29832620
A Family of Quasiprimitive 2-arc Transitive Graphs which Have Non-quasiprimitive Full Automorphism Groups
For each primep? 1 or ?1(mod24), we construct a (PSL(2,p), 2)-arc transitive graph ? of valency 4 such that Aut ?=PSL(2,p) ×Z2. Thus there exists an infinite family of quasiprimitive 2-arc transitive graphs which have non-quasiprimitive full automorphism groups.
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.
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.
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.
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.
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.
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.
10581413
Answering queries with useful bindings
In information-integration systems, sources may have diverse and limited query capabilities. To obtain maximum information from these restrictive sources to answer a query, one can access sources that are not specified in the query (i.e., off-query sources). In this article, we propose a query-planning framework to answer queries in the presence of limited access patterns. In the framework, a query and source descriptions are translated to a recursive datalog program. We then solve optimization problems in this framework, including how to decide whether accessing off-query sources is necessary, how to choose useful sources for a query, and how to test query containment. We develop algorithms to solve these problems, and thus construct an efficient program to answer a query.
16910052
On best restricted range approximation in continuous complex-valued function spaces
To provide a Kolmogorov-type condition for characterizing a best approximation in a continuous complex-valued function space, it is usually assumed that the family of closed convex sets in the complex plane used to restrict the range satisfies a strong interior-point condition, and this excludes the interesting case when some @W"t is a line-segment or a singleton. The main aim of the present paper is to remove this restriction by virtue of a study of the notion of the strong CHIP for an infinite system of closed convex sets in a continuous complex-valued function space.