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Sue Whitesides - One of the best experts on this subject based on the ideXlab platform.

  • curvature constrained shortest paths in a Convex Polygon
    SIAM Journal on Computing, 2002
    Co-Authors: Pankaj K Agarwal, Therese C Biedl, Sylvain Lazard, Steve Robbins, Subhash Suri, Sue Whitesides
    Abstract:

    Let B be a point robot moving in the plane, whose path is constrained to have curvature at most 1, and let $\poly$ be a Convex Polygon with n vertices. We study the collision-free, optimal path-planning problem for B moving between two configurations inside $\poly$. (A configuration specifies both a location and a direction of travel.) We present an O(n2 log n) time algorithm for determining whether a collision-free path exists for B between two given configurations. If such a path exists, the algorithm returns a shortest one. We provide a detailed classification of curvature-constrained shortest paths inside a Convex Polygon and prove several properties of them, which are interesting in their own right. For example, we prove that any such shortest path is comprised of at most eight segments, each of which is a circular arc of unit radius or a straight-line segment. Some of the properties are quite general and shed some light on curvature-constrained shortest paths amid obstacles.

  • curvature constrained shortest paths in a Convex Polygon extended abstract
    Symposium on Computational Geometry, 1998
    Co-Authors: Pankaj K Agarwal, Therese C Biedl, Sylvain Lazard, Steve Robbins, Subhash Suri, Sue Whitesides
    Abstract:

    Let B be a point robot moving in the plane, whose path is constrained to have curvature at most 1, and let P be a Convex Polygon with n vertices. We study the collision-free, optimal path-planning problem for B moving between two configurations inside P (a configuration specifies both a location and a direction of travel). We present an O(n2 log n) time algorithm for determining whether a collision-free path exists for B between two given configurations. If such a path exists, the algorithm returns a shortest one. We provide a detailed classification of curvature-constrained shortest paths inside a Convex Polygon and prove several properties of them, which are interesting in their own right. Some of the properties are quite general and shed some light on curvature-constrained shortest paths amid obstacles.

Pankaj K Agarwal - One of the best experts on this subject based on the ideXlab platform.

  • curvature constrained shortest paths in a Convex Polygon
    SIAM Journal on Computing, 2002
    Co-Authors: Pankaj K Agarwal, Therese C Biedl, Sylvain Lazard, Steve Robbins, Subhash Suri, Sue Whitesides
    Abstract:

    Let B be a point robot moving in the plane, whose path is constrained to have curvature at most 1, and let $\poly$ be a Convex Polygon with n vertices. We study the collision-free, optimal path-planning problem for B moving between two configurations inside $\poly$. (A configuration specifies both a location and a direction of travel.) We present an O(n2 log n) time algorithm for determining whether a collision-free path exists for B between two given configurations. If such a path exists, the algorithm returns a shortest one. We provide a detailed classification of curvature-constrained shortest paths inside a Convex Polygon and prove several properties of them, which are interesting in their own right. For example, we prove that any such shortest path is comprised of at most eight segments, each of which is a circular arc of unit radius or a straight-line segment. Some of the properties are quite general and shed some light on curvature-constrained shortest paths amid obstacles.

  • curvature constrained shortest paths in a Convex Polygon extended abstract
    Symposium on Computational Geometry, 1998
    Co-Authors: Pankaj K Agarwal, Therese C Biedl, Sylvain Lazard, Steve Robbins, Subhash Suri, Sue Whitesides
    Abstract:

    Let B be a point robot moving in the plane, whose path is constrained to have curvature at most 1, and let P be a Convex Polygon with n vertices. We study the collision-free, optimal path-planning problem for B moving between two configurations inside P (a configuration specifies both a location and a direction of travel). We present an O(n2 log n) time algorithm for determining whether a collision-free path exists for B between two given configurations. If such a path exists, the algorithm returns a shortest one. We provide a detailed classification of curvature-constrained shortest paths inside a Convex Polygon and prove several properties of them, which are interesting in their own right. Some of the properties are quite general and shed some light on curvature-constrained shortest paths amid obstacles.

  • largest placement of one Convex Polygon inside another
    Discrete and Computational Geometry, 1998
    Co-Authors: Pankaj K Agarwal, Nina Amenta, Micha Sharir
    Abstract:

    We show that the largest similar copy of a Convex Polygon P with m edges inside a Convex Polygon Q with n edges can be computed in O(mn 2 log n) time. We also show that the combinatorial complexity of the space of all similar copies of P inside Q is O(mn 2 ) , and that it can also be computed in O(mn 2 log n) time.

Zhen Jiang - One of the best experts on this subject based on the ideXlab platform.

  • on constructing the minimum orthogonal Convex Polygon for the fault tolerant routing in 2 d faulty meshes
    IEEE Transactions on Reliability, 2005
    Co-Authors: Zhen Jiang
    Abstract:

    The rectangular faulty block model is the most commonly used fault model for designing fault-tolerant, and deadlock-free routing algorithms in mesh-connected multicomputers. The Convexity of a rectangle facilitates simple, efficient ways to route messages around fault regions using relatively few or no virtual channels to avoid deadlock. However, such a faulty block may include many nonfaulty nodes which are disabled, i.e., they are not involved in the routing process. Therefore, it is important to define a fault region that is Convex, and at the same time, to include a minimum number of nonfaulty nodes. In this paper, we propose an optimal solution that can quickly construct a set of minimum faulty Polygons, called orthogonal Convex Polygons, from a given set of faulty blocks in a 2-D mesh (or 2-D torus). The formation of orthogonal Convex Polygons is implemented using either a centralized, or distributed solution. Both solutions are based on the formation of faulty components, each of which consists of adjacent faulty nodes only, followed by the addition of a minimum number of nonfaulty nodes to make each component a Convex Polygon. Extensive simulation has been done to determine the number of nonfaulty nodes included in the Polygon, and the result obtained is compared with the best existing known result. Results show that the proposed approach can not only find a set of minimum faulty Polygons, but also does so quickly in terms of the number of rounds in the distributed solution.

