A PARALLEL ALGORITHM FOR ENCLOSED AND ENCLOSING TRIANGLES

1992 ◽  
Vol 02 (02) ◽  
pp. 191-214 ◽  
Author(s):  
SHARAT CHANDRAN ◽  
DAVID M. MOUNT
Keyword(s):  
Parallel Algorithms ◽  
Parallel Algorithm ◽  
Convex Polygon ◽  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
New Techniques ◽  
Crcw Pram

We consider the problems of computing the largest area triangle enclosed within a given n-sided convex polygon and the smallest area triangle which encloses a given convex polygon. We show that these problems are closely related by presenting a single sequential linear time algorithm which essentially solves both problems simultaneously. We also present a cost-optimal parallel algorithm that solves both of these problems in O( log log n) time using n/ log log n processors on a CRCW PRAM. In order to achieve these bounds we develop new techniques for the design of parallel algorithms for computational problems involving the rotating calipers method.

scholarly journals A Linear Parallel Algorithm to Compute Bisimulation and Relational Coarsest Partitions

2021 ◽  
pp. 115-133
Author(s):  
Jan Martens ◽  
Jan Friso Groote ◽  
Lars van den Haak ◽  
Pieter Hijma ◽  
Anton Wijs
Keyword(s):  
Parallel Algorithm ◽  
Time Complexity ◽  
Linear Time ◽  
Random Access ◽  
Time Algorithm ◽  
Transition System ◽  
Linear Time Algorithm

AbstractThe most efficient way to calculate strong bisimilarity is by finding the relational coarsest partition of a transition system. We provide the first linear-time algorithm to calculate strong bisimulation using parallel random access machines (PRAMs). More precisely, with n states, m transitions and $$| Act |\le m$$ | A c t | ≤ m action labels, we provide an algorithm for $$\max (n,m)$$ max ( n , m ) processors that calculates strong bisimulation in time $$\mathcal {O}(n+| Act |)$$ O ( n + | A c t | ) and space $$\mathcal {O}(n+m)$$ O ( n + m ) . The best-known PRAM algorithm has time complexity $$\mathcal {O}(n\log n)$$ O ( n log n ) on a smaller number of processors making it less suitable for massive parallel devices such as GPUs. An implementation on a GPU shows that the linear time-bound is achievable on contemporary hardware.

How to Systematically Embed Cycles in Balanced Hypercubes

2017 ◽  
Vol 5 (1) ◽  
pp. 44-56
Author(s):  
Hsuan-Han Chang ◽  
Kuan-Ting Chen ◽  
Pao-Lien Lai
Keyword(s):  
Parallel Algorithms ◽  
Distributed Memory ◽  
Linear Time ◽  
Time Algorithm ◽  
Parallel Computers ◽  
Hamiltonian Cycles ◽  
Linear Time Algorithm ◽  
Systematic Method ◽  
Balanced Hypercube ◽  
Host Graph

The balanced hypercube is a variant of the hypercube structure and has desirable properties like connectivity, regularity, and symmetry. The cycle is a popular interconnection topology and has been widely used in distributed-memory parallel computers. Moreover, parallel algorithms of cycles have been extensively developed and used. The problem of how to embed cycles into a host graph has attracted a great attention in recent years. However, there is no systematic method proposed to generate the desired cycles in balanced hypercubes. In this paper, the authors develop systematic linear time algorithm to construct cycles and Hamiltonian cycles for the balanced hypercube.

GUARD PLACEMENT FOR MAXIMIZING L-VISIBILITY EXTERIOR TO A CONVEX POLYGON

2009 ◽  
Vol 19 (04) ◽  
pp. 357-370
Author(s):  
DEBABRATA BARDHAN ◽  
SANSANKA ROY ◽  
SANDIP DAS
Keyword(s):  
Shortest Path ◽  
Convex Polygon ◽  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Placement Problem ◽  
Maximum Area

Two points a and b are said to be L-visible among a set of polygonal obstacles if the length of the shortest path from a to b avoiding these obstacles is no more than L. For a given convex polygon P with n vertices, Gewali et al.1 addressed the guard placement problem on the boundary of P that covers the maximum area outside to the polygon under L-visibility with P as obstacle. Their proposed algorithm runs in O(n) time if [Formula: see text], where π(P) denotes the perimeter of P. They conjectured that if [Formula: see text], then the problem can be solved in subquadratic time. In this paper, we settle the conjecture in the affirmative sense, by proposing an easy to implement linear time algorithm for any arbitrary value of L.

QUADRANGULAR REFINEMENTS OF CONVEX POLYGONS WITH AN APPLICATION TO FINITE-ELEMENT MESHES

2000 ◽  
Vol 10 (01) ◽  
pp. 1-40 ◽  
Author(s):  
MATTHIAS MÜLLER-HANNEMANN ◽  
KARSTEN WEIHE
Keyword(s):  
Finite Element ◽  
Convex Polygon ◽  
Linear Time ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Convex Polygons ◽  
Minimum Number ◽  
Three Dimensional Space

We present a linear–time algorithm that decomposes a convex polygon conformally into a minimum number of strictly convex quadrilaterals. Moreover, we characterize the polygons that can be decomposed without additional vertices inside the polygon, and we present a linear–time algorithm for such decompositions, too. As an application, we consider the problem of constructing a minimum conformal refinement of a mesh in the three–dimensional space, which approximates the surface of a workpiece. We prove that this problem is strongly [Formula: see text] –hard, and we present a linear-time algorithm with a constant approximation ratio of four.

COMPUTING A SHORTEST WEAKLY EXTERNALLY VISIBLE LINE SEGMENT FOR A SIMPLE POLYGON

1999 ◽  
Vol 09 (01) ◽  
pp. 81-96 ◽  
Author(s):  
BINAY K. BHATTACHARYA ◽  
ASISH MUKHOPADHYAY ◽  
GODFRIED T. TOUSSAINT
Keyword(s):  
Line Segment ◽  
Convex Polygon ◽  
Linear Time ◽  
Simple Polygon ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Suitable Generalization

A simple polygon P is said to be weakly extrenally visible from a line segment L if it lies outside P and for every point p on the boundary of P there is a point q on L such that no point in the interior of [Formula: see text] lies inside P. In this paper, a linear time algorithm is proposed for computing a shortest line segment from which P is weakly externally visible. This is done by a suitable generalization of a linear time algorithm which solves the same problem for a convex polygon.

scholarly journals A linear-time algorithm for computing the voronoi diagram of a convex polygon

1989 ◽  
Vol 4 (6) ◽  
pp. 591-604 ◽  
Author(s):  
Alok Aggarwal ◽  
Leonidas J. Guibas ◽  
James Saxe ◽  
Peter W. Shor
Keyword(s):  
Voronoi Diagram ◽  
Convex Polygon ◽  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm

COMPUTING THE CENTER OF AREA OF A CONVEX POLYGON

2003 ◽  
Vol 13 (05) ◽  
pp. 439-445 ◽  
Author(s):  
PETER BRAß ◽  
LAURA HEINRICH-LITAN ◽  
PAT MORIN
Keyword(s):  
Convex Polygon ◽  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Minimum Area

The center of area of a convex planar set X is the point p for which the minimum area of X intersected by any halfplane containing p is maximized. We describe a simple randomized linear-time algorithm for computing the center of area of a convex n-gon.

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