded negotiations builds on the single-threaded negotiation model and considers the presence of concurrently existing outside options. The model of dynamic multi-threaded negotiations expands the synchronized multi-threaded model by considering the uncertain outside options that may come dynamically in the future. Experimental analysis is provided to characterize the impact of outside options on the negotiation strategy and performances.
6531229
Multiresolution image segmentation integrating Gibbs sampler and region merging algorithm
This work approaches the texture segmentation problem by incorporating Gibbs sampler (i.e., the combination of Markov random fields and simulated annealing) and a region-merging process within a multiresolution structure with "high class resolution and low boundary resolution" at high levels and "low class resolution and high boundary resolution" at lower ones. As the algorithm descends the multiresolution structure, the coarse segmentation results are propagated down to the lower levels so as to reduce the inherent class-boundary uncertainty and to improve the segmentation accuracy. The computational complexity and frequent occurrences of over-segmentation of Gibbs sampler are addressed and the computationally and functionally effective region-merging process is included to allow Gibbs sampler to start its annealing schedule at relatively low pseudo-temperature and to guide the search trajectory away from local minima associated with over-segmented configurations.
1209241
Spectral Energy Minimization for Semi-supervised Learning
Data mining problems often involve a large amount of unlabeled data and there is often very limited known information on the dataset. In such scenario, semi-supervised learning can often improve classification performance by utilizing unlabeled data for learning. In this paper, we proposed a novel approach to semi-supervised learning as as an optimization of both the classification energy and cluster compactness energy in the unlabeled dataset. The resulting integer programming problem is relaxed by a semi-definite relaxation where efficient solution can be obtained. Furthermore, the spectral graph methods provide improved energy minimization via the incorporation of additional criteria. Results on UCI datasets show promising results.