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.
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
15935373
Random Matchings Which Induce Hamilton Cycles and Hamiltonian Decompositions of Random Regular Graphs
Select four perfect matchings of 2n vertices, independently at random. We find the asymptotic probability that each of the first and second matchings forms a Hamilton cycle with each of the third and fourth. This is generalised to embrace any fixed number of perfect matchings, where a prescribed set of pairs of matchings must each produce Hamilton cycles (with suitable restrictions on the prescribed set of pairs). We also show how the result with four matchings implies that a random d-regular graph for fixed even d?4 asymptotically almost surely decomposes into d/2 Hamilton cycles. This completes a general result on the edge-decomposition of a random regular graph into regular spanning subgraphs of given degrees together with Hamilton cycles and verifies conjectures of Janson and of Robinson and Wormald.
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.
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.
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.
14570877
Genetic Elevator Group Control
In a tall building with multiple elevators, it is a notoriously di cult task to control the elevators in the most e cient manner [1].The system proposed in this paper contains two key ideas. First, it continuously generates dispatch functions by adaptation to changes in passenger tra c. Second, it tries to reduce passengers' waiting time by multiple elevator allocation when it is expected that one elevator cannot serve all the passengers for a hall call at a oor.
14647313
Energy-efficient disk replacement and file placement techniques for mobile systems with hard disks
Mobile systems have usually used hard disks as the secondary storage devices because of their high capacity per cost and high I/O throughput. However, their high power consumption is the main limiting factor for extending their adoptions in mobile systems. In this paper, we propose enhanced file placement techniques for mobile platforms with multiple smaller disks (instead of a single large disk). We investigate that how many smaller disks are necessary to obtain energy saving while maintaining the required performance using both a simplified energy model and a realistic trace-based simulator under the proposed multiple disk configurations. We also propose energy-efficient file placement techniques, which aggregate files with common attributes the same set of disks. By skewing I/O operations, the proposed techniques achieve additional energy saving. Experimental results show that the proposed techniques can reduce the energy consumption by up to 43% when eight 1" disks are used instead of a single 2.5" disk with an acceptable increase in the average response time.
7958974
Gaussian scale-space dense disparity estimation with anisotropic disparity-field diffusion
We present a new reliable dense disparity estimation algorithm which employs Gaussian scale-space with anisotropic disparity-field diffusion. This algorithm estimates edge-preserving dense disparity vectors using a diffusive method on iteratively Gaussian-filtered images with a scale, i.e. the Gaussian scale-space. While a Gaussian filter kernel generates a coarser resolution from stereo image pairs, only strong and meaningful boundaries are adoptively selected on the resolution of the filtered images. Then, coarse global disparity vectors are initialized using the boundary constraint. The per-pixel disparity vectors are iteratively obtained by the local adjustment of the global disparity vectors using an energy-minimization framework. The proposed algorithm preserves the boundaries while inner regions are smoothed using anisotropic disparity-field diffusion. In this work, the Gaussian scale-space efficiently avoids illegal matching on a large baseline by the restriction of the range. Moreover, it prevents the computation from iterating into local minima of ill-posed diffusion on large gradient areas e.g. shadow and texture region, etc. The experimental results prove the excellent localization performance preserving the disparity discontinuity of each object.
6280619
Prediction of subcellular localization of proteins using pairwise sequence alignment and support vector machine
Predicting the destination of a protein in a cell is important for annotating the function of the protein. Recent advances have allowed us to develop more accurate methods for predicting the subcellular localization of proteins. One of the most important factors for improving the accuracy of these methods is related to the introduction of new useful features for protein sequences. In this paper we present a new method for extracting appropriate features from the sequence data by computing pairwise sequence alignment scores. As a classifier, support vector machine (SVM) is used. The overall prediction accuracy evaluated by the jackknife validation technique reached 94.70% for the eukaryotic non-plant data set and 92.10% for the eukaryotic plant data set, which is the highest prediction accuracy among the methods reported so far with such data sets. Our experimental results confirm that our feature extraction method based on pairwise sequence alignment is useful for this classification problem.