In this work, we present a time-and VLSI-optimal sorting algorithm for meshes with multiple broad... more In this work, we present a time-and VLSI-optimal sorting algorithm for meshes with multiple broadcasting. Specifically, we show that for every choice of a positive integer constant c, m items left( {n^{frac{1} {2} + frac{1} {{2c}}} leqslant m leqslant n} right) stored in the first leftlceil {frac{m} {{sqrt n }}} rightrceil columns of a mesh with multiple broadcasting of size sqrt {n} x sqrt {n} can be sorted in O({frac{m} {{sqrt n }}}) time.
Location management is one of the most important issues in the design of future cellular systems.... more Location management is one of the most important issues in the design of future cellular systems. It consists of two basic operations: location update and paging. The paging operation is dependent on the corresponding location update operation. The time based, movement based, and distance based location update schemes are three of the most popular dynamic location update schemes. It has been shown that the distance based scheme is more efficient than the movement based. However the distance between two cells is difficult to obtain. The author proposes a coordinate system which can be used to systematically assign IDs to the cells in a cellular system. With this cell ID assignment scheme, the distance between any two cells can be computed easily. Based on our distance computation scheme, a speed adaptive location update scheme is presented. It is shown that the speed adaptive location update scheme is a generalization of both time based and distance based schemes
Problems with solutions based upon integer computations are collectively referred to as integer p... more Problems with solutions based upon integer computations are collectively referred to as integer problems. Such problems occur routinely in pattern recognition, image processing, graph theory, and query processing. The purpose of this paper is to present constant time algorithms for computing the prefix sums of an integer sequence, and for solving the packing problem on reconfigurable meshes. These two algorithms are fundamental in the sense that they afford us efficient solutions to a wide variety of problems. Applications discussed in this paper include integer sorting, converting between the edge-list and the adjacency list representation of a graph, and converting between different representations of a rooted tree. All these problems are solved in constant time. As another application, we show how to compute the perimeter and the area of a binary image of size n ×n in O(loglogn ) time.
Location areas is a popular location management scheme in cellular networks. In the location area... more Location areas is a popular location management scheme in cellular networks. In the location areas scheme, a mobile terminal updates its location whenever it moves into a cell that belongs to a new location area. However, no matter how the location areas are designed, the location update ping-pong effect exists when a mobile terminal moves back and forth between two
ABSTRACT Many practical problems lend themselves to an integer-based solution. Given such special... more ABSTRACT Many practical problems lend themselves to an integer-based solution. Given such specialized data it is sometimes possible to design algorithms which are more efficient than a corresponding general-purpose algorithm. Integer sorting of the most basic integer-related problems. The purpose of this work is to present applications of reconfigurable meshes to constant time computations involving integers. More specifically, we develop a constant time integer sorting algorithm on a reconfigurable mesh and show how this leads to a constant time parentheses matching algorithm.
The channel-assignment problem is central to the integrated circuit fabrication process. Given a ... more The channel-assignment problem is central to the integrated circuit fabrication process. Given a two-sided printed circuit board, we wish to maken pairs of components electrically equivalent. The connections are made using two vertical runs along with a horizontal one. Each horizontal run lies in a channel. The channel-assignment problem involves minimizing the total number of channels used. Recent advances in VLSI have made it possible to build massively parallel machines. To overcome the inefficiency of long distance communications among processors, some parallel architectures have been augmented by bus systems. If such a bus system can be dynamically changed to suit communication needs among processors, it is referred to asreconfigurable. The reconfigurable mesh is one of the practical models featuring a reconfigurable bus system. In this paper, we propose a constant-time algorithm to solve the channel-assignment problem of sizen on a reconfigurable mesh of sizen×n.
Until now, buses have been used exclusively to support fast communication and data transfer needs... more Until now, buses have been used exclusively to support fast communication and data transfer needs within a parallel machine. Recently, the authors have demonstrated novel uses of buses in a multiprocessor reconfigurable architecture. Specifically, we have argued that buses can be successfully used both as topological descriptors and as powerful computational devices. The purpose of this note is to show that this new paradigm can be used for computing the Hough transform -the most widely used technique for detecting lines and curves in binary or grey level images. Specifically, for an N x N digitized image stored in a reconfigurable mesh of size N x N, one pixel per processor, we present an 0 (n x log(N/rr)) time algorithm to compute the Hough transform with n standing for the number of angles in the quantization of the B-space.
IEEE Transactions on Parallel and Distributed Systems, 1995
... 6, NO. 7, JULY 1995 687 Time-Optimal Visibility-Related Algorithms on Meshes with Multiple Br... more ... 6, NO. 7, JULY 1995 687 Time-Optimal Visibility-Related Algorithms on Meshes with Multiple Broadcasting Dharmavani Bhagavathi, Venkata V. Bokka, Himabindu Gurla, Stephan Olariu, James L. Schwing, Member, IEEE, Ivan StojmenoviL, and Jingyuan Zhang ...
