Papers by Suneeta Ramaswami
Flipturning Polygons (Extended Abstract)
This paper is concerned with a pivot of central concern in polymer physics research called a flip... more This paper is concerned with a pivot of central concern in polymer physics research called a flipturn, first defined in an unpublished 1973 paper of Joss and Shannon [4] as follows. A pocket of a nonconvex polygon P is a maximal connected sequence of polygon edges disjoint from the convex hull of P except at its endpoints. The line segment joining the endpoints of a pocket is called the lid. A flipturn rotates a pocket 180 degrees about the midpoint of its lid, or equivalently, reverses the order of the edges of a pocket without changing their lengths or orientations. Figure 1 shows the effect of a single flipturn on a nonconvex orthogonal polygon
ArXiv, 2017
This paper addresses the problem of finding minimum forcing sets in origami. The origami material... more This paper addresses the problem of finding minimum forcing sets in origami. The origami material folds flat along straight lines called creases that can be labeled as mountains or valleys. A forcing set is a subset of creases that force all the other creases to fold according to their labels. The result is a flat folding of the origami material. In this paper we develop a linear time algorithm that finds minimum forcing sets in one dimensional origami.
We perform an experimental comparison of four algorithms for converting a given triangulation T o... more We perform an experimental comparison of four algorithms for converting a given triangulation T of an orientable, connected, boundaryless, and compact surface S in E into a quadrangulation Q of S. All algorithms compute Q by first pairing edge-adjacent triangles of T (of another triangulation of S with the same vertex set) so that every triangle belongs to exactly one pair. Such a perfect pairing is guaranteed for triangulations of boundaryless and compact surfaces (also known as closed surfaces). The common edge of each pair of matched triangles is then removed to give rise to a quadrilateral of Q. We implemented two greedy algorithms, a graph matching algorithm, and a new algorithm presented in this paper, which uses edge contractions and vertex splittings to compute a quadrangulation of the surface in two steps by combining pairings with edge flips. If T has positive genus g, the new algorithm takes O(gn f + g) amortized time to compute a quadrangulation with the same vertex set,...
The assignment problem takes as input two finite point sets S and T and establishes a corresponde... more The assignment problem takes as input two finite point sets S and T and establishes a correspondence between points in S and points in T, such that each point in S maps to exactly one point in T, and each point in T maps to at least one point in S. In this paper we show that this problem has an O(n log n)-time solution, provided that the points in S and T are restricted to lie on a line (linear time, if S and T are presorted).
Journal of Mathematical Modelling and Algorithms
Given a configuration C of geometric objects in R 2 (called the input configuration), a target co... more Given a configuration C of geometric objects in R 2 (called the input configuration), a target configuration T of geometric objects in R 1 , and a class S of allowable sectioning lines we consider in this paper many variations on the following problem: "Is there a line S 2 S such that the section S " C is equivalent by rigid motion to the target T ?" KEYWORDS: Section, projection, tomography, probe, stereology, morphology, recognition. 1 Introduction Mathematical Tomography deals with a set of "techniques of reconstructing internal structures in a body from data collected by detectors (sensitive to some sort of energy) outside the body" [22]. For example, one technique in computerized tomography consists on measuring the attenuation of X-rays between multiple pairs of points outside the body, each pair giving positions for a source and a detector, from that the Radon transform is estimated, and the density distribution approximated. Mathematical methods in t...
Autonomous Robots, 2015
Your article is protected by copyright and all rights are held exclusively by Springer Science +B... more Your article is protected by copyright and all rights are held exclusively by Springer Science +Business Media New York. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".
Springer Tracts in Advanced Robotics, 2009
In this paper we propose novel algorithms for reconfiguring modular robots that are composed of n... more In this paper we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2 × 2 × 2 modules. We respect certain physical constraints: each atom reaches at most unit velocity and (via expansion) can displace at most one other atom. We require that one of the atoms can store a map of the target configuration. Our algorithms involve a total of O(n 2) such atom operations, which are performed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n 2) parallel steps [8, 10, 4] or do not respect the constraints mentioned above [1]. In fact, in the setting considered, our algorithms are optimal, in the sense that certain reconfigurations require Ω (n) parallel steps. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configurations.
