96 resultados para Planar graph
Resumo:
We give a detailed construction of a finite-state transition system for a com-connected Message Sequence Graph. Though this result is well-known in the literature and forms the basis for the solution to several analysis and verification problems concerning MSG specifications, the constructions given in the literature are either not amenable to implementation, or imprecise, or simply incorrect. In contrast we give a detailed construction along with a proof of its correctness. Our transition system is amenable to implementation, and can also be used for a bounded analysis of general (not necessarily com-connected) MSG specifications.
Resumo:
We present a method to statically balance a general treestructured,planar revolute-joint linkage loaded with linear springs or constant forces without using auxiliary links. The balancing methods currently documented in the literature use extra links; some do not apply when there are spring loads and some are restricted to only two-link serial chains. In our method, we suitably combine any non-zero-free-length load spring with another spring to result in an effective zero-free-length spring load. If a link has a single joint (with the parent link), we give a procedure to attach extra zero-free-length springs to it so that forces and moments are balanced for the link. Another consequence of this attachment is that the constraint force of the joint on the parent link becomes equivalent to a zero-free-length spring load. Hence, conceptually,for the parent link, the joint with its child is removed and replaced with the zero-free-length spring. This feature allows recursive application of this procedure from the end-branches of the tree down to the root, satisfying force and moment balance of all the links in the process. Furthermore, this method can easily be extended to the closed-loop revolute-joint linkages, which is also illustrated in the paper.
Resumo:
Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes on a region in Euclidean space, e.g., the unit square. After deployment, the nodes self-organise into a mesh topology. In a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this paper, we analyse the performance of this approximation. We show that nodes with a certain hop distance from a fixed anchor node lie within a certain annulus with probability approach- ing unity as the number of nodes n → ∞. We take a uniform, i.i.d. deployment of n nodes on a unit square, and consider the geometric graph on these nodes with radius r(n) = c q ln n n . We show that, for a given hop distance h of a node from a fixed anchor on the unit square,the Euclidean distance lies within [(1−ǫ)(h−1)r(n), hr(n)],for ǫ > 0, with probability approaching unity as n → ∞.This result shows that it is more likely to expect a node, with hop distance h from the anchor, to lie within this an- nulus centred at the anchor location, and of width roughly r(n), rather than close to a circle whose radius is exactly proportional to h. We show that if the radius r of the ge- ometric graph is fixed, the convergence of the probability is exponentially fast. Similar results hold for a randomised lattice deployment. We provide simulation results that il- lustrate the theory, and serve to show how large n needs to be for the asymptotics to be useful.
Resumo:
An axis-parallel box in $b$-dimensional space is a Cartesian product $R_1 \times R_2 \times \cdots \times R_b$ where $R_i$ (for $1 \leq i \leq b$) is a closed interval of the form $[a_i, b_i]$ on the real line. For a graph $G$, its boxicity is the minimum dimension $b$, such that $G$ is representable as the intersection graph of (axis-parallel) boxes in $b$-dimensional space. The concept of boxicity finds application in various areas of research like ecology, operation research etc. Chandran, Francis and Sivadasan gave an $O(\Delta n^2 \ln^2 n)$ randomized algorithm to construct a box representation for any graph $G$ on $n$ vertices in $\lceil (\Delta + 2)\ln n \rceil$ dimensions, where $\Delta$ is the maximum degree of the graph. They also came up with a deterministic algorithm that runs in $O(n^4 \Delta )$ time. Here, we present an $O(n^2 \Delta^2 \ln n)$ deterministic algorithm that constructs the box representation for any graph in $\lceil (\Delta + 2)\ln n \rceil$ dimensions.
Resumo:
Scan circuit is widely practiced DFT technology. The scan testing procedure consist of state initialization, test application, response capture and observation process. During the state initialization process the scan vectors are shifted into the scan cells and simultaneously the responses captured in last cycle are shifted out. During this shift operation the transitions that arise in the scan cells are propagated to the combinational circuit, which inturn create many more toggling activities in the combinational block and hence increases the dynamic power consumption. The dynamic power consumed during scan shift operation is much more higher than that of normal mode operation.
Resumo:
We consider evolving exponential RGGs in one dimension and characterize the time dependent behavior of some of their topological properties. We consider two evolution models and study one of them detail while providing a summary of the results for the other. In the first model, the inter-nodal gaps evolve according to an exponential AR(1) process that makes the stationary distribution of the node locations exponential. For this model we obtain the one-step conditional connectivity probabilities and extend it to the k-step case. Finite and asymptotic analysis are given. We then obtain the k-step connectivity probability conditioned on the network being disconnected. We also derive the pmf of the first passage time for a connected network to become disconnected. We then describe a random birth-death model where at each instant, the node locations evolve according to an AR(1) process. In addition, a random node is allowed to die while giving birth to a node at another location. We derive properties similar to those above.
Resumo:
In this paper, we present a kinematic theory for Hoberman and other similar foldable linkages. By recognizing that the building blocks of such linkages can be modeled as planar linkages, different classes of possible solutions are systematically obtained including some novel arrangements. Criteria for foldability are arrived by analyzing the algebraic locus of the coupler curve of a PRRP linkage. They help explain generalized Hoberman and other mechanisms reported in the literature. New properties of such mechanisms including the extent of foldability, shape-preservation of the inner and outer profiles, multi-segmented assemblies and heterogeneous circumferential arrangements are derived. The design equations derived here make the conception of even complex planar radially foldable mechanisms systematic and easy. Representative examples are presented to illustrate the usage of the design equations and the kinematic theory.