45651558
The Solution of a Problem of Godsil on Cubic Cayley Graphs
In this short paper, we give a positive answer to a question of C. D. Godsil (1983,Europ. J. Combin.4, 25?32) regarding automorphisms of cubic Cayley graphs of 2-groups: “If Cay(G, S) is a cubic Cayley graph of a 2-groupGandA=AutCay(G, S), doesA1?1 imply Aut(G, S)?1?”
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.
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.
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.
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.
37859404
Single-machine scheduling to minimize the weighted number of early and tardy agreeable jobs
Abstract We consider a single-machine scheduling problem in which every job has a given target start time and a due-date. A job is early if processing commences before its start time and is tardy if it is completed after its due-date. The objective is to minimize the weighted number of early and tardy jobs, with the restriction that the start times and due-dates are “agreeable”, i.e., the start times must increase in the same sequence as the due-dates. We show that the problem is NP-complete in the strong sense. The complexity issues and algorithms for some special cases of this problem are discussed, and heuristic algorithms are developed for the general problem. Computational experiments are conducted to show the effectiveness of the heuristics.
13583163
On certain convex matrix sets
Abstract We study some nonnegative matrix sets and investigate the relations between their extreme points. The results obtained answer a question posed by Marshall and Olkin and extend a result of Fulkerson concerning permutation matrices.
14325657
An approach to reducing the labeling cost of Markov random fields within an infinite label space
This work proposes a novel idea, called SOIL, for reducing the computational complexity of the maximum a posteriori optimization problem using Markov random fields (MRFs). The local characteristics of MRFs are employed so that the searching in a virtually infinite label space is confined in a small finite space. Globally, the number of labels allowed is as many as the number of image sites while locally the optimal label is sampled from a space consisting of the labels assigned to the four-neighbor plus a random one. Neither the prior knowledge about the number of classes nor the estimation phase of the class number is required in this work. The proposed method is applied to the problem of texture segmentation and the result is compared with those obtained from conventional methods.
14960694
Comparative analysis of gene sets in the gene ontology space under the multiple hypothesis testing framework
The gene ontology (GO) resource can be used as a powerful tool to uncover the properties shared among, and specific to, a list of genes produced by high-throughput functional genomics studies, such as microarray studies. In the comparative analysis of several gene lists, researchers maybe interested in knowing which GO terms are enriched in one list of genes but relatively depleted in another. Statistical tests such as Fisher's exact test or Chi-square test can be performed to search for such GO terms. However, because multiple GO terms are tested simultaneously, individual p-values from individual tests do not serve as good indicators for picking GO terms. Furthermore, these multiple tests are highly correlated, usual multiple testing procedures that work under an independence assumption are not applicable. In this paper we introduce a procedure, based on false discovery rate (FDR), to treat this correlated multiple testing problem. This procedure calculates a moderately conserved estimator of q-value for every GO term. We identify the GO terms with q-values that satisfy a desired level as the significant GO terms. This procedure has been implemented into the GoSurfer software. GoSurfer is a windows based graphical data mining tool. It is freely available at http://www.gosurfer.org.
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.