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.
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.
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.
6695356
On orbital regular graphs and frobenius graphs
A graph is called a Frobenius graph if it is a connected orbital graph of a Frobenius group. In this paper, we show first that almost all orbital regular graphs are Frobenius graphs. Then we give a description of Frobenius graphs in terms of a family of (usually smaller) Frobenius graphs which are Cayley graphs for elementary abelian groups. Finally, based on this description, we obtain a formula for calculating the edge-forwarding index of Frobenius graphs.
15840170
Tetravalent edge-transitive Cayley graphs with odd number of vertices
A characterisation is given of edge-transitive Cayley graphs of valency 4 on odd number of vertices. The characterisation is then applied to solve several problems in the area of edge-transitive graphs: answering a question proposed by Xu [Automorphism groups and isomorphisms of Cayley graphs, Discrete Math. 182 (1998) 309-319] regarding normal Cayley graphs; providing a method for constructing edge-transitive graphs of valency 4 with arbitrarily large vertex-stabiliser; constructing and characterising a new family of half-transitive graphs. Also this study leads to a construction of the first family of arc-transitive graphs of valency 4 which are non-Cayley graphs and have a 'nice' isomorphic 2-factorisation.
15126663
Semi-fragile watermarking scheme for authentication of JPEG images
With the increasing popularity of JPEG images, a need arises to devise effective watermarking techniques which consider JPEG compression as an acceptable manipulation. In this paper, we present a semi-fragile watermarking scheme which embeds a watermark in the quantized DCT domain. It is tolerant to JPEG compression to a pre-determined lowest quality factor, but is sensitive to all other malicious attacks, either in spatial or transform domains. Feature codes are extracted based on the relative sign and magnitudes of coefficients, and these are invariant due to an important property of JPEG compression. The employment of a nine-neighborhood mechanism ensures that non-deterministic block-wise dependence is achieved. Analysis and experimental results are provided to support the effectiveness of the scheme.
15908075
On Answering Queries in the Presence of Limited Access Patterns
In information-integration systems, source relations often have limitations on access patterns to their data; i.e., when one must provide values for certain attributes of a relation in order to retrieve its tuples. In this paper we consider the following fundamental problem: can we compute the complete answer to a query by accessing the relations with legal patterns? The complete answer to a query is the answer that we could compute if we could retrieve all the tuples from the relations. We give algorithms for solving the problem for various classes of queries, including conjunctive queries, unions of conjunctive queries, and conjunctive queries with arithmetic comparisons. We prove the problem is undecidable for datalog queries. If the complete answer to a query cannot be computed, we often need to compute its maximal answer. The second problem we study is, given two conjunctive queries on relations with limited access patterns, how to test whether the maximal answer to the first query is contained in the maximal answer to the second one? We show this problem is decidable using the results of monadic programs.
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.
39573011
The adaptive modulated wavelet transform image representation
In this paper, a new, called the adaptive modulated wavelet transform (AMWT) image representation is presented. One of the attractive features is that the informative instantaneous frequencies of images can be taken into account to improve the representation performance via adaptation of the modulating frequencies involved. The transform coefficients in both wavelet and modulated wavelet domains are uniformly quantized with several quantization levels. The computed peak signal-to-noise ratio values and entropies are used as rate distortion curves for performance comparison. Experimental results show that AMWT out performs wavelet transform for representing images containing textures with rapid variation in grays.
9373274
A heuristic for parallel machine scheduling with agreeable due dates to minimize the number of late jobs
Abstract Given a set of identical parallel machines and a set of jobs with different due dates and release times, we consider the problem of finding a schedule such that the number of late jobs is minimized, where the given due dates and release times are assumed to be agreeable. A heuristic algorithm is presented and a dynamic programming lower bounding procedure is developed. Computational experiments are performed to show the effectiveness of the heuristic.