Let B be a point robot in the plane, whose path is constrained to have curvature of at most 1, and let Ω be a set of polygonal obstacles with n vertices. We study the collision-free, optimal path-planning problem for...
详细信息
ISBN:
(纸本)0898713668
Let B be a point robot in the plane, whose path is constrained to have curvature of at most 1, and let Ω be a set of polygonal obstacles with n vertices. We study the collision-free, optimal path-planning problem for B. Given a parameter ϵ, we present an O((n2/ϵ2) log n)-time algorithm for computing a collision-free, curvature-constrained path between two given positions, whose length is at most (1 + ϵ) times the length of an optimal robust path (a path is robust if it remains collision-free even if certain positions on the path are perturbed). Our algorithm thus runs significantly faster than the previously best known algorithm by Jacobs and Canny whose running time is O(n+L/ϵ)2 + n2(n+K/ϵ) log n), where L is the total edge length of the obstacles. More importantly, the running time of our algorithm does not depend on the size of obstacles. The path returned by this algorithm is not necessarily robust. We present an O((n/ϵ)2.5 log n)-time algorithm that returns a robust path whose length is at most (1 + ϵ) times the length of an optimal robust path. We also give a stronger characterization of curvature-constrained shortest paths, which, apart from being crucial for our algorithm, is interesting in its own right. Roughly speaking, we prove that, except in some special cases, a shortest path touches obstacles only at points that have a visible vertex nearby.
In this paper, we discuss a data association problem arising from multitarget tracking. We formulate the problem as a multi-dimensional assignment problem and propose a polynomial time 1.8-approximation algorithm for ...
详细信息
We consider the following Antenna Orientation Problem: Given a connected Unit Disk Graph (UDG) formed by n identical omnidirectional sensors, what is the optimal range (or radius) which is necessary and sufficient for...
详细信息
ISBN:
(纸本)9783642401633
We consider the following Antenna Orientation Problem: Given a connected Unit Disk Graph (UDG) formed by n identical omnidirectional sensors, what is the optimal range (or radius) which is necessary and sufficient for a given antenna beamwidth (or angle) φ so that after replacing the omnidirectional sensors by directional antennae of beamwidth φ we can determine an appropriate orientation of each antenna so that the resulting graph is strongly connected? The problem was first proposed and studied in Caragiannis et al. [3] where they showed that the antenna orientation problem can be solved optimally for φ ≥ 8π/5, and is NP-Hard for φ
Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least k vertices is considered long....
详细信息
Let G = (V,E,w) be an undirected graph with nonnegative edge weight w, and r be a nonnegative vertex weight. The product-requirement optimum communication spanning tree (PROCT) problem is to find a spanning tree T min...
详细信息
In this paper we demonstrate a general method of designing constant-factor approximation algorithms for some discrete optimization problems with cardinality constraints. The core of the method is a simple deterministi...
详细信息
Existing research has demonstrated that effective Routing and Wavelength Assignment (RWA) algorithm and wavelength conversion are two primary vehicles for improving the networks performance. In this paper, we consider...
详细信息
A large number of network applications today allow several users to interact together using the many-to-many service mode. In many-to-many communication, also referred to as group communication, a session consists of ...
详细信息
The Street sweeping problem (SSP) is a variation of the Windy postman problem (WPP) in which we must construct two tours traversing every edge, and each edge must be traversed once in each direction: one on the first ...
详细信息
A radiocommunication system has to satisfy the channel requests in its service area subject to the constraints that the number of channels is limited and co-channel interference must be excluded. This paper explores t...
详细信息
暂无评论