  • on constructing the minimum orthogonal Convex Polygon in 2 d faulty meshes
    International Parallel and Distributed Processing Symposium, 2004
    Co-Authors: Zhen Jiang
    Abstract:

    Summary form only given. The rectangular faulty block model is the most commonly used fault model for designing fault-tolerant and deadlock-free routing algorithms in mesh-connected multicomputer. The Convexity of a rectangle facilitates simple and efficient ways to route messages around fault regions using relatively few or no virtual channels to avoid deadlock. However, such a faulty block may include many nonfaulty nodes which are disabled, i.e., they are not involved in the routing process. Therefore, it is important to define a fault region that is Convex and, at the same time, to include a minimum number of nonfaulty nodes. We propose an optimal solution that can quickly construct a set of minimum faulty Polygons, called orthogonal Convex Polygons, from a given set of faulty blocks in a 2-D mesh (or 2-D torus). The formation of orthogonal Convex Polygons is implemented using either a centralized or distributed solution. Both solutions are based on the formation of faulty components each of which consists of adjacent faulty nodes only, followed by the addition of a minimum number of nonfaulty nodes to make each component a Convex Polygon. Extensive simulation has been done to determine the number of nonfaulty nodes included in the Polygon, and the result obtained is compared with the best existing known result. Results show that the proposed approach can not only find a set of minimum faulty Polygons but also does so quickly in terms of the number of rounds of information exchanges and updates between neighbors in the distributed solution.

Asish Mukhopadhyay - One of the best experts on this subject based on the ideXlab platform.

  • on intersecting a set of isothetic line segments with a Convex Polygon of minimum area
    International Journal of Computational Geometry and Applications, 2009
    Co-Authors: Asish Mukhopadhyay, Eugene Greene, S V Rao
    Abstract:

    We describe an O(n2)-time algorithm for computing a minimum-area Convex Polygon that intersects a set of n isothetic line segments.

  • on intersecting a set of parallel line segments with a Convex Polygon of minimum area
    Information Processing Letters, 2008
    Co-Authors: Asish Mukhopadhyay, Chanchal Kumar, Eugene Greene, Binay K Bhattacharya
    Abstract:

    Let S = {l1, l2, l3, . . . , ln} be a set of n vertical line segments in the plane. Though not essential, to simplify proofs we assume that no two li ’s are on the same vertical line. A Convex Polygon weakly intersects S if it contains a point of each line segment on its boundary or interior. In this paper, we propose an O(n logn) algorithm for the problem of finding a minimum area Convex Polygon that weakly intersects S. The principal motivation behind this paper is the open problem proposed by Tamir [5] at the fourth Computational Geometry day at NYU to decide if there exists a Convex Polygon whose boundary intersects a set of arbitrarily oriented line segments.

  • on the minimum perimeter triangle enclosing a Convex Polygon
    Lecture Notes in Computer Science, 2003
    Co-Authors: Binay K Bhattacharya, Asish Mukhopadhyay
    Abstract:

    We consider the problem of computing a minimum perimeter triangle enclosing a Convex Polygon. This problem defied a linear-time solution due to the absence of a property called the interspersing property. This property was crucial in the linear-time solution for the minimum area triangle enclosing a Convex Polygon. We have discovered a non-trivial interspersing property for the minimum perimeter problem. This resulted in an optimal solution to the minimum perimeter triangle problem.

Subhash Suri - One of the best experts on this subject based on the ideXlab platform.

  • curvature constrained shortest paths in a Convex Polygon
    SIAM Journal on Computing, 2002
    Co-Authors: Pankaj K Agarwal, Therese C Biedl, Sylvain Lazard, Steve Robbins, Subhash Suri, Sue Whitesides
    Abstract:

    Let B be a point robot moving in the plane, whose path is constrained to have curvature at most 1, and let $\poly$ be a Convex Polygon with n vertices. We study the collision-free, optimal path-planning problem for B moving between two configurations inside $\poly$. (A configuration specifies both a location and a direction of travel.) We present an O(n2 log n) time algorithm for determining whether a collision-free path exists for B between two given configurations. If such a path exists, the algorithm returns a shortest one. We provide a detailed classification of curvature-constrained shortest paths inside a Convex Polygon and prove several properties of them, which are interesting in their own right. For example, we prove that any such shortest path is comprised of at most eight segments, each of which is a circular arc of unit radius or a straight-line segment. Some of the properties are quite general and shed some light on curvature-constrained shortest paths amid obstacles.

  • curvature constrained shortest paths in a Convex Polygon extended abstract
    Symposium on Computational Geometry, 1998
    Co-Authors: Pankaj K Agarwal, Therese C Biedl, Sylvain Lazard, Steve Robbins, Subhash Suri, Sue Whitesides
    Abstract:

    Let B be a point robot moving in the plane, whose path is constrained to have curvature at most 1, and let P be a Convex Polygon with n vertices. We study the collision-free, optimal path-planning problem for B moving between two configurations inside P (a configuration specifies both a location and a direction of travel). We present an O(n2 log n) time algorithm for determining whether a collision-free path exists for B between two given configurations. If such a path exists, the algorithm returns a shortest one. We provide a detailed classification of curvature-constrained shortest paths inside a Convex Polygon and prove several properties of them, which are interesting in their own right. Some of the properties are quite general and shed some light on curvature-constrained shortest paths amid obstacles.