Recently it has been noticed that for semigroup computations and for selection, rectangular meshe... more Recently it has been noticed that for semigroup computations and for selection, rectangular meshes with multiple broadcasting yield faster algorithms than their square counterparts. The contribution of this paper is to provide yet another example of a fundamental problem for which this phenomenon occurs.
In this paper we propose time-optimal convex hull algorithms for two classes of enhanced meshes. ... more In this paper we propose time-optimal convex hull algorithms for two classes of enhanced meshes. Our first algorithm computes the convex hull of an arbitrary set ofn points in the plane inO (logn) time on a mesh with multiple broadcasting of sizen×n. The second algorithm shows that the same problem can be solved inO (1) time on a reconfigurable mesh of sizen×n. Both algorithms achieve time lower bounds for their respective model of computation.
IEEE Transactions on Parallel and Distributed Systems, 1992
A family of intervals on the real line provides a natural model for a vast number of scheduling a... more A family of intervals on the real line provides a natural model for a vast number of scheduling and VLSI problems. Recently, a number of parallel algorithms to solve a variety of practical problems on such a family of intervals have been proposed in the literature. The authors develop computational tools and show how they can be used for the
Journal of Parallel and Distributed Computing, 1995
The purpose of this work is to present simple time-optimal algorithms for a number of convexity-r... more The purpose of this work is to present simple time-optimal algorithms for a number of convexity-related problems on meshes with multiple broadcasting. More speci cally, we show that with an nvertex convex polygon P as input, the tasks of computing the perimeter, the area, the diameter, the width, the modality, the smallest-area enclosing rectangle, and the largest-area inscribed triangle sharing an edge with P , can be solved in O(log n) time on a mesh with multiple broadcasting of size n n. Furthermore, this is proved time-optimal in this model of computation. Similarly, we show that with two n-vertex convex polygons P and Q as input, the tasks of detecting whether P lies inside Q and of computing the maximum distance between P and Q can be solved in O(log n) time, which turns out to be time-optimal. We further show that in case P and Q are separable, task of computing the minimum distance between P and Q can be performed in O(1) time on a mesh with multiple broadcasting of size n n.
International Journal of Foundations of Computer Science, 1992
Encoding the shape of a binary tree is a basic step in a number of algorithms in integrated circu... more Encoding the shape of a binary tree is a basic step in a number of algorithms in integrated circuit design, automated theorem proving, and game playing. We propose cost-optimal parallel algorithms to solve the binary tree encoding/decoding problem. Specifically, we encode the relevant shape information of an n-node binary tree in a 2n bitstring. Conversely, given an arbitrary 2n bitstring we reconstruct the shape of the corresponding binary tree, if such a tree exists. All our algorithms run in O(log n) time using O(n/log n) processors in the EREW-PRAM model of computation.
IEEE Transactions on Parallel and Distributed Systems, 1994
A U.S.A. bstract e One of the fundamental algorithmic problems in computer science involves selec... more A U.S.A. bstract e One of the fundamental algorithmic problems in computer science involves selecting th -th smallest element in a collection of elements. We propose an algorithm design m k A n ethodology to solve the selection problem on meshes with multiple broadcasting. Our methodology leads to a selection algorithm that runs in O( ) time on a mesh n (log n ) 4 n 3/8 1/4 5/8 1/4 1/8 3/ (log n ) n /(log n ) a l with multiple broadcasting of size ×
One of the fundamental algorithmic problems in computer science involves selecting thekth smalles... more One of the fundamental algorithmic problems in computer science involves selecting thekth smallest element in a setS ofn elements. In this paper we present a fast selection algorithm which runs inO(n 1/8 logn) time on a mesh with multiple broadcasting of sizen 3/8 ×n 5/8. Our result shows that, just like semigroup computations, selection can be done much faster on a suitably chosen rectangular mesh than on square meshes. We also show that if every processor can storen 1/9 items, then our selection algorithm runs inO(n 1/9 logn) time on a mesh with multiple broadcasting of sizen 1/3 ×n 5/9.
run in O(logn) time and O(log" n) time, respectively. In fact, our convex hull algorithm applies ... more run in O(logn) time and O(log" n) time, respectively. In fact, our convex hull algorithm applies to ordered points in the plane as well: with an ordered set S of n such points stored one of size VS X tp er processor in a reconfigurable mesh n, our algorithm computes the convex hull of S in 0 (log2 n).
In this work, we present a time-and VLSI-optimal sorting algorithm for meshes with multiple broad... more In this work, we present a time-and VLSI-optimal sorting algorithm for meshes with multiple broadcasting. Specifically, we show that for every choice of a positive integer constant c, m items left( {n^{frac{1} {2} + frac{1} {{2c}}} leqslant m leqslant n} right) stored in the first leftlceil {frac{m} {{sqrt n }}} rightrceil columns of a mesh with multiple broadcasting of size sqrt {n} x sqrt {n} can be sorted in O({frac{m} {{sqrt n }}}) time.
