6225887
Hamiltonian decompositions of random bipartite regular graphs
We prove a complete hamiltonian decomposition theorem for random bipartite regular graphs, thereby verifying a conjecture of Robinson and Wormald. The main step is to prove contiguity (a kind of asymptotic equivalence) of two probabilistic models of 4-regular bipartite graphs; namely, the uniform model, and the model obtained by taking the union of two independent, uniformly chosen bipartite Hamilton cycles, conditioned on forming no multiple edges. The proof uses the small subgraph conditioning method to establish contiguity, while the differential equation method is used to analyse a critical quantity.
18028546
Divide and conquer martingales and the number of triangles in a random graph
The goal of this paper is to present a novel application of a recent and useful martingale inequality. As an illustration, we prove an essentially sharp bound for the probability that a random graph contains significantly more triangles than expected.
11005224
A phase transition for avoiding a giant component
Let c be a constant and (e1, f1), (e2, f2), . . . , (ecn, fcn) be a sequence of ordered pairs of edges from the complete graph Kn chosen uniformly and independently at random. We prove that there exists a constant c2 such that if c > c2 then whp every graph which contains at least one edge from each ordered pair (ei, fi) has a component of size Ω(n) and if c < c2 then whp there is a graph containing at least one edge from each pair that has no component with more than O ( n1−2 ) vertices, where 2 is a constant that depends on c2− c. The constant c2 is roughly 0.97677.
3103350
Random Matchings in Regular Graphs
d-regular graph G, let M be chosen uniformly at random from the set of all matchings of G, and for let be the probability that M does not cover x.We show that for large d, the 's and the mean μ and variance of are determined to within small tolerances just by d and (in the case of μ and ) :
Theorem. For any d-regular graph G,
(a), so that ,
(b),where the rates of convergence depend only on d.
2320085
Generating random regular graphs
Random regular graphs play a central role in combinatorics and theoretical computer science. In this paper, we analyze a simple algorithm introduced by Steger and Wormald [9] and prove that it produces an asymptotically uniform random regular graph in a polynomial time. Precisely, for fixed d and n with d=O(n1/3-ε), it is shown that the algorithm generates an asymptotically uniform random d-regular graph on n vertices in time O(nd2). This confirms a conjecture of Wormald. The key ingredient in the proof is a recently developed concentration inequality by the second author.Besides being perhaps the only algorithm which works for relatively large d in practical time, our result also has a significant theoretical value, as it can be used to derive many properties of uniform random regular graphs.
12050804
On the asymmetry of random regular graphs and random graphs
This paper studies the symmetry of random regular graphs and random graphs. Our main result shows that for all 3 ≤ d ≤ n - 4 the random d-regular graph on n vertices almost surely has no nontrivial automorphisms. This answers an open question of N. Wormald [13].
62653029
The BlackWidow High-Radix Clos Network
This paper describes the radix-64 folded-Clos network of the Cray BlackWidow scalable vector multiprocessor. We describe the BlackWidow network which scales to 32K processors with a worstcase diameter of seven hops, and the underlying high-radix router microarchitecture and its implementation. By using a high-radix router with many narrow channels we are able to take advantage of the higher pin density and faster signaling rates available in modern ASIC technology. The BlackWidow router is an 800 MHz ASIC with 64 18.75Gb/s bidirectional ports for an aggregate offchip bandwidth of 2.4Tb/s. Each port consists of three 6.25Gb/s differential signals in each direction. The router supports deterministic and adaptive packet routing with separate buffering for request and reply virtual channels. The router is organized hierarchically [13] as an 8�8 array of tiles which simplifies arbitration by avoiding long wires in the arbiters. Each tile of the array contains a router port, its associated buffering, and an 8�8 router subswitch. The router ASIC is implemented in a 90nm CMOS standard cell ASIC technology and went from concept to tapeout in 17 months.
10913816
A Web Services-enabled marketplace architecture for negotiation process management
As the eBusiness environment becomes more pervasive and dynamic, negotiations between companies are required more frequently than ever. Despite its potential value and the progress in research, the adoption of negotiation systems has been slow in practice. We believe one reason for this is insufficient consideration of process management aspects such as process design, description, and deployment. Business negotiations must be approached from the process management perspective since they take place in the context of corporate processes such as procurement or sales.In this paper, we study system support and automation of business-to-business (B2B) negotiations from the process management perspective. We propose a Web Services-enabled marketplace architecture for negotiation process management and refine it by adding pattern-based process composition. We validate the concept by implementing the proposed architecture using BPEL4WS and evaluating it from various perspectives.
2251486
Euclidean and Hermitian self-dual MDS codes over large finite fields
The first author constructed new extremal binary self-dual codes (IEEE Trans. Inform. Theory 47 (2001) 386-393) and new self-dual codes over GF(4) with the highest known minimum weights (IEEE Trans. Inform. Theory 47 (2001) 1575-1580). The method used was to build self-dual codes from a given self-dual code of a smaller length. In this paper, we develop a complete generalization of this method for the Euclidean and Hermitian self-dual codes over finite fields GF(q). Using this method we construct many Euclidean and Hermitian self-dual MDS (or near MDS) codes of length up to 12 over various finite fields GF(q), where q = 8, 9, 16, 25, 32, 41, 49, 53, 64, 81, and 128. Our results on the minimum weights of (near) MDS self-dual codes over large fields give a better bound than the Pless-Pierce bound obtained from a modified Gilbert-Varshamov bound.
1514813
Temporal Query Processing Using Spatially-Partitioned Method
In this paper, we propose a general spatiallypartitioned temporal operation model, called 3D-TOM, and partition-based join algorithms for various types of temporal join in the proposed model. The temporal operators addressed in this paper include overlap, precede, follow, and equal. Some factors which a ect the performance of the proposed method are also discussed.
2978705
Reconstructing the Temporal Ordering of Biological Samples Using Microarray Data
MOTIVATION
Accurate time series for biological processes are difficult to estimate due to problems of synchronization, temporal sampling and rate heterogeneity. Methods are needed that can utilize multi-dimensional data, such as those resulting from DNA microarray experiments, in order to reconstruct time series from unordered or poorly ordered sets of observations.


RESULTS
We present a set of algorithms for estimating temporal orderings from unordered sets of sample elements. The techniques we describe are based on modifications of a minimum-spanning tree calculated from a weighted, undirected graph. We demonstrate the efficacy of our approach by applying these techniques to an artificial data set as well as several gene expression data sets derived from DNA microarray experiments. In addition to estimating orderings, the techniques we describe also provide useful heuristics for assessing relevant properties of sample datasets such as noise and sampling intensity, and we show how a data structure called a PQ-tree can be used to represent uncertainty in a reconstructed ordering.


AVAILABILITY
Academic implementations of the ordering algorithms are available as source code (in the programming language Python) on our web site, along with documentation on their use. The artificial 'jelly roll' data set upon which the algorithm was tested is also available from this web site. The publicly available gene expression data may be found at http://genome-www.stanford.edu/cellcycle/ and http://caulobacter.stanford.edu/CellCycle/.