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.
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.
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.
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.
5817098
Neural Network Normalization for Genetic Search
An arbitrary neural network has a number of functionally equivalent other networks. This causes redundancy in genetic representation of neural networks, which considerably undermines the merit of crossover in GAs [1]. This problem has received considerable attention in the past and has also been called the “competing conventions” problem [2].
30180926
Group Key Agreement Protocol Among Mobile Devices in Different Cells
Mobile communication has become more pervasive and it is considered as one of main concerns of IP telephony, video conferencing, multi-user games and etc. in mobile environments. These applications require secure group communication between a multitude of mobile devices owned by group members. Most of the published group key agreement protocols are based on a model which consists of a stationary base station and a cluster of mobile devices. In this paper, we assume a more realistic scenario in which secret group key is established between several base stations and mobile devices in different cells. We present new group key protocol among mobile devices in different cells and analyze its security.
1268203
Quantum-Inspired Evolutionary Algorithm-Based Face Verification
Face verification is considered to be the main part of the face detection system. To detect human faces in images, face candidates are extracted and face verification is performed. This paper proposes a new face verification algorithm using Quantum-inspired Evolutionary Algorithm (QEA). The proposed verification system is based on Principal Components Analysis (PCA). Although PCA related algorithms have shown outstanding performance, the problem lies in the selection of eigenvectors. They may not be the optimal ones for representing the face features. Moreover, a threshold value should be selected properly considering the verification rate and false alarm rate. To solve these problems, QEA is employed to find out the optimal distance measure under the predetermined threshold value which distinguishes between face images and non-face images. The proposed verification system is tested on the AR face database and the results are compared with the previous works to show the improvement in performance.
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.
701944
Simulation-Based Security Testing for Continuity of Essential Service
One of the most important characteristic of essential service in the computer network is its continuity. If the continuity of essential service is not guaranteed, it causes a big problem in normal operation of computer network. In our research, we suggest the simulation-based security testing for the continuity of essential service. Especially, the security testing sequence and Experimental Frame is designed to get indexes related to the continuity of essential service. We choose three testing indexes that represent the degree of service continuity and testing methods to get those indexes. Also, to explain the indexes and the testing methods, two testing examples are presented.