Lecture Notes in Computer Science, 2003
We analyze several perfect-information combinatorial games played on planar triangulations. We in... more We analyze several perfect-information combinatorial games played on planar triangulations. We introduce three broad categories of such games: constructing, transforming, and marking triangulations. In various situations, we develop polynomial-time algorithms to determine who wins a given game under optimal play, and to find a winning strategy. Along the way, we show connections to existing combinatorial games such as Kayles.
Proceedings of the twenty-fifth annual symposium on Computational geometry, 2009
In this paper, we present an algorithm that utilizes a quadtree data structure to construct a qua... more In this paper, we present an algorithm that utilizes a quadtree data structure to construct a quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than 18.43 • (= arctan(1 3)) or greater than 171.86 • (= 135 • + 2 arctan(1 3)). This is the first known result, to the best of our knowledge, on a direct quadrilateral mesh generation algorithm with a provable guarantee on the angles.
Robotica, 2011
SUMMARYIn this paper, we propose novel algorithms for reconfiguring modular robots that are compo... more SUMMARYIn this paper, we propose novel algorithms for reconfiguring modular robots that are composed ofnatoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2 × 2 × 2 modules. We respect certain physical constraints: each atom reaches at most constant velocity and can displace at most a constant number of other atoms. We assume that one of the atoms has access to the coordinates of atoms in the target configuration.Our algorithms involve a total ofO(n2) atom operations, which are performed inO(n) parallel steps. This improves on previous reconfiguration algorithms, which either useO(n2) parallel steps or do not respect the constraints mentioned above. In fact, in the settings considered, our algorithms are optimal. A further advantage of our algorithms is that reconfiguration can take place within the union of the source ...
Journal of Parallel and Distributed Computing, 1995
The motion planning problem for an object with two degrees of freedom moving in the plane can be ... more The motion planning problem for an object with two degrees of freedom moving in the plane can be stated as follows: Given a set of polygonal obstacles in the plane, and a two-dimensional mobile object B with two degrees of freedom, determine if it is possible to move B from a start position to a nal position while avoiding the obstacles. If so, plan a path for such a motion. Techniques from computational geometry have been used to develop exact algorithms for this fundamental case of motion planning. In this paper we obtain optimal mesh implementations of two di erent methods for planning motion in the plane. We do this by rst presenting optimal mesh algorithms for some geometric problems that, in addition to being important substeps in motion planning, have numerous independent applications in computational geometry. In particular, we rst show that the Voronoi diagram of a set of n nonintersecting (except possibly at endpoints) line segments in the plane can be constructed in O(p n) time on a p n p n mesh, which is optimal for the mesh. Consequently, we obtain an optimal mesh implementation of the sequential motion planning algorithm described in 21]; in other words, given a disc B and a polygonal obstacle set of size n, we can plan a path (if it exists) for the motion of B from a start position to a nal position in O(p n) time on a mesh of size n. We also show that the shortest path motion between a start position and a nal position for a convex object B (of constant size) moving among convex polygonal obstacles of total size n can be found in O(n) time on an n n mesh, which is worst-case optimal.
Journal of Computational Biology, 2006
The restriction scaffold assignment problem takes as input two finite point sets S and T (with S ... more The restriction scaffold assignment problem takes as input two finite point sets S and T (with S containing more points than T) and establishes a correspondence between points in S and points in T , such that each point in S maps to exactly one point in T , and each point in T maps to at least one point in S. In this paper we show that this problem has an O(n log n)time solution, provided that the points in S and T are restricted to lie on a line (linear time, if S and T are presorted).
Fast implementation of depth contours using topological sweep
ACM-SIAM Symposium on Discrete Algorithms, 2001
The concept of location depth was introduced in statistics as a way to extend the univariate noti... more The concept of location depth was introduced in statistics as a way to extend the univariate notion of ranking to a bivariate configuration of data points. It has been used successfully for robust estimation, hypothesis testing, and graphical display. These require the computation of depth regions, which form a collection of nested polygons. The center of the deepest region is
Graphs and Combinatorics, 2007
Let S and T be two sets of points with total cardinality n. The minimum-cost many-to-many matchin... more Let S and T be two sets of points with total cardinality n. The minimum-cost many-to-many matching problem matches each point in S to at least one point in T and each point in T to at least one point in S, such that sum of the matching costs is minimized. Here we examine the special case where both S and T lie on the line and the cost of matching s ∈ S to t ∈ T is equal to the distance between s and t. In this context, we provide an algorithm that determines a minimum-cost many-to-many matching in O(n log n) time, improving the previous best time complexity of O(n 2) for the same problem.
