In this paper, we propose a novel sampling-based planner for multi-goal path planning among obstacles, where the objective is to visit predefined target locations while minimizing travel costs. The order of visiting targets often achieved by solving Traveling Salesman Problem (TSP) or its variants. TSP requires define costs between individual targets, which - in map with obstacles compute mutua...

In this work, we are concerned with path-dependent random diffusions. Under certain ergodic condition, show that the diffusion under consideration has a unique invariant probability measure and converges exponentially to its equilibrium Wasserstein distance. Also, demonstrate time discretization of involved admits (numerical) preserves corresponding property when step size is sufficiently small...

Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...

due to business and environmental issues, the efficient design of an integrated forward/reverse logistics network has recently attracted more attention from researchers. the significance of transportation cost and customer satisfaction spurs an interest in developing a flexible network design model with different delivery paths. this paper proposes a flexible mixed-integer programming model to ...

We study two types of two player, perfect information games with no chance moves, played on the edge set of the binomial random graph G(n, p). In each round of the (1 : q) Waiter-Client Hamiltonicity game, the first player, called Waiter, offers the second player, called Client, q + 1 edges of G(n, p) which have not been offered previously. Client then chooses one of these edges, which he claim...

We investigate the sample path properties of Martin-Löf random Brownian motion. We show (1) that many classical results which are known to hold almost surely hold for every Martin-Löf random Brownian path, (2) that the effective dimension of zeroes of a Martin-Löf random Brownian path must be at least 1/2, and conversely that every real with effective dimension greater than 1/2 must be a zero o...

Weconsider a directed graph on the integerswith a directed edge fromvertex i to j present with probability n−1, whenever i < j , independently of all other edges. Moreover, to each edge (i, j) we assign weight n−1(j − i). We show that the closure of vertex 0 in such a weighted random graph converges in distribution to the Poisson-weighted infinite tree as n → ∞. In addition, we derive limit the...

Suppose that a random graph begins with n isolated vertices and evolves by edges being added at random, conditional upon all vertex degrees being at most 2. The final graph is usually 2-regular, but is not uniformly distributed. Some properties of this final graph are already known, but the asymptotic probability of being a Hamilton cycle was not known. We answer this question along with some r...

We introduce a new setting of algorithmic problems in random graphs, studying the minimum number of queries one needs to ask about the adjacency between pairs of vertices of G(n, p) in order to typically find a subgraph possessing a given target property. We show that if p ≥ lnn+ln lnn+ω(1) n , then one can find a Hamilton cycle with high probability after exposing (1+o(1))n edges. Our result i...

We count labelled chordal graphs with no induced path of length 3, both exactly and asymptotically. These graphs correspond to rooted trees in which no vertex has exactly one child, and each vertex has been expanded to a clique. Some properties of random graphs of this type are also derived. The corresponding unlabelled graphs are in 1-1 correspondence with unlabelled rooted trees on the same n...