5540644
On Isomorphisms of Finite Cayley Graphs
Abstract A Cayley graph Cay(G,S) of a groupGis called a CI-graph if wheneverTis another subset ofGfor which Cay(G,S)≅ Cay(G,T), there exists an automorphism σ ofGsuch thatS^σ =  T. For a positive integerm, the groupGis said to have them-CI property if all Cayley graphs ofGof valencymare CI-graphs; further, ifGhas thek-CI property for allk ≤ m, thenGis called anm-CI-group, and a |G|-CI-groupGis called a CI-group. In this paper, we prove that Ais not a 5-CI-group, that SL(2,5) is not a 6-CI-group, and that all finite 6-CI-groups are soluble. Then we show that a nonabelian simple group has the 4-CI property if and only if it is A5, and that no nonabelian simple group has the 5-CI property. Also we give nine new examples of CI-groups of small order, which were found to be CI-groups with the assistance of a computer.
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.
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.
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.
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.
5432512
RankSQL: query algebra and optimization for relational top-k queries
This paper introduces RankSQL, a system that provides a systematic and principled framework to support efficient evaluations of ranking (top-k) queries in relational database systems (RDBMS), by extending relational algebra and query optimization. Previously, top-k query processing is studied in the middleware scenario or in RDBMS in a "piecemeal" fashion, i.e., focusing on specific operator or sitting outside the core of query engines. In contrast, we aim to support ranking as a first-class database construct. As a key insight, the new ranking relationship can be viewed as another logical property of data, parallel to the "membership" property of relational data model. While membership is essentially supported in RDBMS, the same support for ranking is clearly lacking. We address the fundamental integration of ranking in RDBMS in a way similar to how membership, i.e., Boolean filtering, is supported. We extend relational algebra by proposing a rank-relational model to capture the ranking property, and introducing new and extended operators to support ranking as a first-class construct. Enabled by the extended algebra, we present a pipelined and incremental execution model of ranking query plans (that cannot be expressed traditionally) based on a fundamental ranking principle. To optimize top-k queries, we propose a dimensional enumeration algorithm to explore the extended plan space by enumerating plans along two dual dimensions: ranking and membership. We also propose a sampling-based method to estimate the cardinality of rank-aware operators, for costing plans. Our experiments show the validity of our framework and the accuracy of the proposed estimation model.
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.
29028846
Reuse or Never Reuse the Deleted Labels in XML Query Processing Based on Labeling Schemes
To facilitate the XML query processing, several kinds of labeling schemes have been proposed. Based on the labeling schemes, the ancestor-descendant and parent-child relationships in XML queries can be quickly determined without accessing the original XML file. Recently, more researches are focused on how to update the labels when nodes are inserted into the XML. However how to process the deleted labels are not discussed previously. We think that the deleted labels can be processed in two different directions: (1) reuse all the deleted labels to control the label size increasing speed and improve the query performance; (2) never reuse the deleted labels to query different versions of the XML data based on labeling schemes. In this paper, we firstly introduce our previous work, called QED, which can completely avoid the re-labeling in XML updates. Secondly based on QED we propose a new algorithm, called Reuse, which can reuse all the deleted labels to control the label size increasing speed; meanwhile the Reuse algorithm can completely avoid the re-labeling also. Thirdly to query different versions of the XML data, we propose another new algorithm, called NeverReuse, which is the only approach that never reuses any deleted labels. Extensive experimental results show that the algorithms proposed in this paper can control the label size increasing speed when reusing all the deleted labels, and is the only approach to query different versions of the XML data based on labeling schemes.
2062689
Optimizing Large Join Queries in Mediation Systems
In data integration systems, queries posed to a mediator need to be translated into a sequence of queries to the underlying data sources. In a heterogeneous environment, with sources of diverse and limited query capabilities, not all the translations are feasible. In this paper, we study the problem of finding feasible and efficient query plans for mediator systems. We consider conjunctive queries on mediators and model the source capabilities through attribute-binding adornments. We use a simple cost model that focuses on the major costs in mediation systems, those involved with sending queries to sources and getting answers back. Under this metric, we develop two algorithms for source query sequencing - one based on a simple greedy strategy and another based on a partitioning scheme. The first algorithm produces optimal plans in some scenarios, and we show a linear bound on its worst case performance when it misses optimal plans. The second algorithm generates optimal plans in more scenarios, while having no bound on the margin by which it misses the optimal plans. We also report on the results of the experiments that study the performance of the two algorithms.
46337154
Minimum cross entropy thresholding
Abstract The threshold selection problem is solved by minimizing the cross entropy between the image and its segmented version. The cross entropy is formulated in a pixel-to-pixel basis between the two images and a computationally attractive algorithm employing the histogram is developed. Without making a priori assumptions about the population distribution, this method provides an unbiased estimate of a binarized version of the image in an information theoretic sense.