18486242
Perfect matchings in random uniform hypergraphs
Let ℋk(n, p) be the random k-uniform hypergraph on V = [n] with edge probability p. Motivated by a theorem of Erdős and Renyi 7 regarding when a random graph G(n, p) = ℋ2(n, p) has a perfect matching, the following conjecture may be raised. (See J. Schmidt and E. Shamir 16 for a weaker version.) Conjecture. Let k|n for fixed k ≥ 3, and the expected degree d(n, p) = p(). Then 
 
 
 
 
 
 
(Erdős and Renyi 7 proved this for G(n, p).) Assuming d(n, p)/n1/2 ∞, Schmidt and Shamir 16 were able to prove that ℋk(n, p) contains a perfect matching with probability 1 − o(1). Frieze and Janson 8 showed that a weaker condition d(n, p)/n1/3 ∞ was enough. In this paper, we further weaken the condition to 
 
 
 
 
 
 
A condition for a similar problem about a perfect triangle packing of G(n, p) is also obtained. A perfect triangle packing of a graph is a collection of vertex disjoint triangles whose union is the entire vertex set. Improving a condition p ≥ cn−2/3+1/15 of Krivelevich 12, it is shown that if 3|n and p ≫ n−2/3+1/18, then 
 
 
 
 
 
 
© 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 111–132, 2003
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.
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].
10769698
Regular subgraphs of random graphs
In this paper, we prove that there exists a function ρk = (4 + o(1))k such that G(n, ρ/n) contains a k-regular graph with high probability whenever ρ > ρk. In the case of k = 3, it is also shown that G(n, ρ/n) contains a 3-regular graph with high probability whenever ρ > λ ≈ 5.1494. These are the first constant bounds on the average degree in G(n, p) for the existence of a k-regular subgraph. We also discuss the appearance of 3-regular subgraphs in cores of random graphs.
14012710
Interference-Minimizing Colorings of Regular Graphs
Communications problems that involve frequency interference, such as the channel assignment problem in the design of cellular telephone networks, can be cast as graph coloring problems in which the frequencies (colors) assigned to an edge's vertices interfere if they are too similar. The paper considers situations modeled by vertex-coloring d-regular graphs with n vertices using a color set 1, 2,..., n, where colors i and j are said to interfere if their circular distance $\min \{ | i-j | , n- | i-j | \}$ does not exceed a given threshold value $\alpha$. Given a d-regular graph G and threshold $\alpha$, an interference-minimizing coloring is a coloring of vertices that minimizes the number of edges that interfere. Let $I_\alpha (G)$ denote the minimum number of interfering edges in such a coloring of $G$. For most triples $(n, \alpha ,d),$ we determine the minimum value of $I_\alpha (G)$ over all d-regular graphs and find graphs that attain it. In determining when this minimum value is 0, we prove that for $r \geq 3$ there exists a d-regular graph G on n vertices that is r-colorable whenever $d \leq (1- \frac{1}{r}) n-1$ and nd is even. We also study the maximum value of $I_\alpha (G)$ over all d-regular graphs and find graphs that attain this maximum in many cases.
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.
16087620
A Corpus-Based Learning Method of Compound Noun Indexing Rules for Korean
In Korean information retrieval, compound nouns play an important role in improving precision in search experiments. There are two major approaches to compound noun indexing in Korean: statistical and linguistic. Each method, however, has its own shortcomings, such as limitations when indexing diverse types of compound nouns, over-generation of compound nouns, and data sparseness in training. In this paper, we propose a corpus-based learning method, which can index diverse types of compound nouns using rules automatically extracted from a large corpus. The automatic learning method is more portable and requires less human effort, although it exhibits a performance level similar to the manual-linguistic approach. We also present a new filtering method to solve the problems of compound noun over-generation and data sparseness.
12627938
Exploring Fault-Tolerant Network-on-Chip Architectures
The advent of deep sub-micron technology has exacerbated reliability issues in on-chip interconnects. In particular, single event upsets, such as soft errors, and hard faults are rapidly becoming a force to be reckoned with. This spiraling trend highlights the importance of detailed analysis of these reliability hazards and the incorporation of comprehensive protection measures into all network-on-chip (NoC) designs. In this paper, we examine the impact of transient failures on the reliability of on-chip interconnects and develop comprehensive counter-measures to either prevent or recover from them. In this regard, we propose several novel schemes to remedy various kinds of soft error symptoms, while keeping area and power overhead at a minimum. Our proposed solutions are architected to fully exploit the available infrastructures in an NoC and enable versatile reuse of valuable resources. The effectiveness of the proposed techniques has been validated using a cycle-accurate simulator
5951770
MetaCore: an application specific DSP development system
This paper describes the MetaCore system which is an ASIP (Application-Specific Instruction set Processor) development system targeted for DSP applications. The goal of MetaCore system is to offer an efficient design methodology meeting specifications given as a combination of performance, cost and design turnaround time.
MetaCore system consists of two major design stages: design exploration and design generation. In the design exploration stage, MetaCore system accepts a set of benchmark programs and a formal specification of ISA (Instruction Set Architecture), and estimates the hardware cost and performance for each hardware configuration being explored. Once a hardware configuration is chosen, the system helps generate a VLSI processor design in the form of HDL along with the application program development tools such as C compiler, assembler and instruction set simulator.
3207967
ArrayXPath: mapping and visualizing microarray gene-expression data with integrated biological pathway resources using Scalable Vector Graphics
Biological pathways can provide key information on the organization of biological systems. ArrayXPath (http://www.snubi.org/software/ArrayXPath/) is a web-based service for mapping and visualizing microarray gene-expression data for integrated biological pathway resources using Scalable Vector Graphics (SVG). By integrating major bio-databases and searching pathway resources, ArrayXPath automatically maps different types of identifiers from microarray probes and pathway elements. When one inputs gene-expression clusters, ArrayXPath produces a list of the best matching pathways for each cluster. We applied Fisher's exact test and the false discovery rate (FDR) to evaluate the statistical significance of the association between a cluster and a pathway while correcting the multiple-comparison problem. ArrayXPath produces Javascript-enabled SVGs for web-enabled interactive visualization of pathways integrated with gene-expression profiles.
3197241
Explicit construction of families of LDPC codes with no 4-cycles
Low-density parity-check (LDPC) codes are serious contenders to turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m/spl ges/2, Lazebnik and Ustimenko construct a q-regular bipartite graph D(m,q) on 2q/sup m/ vertices, which has girth at least 2/spl lceil/m/2/spl rceil/+4. We regard these graphs as Tanner graphs of binary codes LU(m,q). We can determine the dimension and minimum weight of LU(2,q), and show that the weight of its minimum stopping set is at least q+2 for q odd and exactly q+2 for q even. We know that D(2,q) has girth 6 and diameter 4, whereas D(3,q) has girth 8 and diameter 6. We prove that for an odd prime p, LU(3,p) is a [p/sup 3/,k] code with k/spl ges/(p/sup 3/-2p/sup 2/+3p-2)/2. We show that the minimum weight and the weight of the minimum stopping set of LU(3,q) are at least 2q and they are exactly 2q for many LU(3,q) codes. We find some interesting LDPC codes by our partial row construction. We also give simulation results for some of our codes.