Discrete and Computational Geometry, 2002
A flipturn transforms a nonconvex simple polygon into another simple polygon by rotating a concav... more A flipturn transforms a nonconvex simple polygon into another simple polygon by rotating a concavity 180 • around the midpoint of its bounding convex hull edge. Joss and Shannon proved in 1973 that a sequence of flipturns eventually transforms any simple polygon into a convex polygon. This paper describes several new results about such flipturn sequences. We show that any orthogonal polygon is convexified after at most n − 5 arbitrary flipturns, or at most 5(n −4)/6 well-chosen flipturns, improving the previously best upper bound of (n − 1)!/2. We also show that any simple polygon can be convexified by at most n 2 −4n +1 flipturns, generalizing earlier results of Ahn et al. These bounds depend critically on how degenerate cases are handled; we carefully explore several possibilities. We prove that computing the longest flipturn sequence for a simple polygon is NP-hard. Finally, we show that although flipturn sequences for the same polygon can have significantly different lengths, the shape and position of the final convex polygon is the same for all sequences and can be computed in O(n log n) time.
Computational Geometry, 2009
In this paper we propose a novel algorithm that, given a source robot S and a target robot T , re... more In this paper we propose a novel algorithm that, given a source robot S and a target robot T , reconfigures S into T. Both S and T are robots composed of n atoms arranged in 2 × 2 × 2 meta-modules. The reconfiguration involves a total of O (n) atomic operations (expand, contract, attach, detach) and is performed in O (n) parallel steps. This improves on previous reconfiguration algorithms [D.
Computational Geometry, 1998
We study the problem of converting triangulated domains to quadrangulations, under a variety of c... more We study the problem of converting triangulated domains to quadrangulations, under a variety of constraints. We obtain a variety of characterizations for when a triangulation (of some structure such as a polygon, set of points, line segments or planar subdivision) admits a quadrangulation without the use of Steiner points, or with a bounded number of Steiner points. We also investigate the effect of demanding that the Steiner points be added in the interior or exterior of a triangulated simple polygon and propose efficient algorithms for accomplishing these tasks. For example, we give a linear-time method that quadrangulates a triangulated simple polygon with the minimum number of outer Steiner points required for that triangulation. We show that this minimum can be at most Ln/3J, and that there exist polygons that require this many such Steiner points. We also show that a triangulated simple n-gon may be quadrangulated with at most [n/4J Steiner points inside the polygon and at most one outside. This algorithm also allows us to obtain, in linear time, quadrangulations from general triangulated domains (such as triangulations of polygons with holes, a set of points or line segments) with a bounded number of Steiner points.
Algorithmica, 2002
We present an optimal parallel randomized algorithm for the Voronoi diagram of a set of n noninte... more We present an optimal parallel randomized algorithm for the Voronoi diagram of a set of n nonintersecting (except possibly at endpoints) line segments in the plane. Our algorithm runs in O(log n) time with high probability using O(n) processors on a CRCW PRAM. This algorithm is optimal in terms of work done since the sequential time bound for this problem is (n log n). Our algorithm improves by an O(log n) factor the previously best known deterministic parallel algorithm, given by Goodrich,Ó'Dúnlaing, and Yap, which runs in O(log 2 n) time using O(n) processors. We obtain this result by using a new "two-stage" random sampling technique. By choosing large samples in the first stage of the algorithm, we avoid the hurdle of problem-size "blow-up" that is typical in recursive parallel geometric algorithms. We combine the two-stage sampling technique with efficient search and merge procedures to obtain an optimal algorithm. This technique gives an alternative optimal algorithm for the Voronoi diagram of points as well (all other optimal parallel algorithms for this problem use the transformation to three-dimensional half-space intersection).
Quadrilateral Meshes for the Registration of Human Brain Images
Finite element analysis (FEA) is a powerful tool for numerically solving differential equations o... more Finite element analysis (FEA) is a powerful tool for numerically solving differential equations or variational problems that arise during structural modeling in engineering and the applied sciences. A key feature of FEA is the specification of a mesh over the problem domain. Triangular meshes have been extensively investigated by the meshing community, and their theoretical properties are now well understood,[1]; however, the generation of good quadrilateral meshes is not as well understood. Most automated mesh generators cater to ...
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Papers by Suneeta Ramaswami