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].
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.
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.
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.
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.
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.
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.
8536996
Goal and scenario based domain requirements analysis environment
Identifying and representing domain requirements among products in a product family are crucial activities for a successful software reuse. The domain requirements should be not only identified based on the business goal, which drives marketing plan, product plan, and differences among products, but also represented as familiar notations in order to support developing a particular product in the product family. Thus, our proposal is to identify the domain requirements through goals and scenarios, and represent them as variable use cases for a product family. Especially, for identification of the domain requirements, we propose four abstraction levels of requirements in a product family, and goal and scenario modeling. For representation of them, variable use case model is suggested, and also the use case transfer rules are proposed so as to bridge the gap between the identification and representation activity. The paper illustrates the application of the approach within a supporting tool using the HIS (Home Integration System) example.
6014517
The Real-Time Development and Deployment of a Cooperative Multi-UAV System
This paper presents a systems view of the Autonomous Nav- igation and Sensing Experimental Research (ANSER) project. ANSER is one of the most advanced UAV projects of its kind, which is aimed at demonstrating Decentralised Data Fusion (DDF) and Simultaneous Localisation and Map (SLAM) building on multiple cooperative UAVs. The demonstration of DDF and SLAM require both navigation and terrain sensors to be carried onboard by the UAVs. These include an INS/GPS navigation system, millimeter wave (MMW) radar, and both a single vision node and a vision node augmented with a laser system. This paper presents the implementation of the algorithms, sensors and platforms, along with their interaction to address this demonstration. Furthermore, the paper will present the high fidelity real time simulator which is implemented to thoroughly test all algorithms and sensors before actual implementation in the environment.
28523270
Goal based agent-oriented software modeling
This paper presents a goal based modeling method for an agent-oriented software system. In modeling research for agent-oriented software, problems often emerged in that the properties of an agent system were not efficiently reflected in the development phase (analysis, design, etc.), because the techniques based on the other software paradigm are adopted to develop agent-oriented software. The result of analysis differs depending on which paradigm is used. An agent is goal-oriented, which necessitates a shift in paradigm. Therefore, the modeling method for an agent system should start from the concept of goal.
16116503
Evolutionary programming techniques for constrained optimization problems
Two evolutionary programming (EP) methods are proposed for handling nonlinear constrained optimization problems. The first, a hybrid EP, is useful when addressing heavily constrained optimization problems both in terms of computational efficiency and solution accuracy. But this method offers an exact solution only if both the mathematical form of the objective function to be minimized/maximized and its gradient are known. The second method, a two-phase EP (TPEP) removes these restrictions. The first phase uses the standard EP, while an EP formulation of the augmented Lagrangian method is employed in the second phase. Through the use of Lagrange multipliers and by gradually placing emphasis on violated constraints in the objective function whenever the best solution does not fulfill the constraints, the trial solutions are driven to the optimal point where all constraints are satisfied. Simulations indicate that the TPEP achieves an exact global solution without gradient information, with less computation time than the other optimization methods studied here, for general constrained optimization problems.