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.
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.
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.
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.
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.
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.
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.
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.
3194322
Efficient record linkage in large data sets
This paper describes an efficient approach to record linkage. Given two lists of records, the record-linkage problem consists of determining all pairs that are similar to each other where the overall similarity between two records is defined based on domain-specific similarities over individual attributes constituting the record. The record-linkage problem arises naturally in the context of data cleansing that usually precedes data analysis and mining. We explore a novel approach to this problem. For each attribute of records, we first map values to a multidimensional Euclidean space that preserves domain-specific similarity. Many mapping algorithms can be applied, and we use the FastMap approach as an example. Given the merging rule that defines when two records are Similar a set of attributes are chosen along which the merge will proceed A multidimensional similarity join over the chosen attributes is used to determine similar pairs of records. Our extensive experiments using real data sets show that our solution has very good efficiency and accuracy.
5288493
Indexing of variable length multi-attribute motion data
Haptic data such as 3D motion capture data and sign language animation data are new forms of multimedia data. The motion data is multi-attribute, and indexing of multi-attribute data is important for quickly pruning the majority of irrelevant motions in order to have real-time animation applications. Indexing of multi-attribute data has been attempted for data of a few attributes by using R-tree or its variants after dimensionality reduction. In this paper, we exploit the singular value decomposition (SVD) properties of multi-attribute motion data matrices to obtain one representative vector for each of the motion data matrices of dozens or hundreds of attributes. Based on this representative vector, we propose a simple and efficient interval-tree based index structure for indexing motion data with large amount of attributes. At each tree level, only one component of the query vector needs to be checked during searching, comparing to all the components of the query vector that should get involved if an R-tree or its variants are used for indexing. Searching time is independent of the number of pattern motions indexed by the tree, making the index structure well scalable to large data repositories. Experiments show that up to 91∼93% irrelevant motions can be pruned for a query with no false dismissals, and the query searching time is less than 30 μ <i>s</i> with the existence of motion variations.