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Joseph S. B. Mitchell

Bio: Joseph S. B. Mitchell is an academic researcher. The author has contributed to research in topics: Yen's algorithm & Shortest Path Faster Algorithm. The author has an hindex of 1, co-authored 1 publications receiving 395 citations.

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Journal ArticleDOI
01 Jul 2005
TL;DR: To compute the shortest path between two given points, a lower-bound property of the approximate geodesic algorithm is used to efficiently prune the frontier of the MMP algorithm, thereby obtaining an exact solution even more quickly.
Abstract: The computation of geodesic paths and distances on triangle meshes is a common operation in many computer graphics applications. We present several practical algorithms for computing such geodesics from a source point to one or all other points efficiently. First, we describe an implementation of the exact "single source, all destination" algorithm presented by Mitchell, Mount, and Papadimitriou (MMP). We show that the algorithm runs much faster in practice than suggested by worst case analysis. Next, we extend the algorithm with a merging operation to obtain computationally efficient and accurate approximations with bounded error. Finally, to compute the shortest path between two given points, we use a lower-bound property of our approximate geodesic algorithm to efficiently prune the frontier of the MMP algorithm. thereby obtaining an exact solution even more quickly.

480 citations

Proceedings ArticleDOI
29 Sep 2006
TL;DR: This paper proposes a simple, distributed algorithm that correctly detects nodes on the boundaries and connects them into meaningful boundary cycles, and obtains as a byproduct the medial axis of the sensor field, which has applications in creating virtual coordinates for routing.
Abstract: Wireless sensor networks are tightly associated with the underlying environment in which the sensors are deployed. The global topology of the network is of great importance to both sensor network applications and the implementation of networking functionalities. In this paper we study the problem of topology discovery, in particular, identifying boundaries in a sensor network. Suppose a large number of sensor nodes are scattered in a geometric region, with nearby nodes communicating with each other directly. Our goal is to find the boundary nodes by using only connectivity information. We do not assume any knowledge of the node locations or inter-distances, nor do we enforce that the communication graph follows the unit disk graph model. We propose a simple, distributed algorithm that correctly detects nodes on the boundaries and connects them into meaningful boundary cycles. We obtain as a byproduct the medial axis of the sensor field, which has applications in creating virtual coordinates for routing. We show by extensive simulation that the algorithm gives good results even for networks with low density. We also prove rigorously the correctness of the algorithm for continuous geometric domains.

399 citations

Journal ArticleDOI
Martin Kröger1
TL;DR: An algorithm which returns a shortest path and related number of entanglements for a given configuration of a polymeric system in 2 or 3 dimensions is presented and the method is applied to study the 'concentration' dependence of the degree ofEntanglement in phantom chain systems.

368 citations

Journal ArticleDOI
TL;DR: An interpolation‐based planning and replanning algorithm for generating low‐cost paths through uniform and nonuniform resolution grids that addresses two of the most significant shortcomings of grid‐based path planning: the quality of the paths produced and the memory and computational requirements of planning over grids.
Abstract: We present an interpolation-based planning and replanning algorithm for generating low-cost paths through uniform and nonuniform resolution grids. Most grid-based path planners use discrete state transitions that artificially constrain an agent's motion to a small set of possible headings (e.g., 0, π/4, π/2, etc.). As a result, even “optimal” grid-based planners produce unnatural, suboptimal paths. Our approach uses linear interpolation during planning to calculate accurate path cost estimates for arbitrary positions within each grid cell and produce paths with a range of continuous headings. Consequently, it is particularly well suited to planning low-cost trajectories for mobile robots. In this paper, we introduce a version of the algorithm for uniform resolution grids and a version for nonuniform resolution grids. Together, these approaches address two of the most significant shortcomings of grid-based path planning: the quality of the paths produced and the memory and computational requirements of planning over grids. We demonstrate our approaches on a number of example planning problems, compare them to related algorithms, and present several implementations on real robotic systems.

366 citations

Book ChapterDOI
01 Jan 2007
TL;DR: This approach uses linear interpolation during planning to calculate accurate path cost estimates for arbitrary positions within each grid cell and to produce paths with a range of continuous headings, which is particularly well suited to planning low-cost trajectories for mobile robots.
Abstract: We present an interpolation-based planning and replanning algorithm for generating direct, low-cost paths through nonuniform cost grids. Most grid-based path planners use discrete state transitions that artificially constrain an agent’s motion to a small set of possible headings (e.g. 0, \( \frac{\pi } {4},\frac{\pi } {2} \), etc). As a result, even ‘optimal’ grid-based planners produce unnatural, suboptimal paths. Our approach uses linear interpolation during planning to calculate accurate path cost estimates for arbitrary positions within each grid cell and to produce paths with a range of continuous headings. Consequently, it is particularly well suited to planning low-cost trajectories for mobile robots. In this paper, we introduce the algorithm and present a number of example applications and results.

244 citations