This entry contains proofs for the textbook results about the distributions of the height and internal path length of random binary search trees (BSTs), i. e. BSTs that are formed by taking an empty BST and inserting elements from a fixed set in random order. In particular, we prove a logarithmic upper bound on the expected height and the Θ(n log n) closed-form solution for the expected interna...

Small-world networks, according to Watts and Strogatz, are a class of networks that are "highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs." These characteristics result in networks with unique properties of regional specialization with efficient information transfer. Social networks are intuitive examples of this organization, in which cliq...

This paper presents a novel real-time path planning algorithm for an autonomous mobile agent in completely unknown environment. In this algorithm, all the planned paths are described and stored in the form of vectors in the algorithm. Only the rotation angle and the movement distance in a single direction are considered when the autonomous moves along the planned paths. The algorithm combines r...

A hierarchical memetic algorithm (MA) is proposed for the path planning and formation control of swarm robots. The proposed algorithm consists of a global path planner (GPP) and a local motion planner (LMP). The GPP plans a trajectory within the Voronoi diagram (VD) of the free space. An MA with a non‐random initial population plans a series of configu...

Received Aug 11, 2013 Revised Feb 20, 2014 Accepted Mar 10, 2014 A based on Rapidly-exploring Random Tree (RRT) and Particle Swarm Optimizer (PSO) for path planning of the robot is proposed. First the grid method is built to describe the working space of the mobile robot, then the Rapidly-exploring Random Tree algorithm is used to obtain the global navigation path, and the Particle Swarm Optimi...

We consider the individual points on a Martin-Löf random path of Brownian motion. We show (1) that Khintchine’s law of the iterated logarithm holds at almost all points; and (2) there exist points (besides the trivial example of the origin) having effective dimension < 1. The proof of (1) amounts essentially to showing for almost all times t, the path f is random relative to t and the dimension...

We investigate simplified models of computer data networks and examine how the introduction of additional random links influences the performance of these networks. In general, the impact of additional random links on the performance of the network strongly depends on the routing algorithm used in the network. Significant performance gains can be achieved if the routing is based on “geometrical...

organizations are networks of unites and individuals enhancing organizational performance through cooperation and synergy. it is achieved by developing meaningful and purposeful communications of unites and individuals .thus, it is essential to make organizational communications efficient in order to achieve organizational purposes. in this essay, we examined the variables and factors affecting...

We examined how people perceive their path of traveling from optic flow. Observers viewed displays simulating their traveling on a circular path over a textured ground, a random-dot ground, or a dynamic random-dot ground display in which dots were periodically redrawn to remove extended dot motion trajectories (flow lines) in the flow field. Five viewing conditions were tested in which the simu...

Let {ξ(n)}n∈Z be a two-color random scenery, that is, a random coloring of Z in two colors, such that the ξ(i)’s are i.i.d. Bernoulli variables with parameter 1 2 . Let {S(n)}n∈N be a symmetric random walk starting at 0. Our main result shows that a.s., ξ ◦ S (the composition of ξ and S) determines ξ up to translation and reflection. In other words, by observing the scenery ξ along the random w...