scholarly journals Parallel Algorithms for Single-Layer Channel Routing

1997 ◽  
Vol 07 (03) ◽  
pp. 267-277
Author(s):  
Ronald I. Greenberg ◽  
Shih-Chuan Hung ◽  
Jau-Der Shih
Keyword(s):  
Parallel Algorithms ◽  
Linear Time ◽  
Single Layer ◽  
Channel Routing ◽  
Processor Time ◽  
Channel Boundary ◽  
Crew Pram ◽  
Minimum Separation ◽  
Crcw Pram ◽  
River Routing

We provide efficient parallel algorithms for the minimum separation, offset range, and optimal offset problems for single-layer channel routing. We consider all the variations of these problems that are known to have linear-time sequential solutions rather than limiting attention to the "river-routing" context, where single-sided connections are disallowed. For the minimum separation problem, we obtain O( lg N) time on a CREW PRAM or [Formula: see text] time on a (common) CRCW PRAM, both with optimal work (processor-time product) of O(N), where $N$ is the number of terminals. For the offset range problem, we obtain the same time and processor bounds as long as only one side of the channel contains single-sided nets. For the optimal offset problem with single-sided nets on one side of the channel, we obtain time O( lg N lg lg N) on a CREW PRAM or [Formula: see text] time on a CRCW PRAM with O(N lg lg N) work. Not only does this improve on previous results for river routing, but we can obtain an even better time of O(( lg lg N)2) on the CRCW PRAM in the river routing context. In addition, wherever our results allow a channel boundary to contain single-sided nets, the results also apply when that boundary is ragged and N incorporates the number of bendpoints.

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.

PARALLEL ALGORITHMS FOR HAMILTONIAN 2-SEPARATOR CHORDAL GRAPHS

2002 ◽  
Vol 12 (01) ◽  
pp. 51-64 ◽  
Author(s):  
B. S. PANDA ◽  
VIJAY NATARAJAN ◽  
SAJAL K. DAS
Keyword(s):  
Parallel Algorithms ◽  
Parallel Algorithm ◽  
Hamiltonian Cycle ◽  
Chordal Graph ◽  
Chordal Graphs ◽  
Pram Model ◽  
Crew Pram ◽  
Crcw Pram

In this paper we propose a parallel algorithm to construct a one-sided monotone polygon from a Hamiltonian 2-separator chordal graph. The algorithm requires O( log n) time and O(n) processors on the CREW PRAM model, where n is the number of vertices and m is the number of edges in the graph. We also propose parallel algorithms to recognize Hamiltonian 2-separator chordal graphs and to construct a Hamiltonian cycle in such a graph. They run in O( log 2 n) time using O(mn) processors on the CRCW PRAM model and O( log 2 n) time using O(m) processors on the CREW PRAM model, respectively.

scholarly journals EFFICIENT PARALLEL ALGORITHMS ON DISTANCE HEREDITARY GRAPHS

1999 ◽  
Vol 09 (01) ◽  
pp. 43-52 ◽  
Author(s):  
SUN-YUAN HSIEH ◽  
CHIN-WEN HO ◽  
TSAN-SHENG HSU ◽  
MING-TAT KO ◽  
GEN-HUEY CHEN
Keyword(s):  
Parallel Algorithms ◽  
Steiner Tree ◽  
Dominating Set ◽  
Parallel Computations ◽  
Connected Dominating Set ◽  
View Point ◽  
Induced Subgraph ◽  
Crew Pram ◽  
Crcw Pram

Distance hereditary graphs are graphs in which every two vertices have the same distance in every connected induced subgraph containing them. In this paper, we study properties of distance hereditary graphs from the view point of parallel computations. We present efficient parallel algorithms for finding a minimum weighted connected dominating set, a minimum weighted Steiner tree, which take O( log n) time using O(n + m) processors on CRCW PRAM, where n and m are the number of vertices and edges of a given graph, respectively. We also find a maximum weighted clique of a distance hereditary graph in O( log 2 n) time using O(n + m) processors on a CREW PRAM.

scholarly journals Length of Maximal Common Subsequences

1992 ◽  
Vol 21 (426) ◽  
Author(s):  
Kim Skak Larsen
Keyword(s):  
Dynamic Programming ◽  
Parallel Algorithm ◽  
Linear Time ◽  
Programming Approach ◽  
Simple Modification ◽  
Dynamic Programming Approach ◽  
Pram Model ◽  
Crew Pram ◽  
The Common ◽  
Crcw Pram

