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.
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.
247296
On Finite s-Transitive Graphs of Odd Order
It is shown that, for a positive integer s, there exists an s-transitive graph of odd order if and only if s?3 and that, for s=2 or 3, an s-transitive graph of odd order is a normal cover of a graph for which there is an automorphism group that is almost simple and s-transitive.
22734385
On cubic Cayley graphs of finite simple groups
For a finite group G, a Cayley graph Cay(G,S) is said to be normal if the group GR of right translations on G is a normal subgroup of the full automorphism group of Cay(G,S). In this paper, we prove that, for most finite simple groups G, connected cubic Cayley graphs of G are all normal. Then we apply this result to study a problem related to isomorphisms of Cayley graphs, and a problem regarding graphical regular representations of finite simple groups. The proof of the main result depends on the classification of finite simple groups.
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.
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.
2190827
Chosen-Plaintext Cryptanalysis of a Clipped-Neural-Network-Based Chaotic Cipher
At ISNN'04, a novel symmetric cipher was proposed, by combining a chaotic signal and a clipped neural network (CNN) for encryption. The present paper analyzes the security of this chaotic cipher against chosen-plaintext attacks, and points out that this cipher can be broken by a chosen-plaintext attack. Experimental analyses are given to support the feasibility of the proposed attack.
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.
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.
7959495
Distributed multi-hop scheduling and medium access with delay and throughput constraints
Providing quality of service in random access multi-hop wireless networks requires support from both medium access and packet scheduling algorithms. However, due to the distributed nature of ad hoc networks, nodes may not be able to determine the next packet that would be transmitted in a (hypothetical) centralized and ideal dynamic priority scheduler. In this paper, we develop two mechanisms for QoS communication in multi-hop wireless networks. First, we devise distributed priority scheduling a technique that piggybacks the priority tag of a node's head-of-line packet onto handshake and data packets; e.g., RTS/DATA packets in IEEE 802.11. By monitoring transmitted packets, each node maintains a scheduling table which is used to assess the node's priority level relative to other nodes. We then incorporate this scheduling table into existing IEEE 802.11 priority back-off schemes to approximate the idealized schedule. Second, we observe that congestion, link errors, and the random nature of medium access prohibit an exact realization of the ideal schedule. Consequently, we devise a scheduling scheme termedmulti-hop coordinationso that downstream nodes can increase a packet's relative priority to make up for excessive delays incurred upstream. We next develop a simple analytical model to quantitatively explore these two mechanisms. In the former case, we study the impact of the probability of overhearing another packet's priority index on the scheme's ability to achieve the ideal schedule. In the latter case, we explore the role of multi-hop coordination in increasing the probability that a packet satisfies its end-to-end QoS target. Finally, we perform a set of ns-2 simulations to study the scheme's performance under more realistic conditions.
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.