<p>The problem of computing the length of the maximal common subsequences of two strings is quite well examined in the sequential case. There are many variations, but the standard approach is to compute the length in quadratic time using dynamic programming. A linear-time parallel algorithm can be obtained via a simple modification of this strategy by letting a linear number of processors sweep through the table created for the dynamic programming approach.</p><p>However, the contribution of this paper is to show that the problem is in NC. More specifically, we show that the length of the maximal common subsequences of two strings <em>s</em> and <em>t</em> can be computed in time O(log |s| € log |t|) in the CREW PRAM model and in time Theta(min(log |s|, log |t|)) in the COMMON CRCW PRAM model.</p>

scholarly journals Minimum separation for single-layer channel routing

1992 ◽  
Vol 43 (4) ◽  
pp. 201-205 ◽  
Author(s):  
Ronald I. Greenberg ◽  
F. Miller Maley
Keyword(s):  
Single Layer ◽  
Channel Routing ◽  
Minimum Separation

SUB-LOGARITHMIC ALGORITHMS FOR THE LARGEST EMPTY RECTANGLE PROBLEM

1993 ◽  
Vol 03 (01) ◽  
pp. 79-85
Author(s):  
STEPHAN OLARIU ◽  
WENHUI SHEN ◽  
LARRY WILSON
Keyword(s):  
Parallel Algorithms ◽  
Erew Pram ◽  
Pram Model ◽  
The Common ◽  
Crcw Pram ◽  
Natural Way

We show that the Largest Empty Rectangle problem can be solved by reducing it, in a natural way, to the All Nearest Smaller Values problem. We provide two classes of algorithms: the first one assumes that the input points are available sorted by x (resp. y) coordinate. Our algorithm corresponding to this case runs in O(log log n) time using [Formula: see text] processors in the Common-CRCW-PRAM model. For unsorted input, we present algorithms that run in [Formula: see text] time using [Formula: see text] processors in the Common-CRCW-PRAM, or in O( log n) time using [Formula: see text] processors in the EREW-PRAM model. No sub-logarithmic time parallel algorithms have been previously reported for this problem.

scholarly journals SEQUENTIAL AND PARALLEL ALGORITHMS FOR THE k CLOSEST PAIRS PROBLEM

1995 ◽  
Vol 05 (03) ◽  
pp. 273-288 ◽  
Author(s):  
HANS-PETER LENHOF ◽  
MICHIEL SMID
Keyword(s):  
Decision Tree ◽  
Parallel Algorithms ◽  
Dimensional Space ◽  
Decision Tree Model ◽  
Sequential Algorithm ◽  
Tree Model ◽  
Parallel Time ◽  
Parallel Version ◽  
Pram Model ◽  
Crcw Pram

Let S be a set of n points in D-dimensional space, where D is a constant, and let k be an integer between 1 and [Formula: see text]. A new and simpler proof is given of Salowe’s theorem, i.e., a sequential algorithm is given that computes the k closest pairs in the set S in O(n log n+k) time, using O(n+k) space. The algorithm fits in the algebraic decision tree model and is, therefore, optimal. Salowe’s algorithm seems difficult to parallelize. A parallel version of our algorithm is given for the CRCW-PRAM model. This version runs in O((log n)2 log log n) expected parallel time and has an O(n log n log log n+k) time-processor product. Finally, actual running times are given of an implementation of our sequential algorithm.

ON PARALLEL PREFIX COMPUTATION

1994 ◽  
Vol 04 (04) ◽  
pp. 429-436 ◽  
Author(s):  
SANJEEV SAXENA ◽  
P.C.P. BHATT ◽  
V.C. PRASAD
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Optimal Time ◽  
Word Size ◽  
Parallel Prefix ◽  
Parallel Merge ◽  
Merge Sort ◽  
Sort Algorithm ◽  
Crcw Pram ◽  
Prefix Sums

We prove that prefix sums of n integers of at most b bits can be found on a COMMON CRCW PRAM in [Formula: see text] time with a linear time-processor product. The algorithm is optimally fast, for any polynomial number of processors. In particular, if [Formula: see text] the time taken is [Formula: see text]. This is a generalisation of previous result. The previous [Formula: see text] time algorithm was valid only for O(log n)-bit numbers. Application of this algorithm to r-way parallel merge sort algorithm is also considered. We also consider a more realistic PRAM variant, in which the word size, m, may be smaller than b (m≥log n). On this model, prefix sums can be found in [Formula: see text] optimal time.

scholarly journals Simple and Work-Efficient Parallel Algorithms for the Minimum Spanning Tree Problem

1997 ◽  
Vol 07 (01) ◽  
pp. 25-37 ◽  
Author(s):  
Christos D. Zaroliagis
Keyword(s):  
Parallel Algorithms ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Erew Pram ◽  
Minimum Spanning Tree Problem ◽  
Crcw Pram

Two Simple and work-efficient parallel algorithms for the minimum spanning tree problem are presented. Both algorithms perform O(m log n) work. The first algorithm runs in O( log 2 n) time on an EREW PRAM, while the second algorithm runs in O( log n) time on a COMMON CRCW PRAM.

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