Location management is one of the most important issues in the design of future cellular systems.... more Location management is one of the most important issues in the design of future cellular systems. It consists of two basic operations: location update and paging. The paging operation is dependent on the corresponding location update operation. The time based, movement based, and distance based location update schemes are three of the most popular dynamic location update schemes. It has been shown that the distance based scheme is more efficient than the movement based. However the distance between two cells is difficult to obtain. The author proposes a coordinate system which can be used to systematically assign IDs to the cells in a cellular system. With this cell ID assignment scheme, the distance between any two cells can be computed easily. Based on our distance computation scheme, a speed adaptive location update scheme is presented. It is shown that the speed adaptive location update scheme is a generalization of both time based and distance based schemes
Problems with solutions based upon integer computations are collectively referred to as integer p... more Problems with solutions based upon integer computations are collectively referred to as integer problems. Such problems occur routinely in pattern recognition, image processing, graph theory, and query processing. The purpose of this paper is to present constant time algorithms for computing the prefix sums of an integer sequence, and for solving the packing problem on reconfigurable meshes. These two algorithms are fundamental in the sense that they afford us efficient solutions to a wide variety of problems. Applications discussed in this paper include integer sorting, converting between the edge-list and the adjacency list representation of a graph, and converting between different representations of a rooted tree. All these problems are solved in constant time. As another application, we show how to compute the perimeter and the area of a binary image of size n ×n in O(loglogn ) time.
Location areas is a popular location management scheme in cellular networks. In the location area... more Location areas is a popular location management scheme in cellular networks. In the location areas scheme, a mobile terminal updates its location whenever it moves into a cell that belongs to a new location area. However, no matter how the location areas are designed, the location update ping-pong effect exists when a mobile terminal moves back and forth between two
ABSTRACT Many practical problems lend themselves to an integer-based solution. Given such special... more ABSTRACT Many practical problems lend themselves to an integer-based solution. Given such specialized data it is sometimes possible to design algorithms which are more efficient than a corresponding general-purpose algorithm. Integer sorting of the most basic integer-related problems. The purpose of this work is to present applications of reconfigurable meshes to constant time computations involving integers. More specifically, we develop a constant time integer sorting algorithm on a reconfigurable mesh and show how this leads to a constant time parentheses matching algorithm.
The channel-assignment problem is central to the integrated circuit fabrication process. Given a ... more The channel-assignment problem is central to the integrated circuit fabrication process. Given a two-sided printed circuit board, we wish to maken pairs of components electrically equivalent. The connections are made using two vertical runs along with a horizontal one. Each horizontal run lies in a channel. The channel-assignment problem involves minimizing the total number of channels used. Recent advances in VLSI have made it possible to build massively parallel machines. To overcome the inefficiency of long distance communications among processors, some parallel architectures have been augmented by bus systems. If such a bus system can be dynamically changed to suit communication needs among processors, it is referred to asreconfigurable. The reconfigurable mesh is one of the practical models featuring a reconfigurable bus system. In this paper, we propose a constant-time algorithm to solve the channel-assignment problem of sizen on a reconfigurable mesh of sizen×n.
Until now, buses have been used exclusively to support fast communication and data transfer needs... more Until now, buses have been used exclusively to support fast communication and data transfer needs within a parallel machine. Recently, the authors have demonstrated novel uses of buses in a multiprocessor reconfigurable architecture. Specifically, we have argued that buses can be successfully used both as topological descriptors and as powerful computational devices. The purpose of this note is to show that this new paradigm can be used for computing the Hough transform -the most widely used technique for detecting lines and curves in binary or grey level images. Specifically, for an N x N digitized image stored in a reconfigurable mesh of size N x N, one pixel per processor, we present an 0 (n x log(N/rr)) time algorithm to compute the Hough transform with n standing for the number of angles in the quantization of the B-space.
IEEE Transactions on Parallel and Distributed Systems, 1995
... 6, NO. 7, JULY 1995 687 Time-Optimal Visibility-Related Algorithms on Meshes with Multiple Br... more ... 6, NO. 7, JULY 1995 687 Time-Optimal Visibility-Related Algorithms on Meshes with Multiple Broadcasting Dharmavani Bhagavathi, Venkata V. Bokka, Himabindu Gurla, Stephan Olariu, James L. Schwing, Member, IEEE, Ivan StojmenoviL, and Jingyuan Zhang ...
Recently it has been noticed that for semigroup computations and for selection, rectangular meshe... more Recently it has been noticed that for semigroup computations and for selection, rectangular meshes with multiple broadcasting yield faster algorithms than their square counterparts. The contribution of this paper is to provide yet another example of a fundamental problem for which this phenomenon occurs.
In this paper we propose time-optimal convex hull algorithms for two classes of enhanced meshes. ... more In this paper we propose time-optimal convex hull algorithms for two classes of enhanced meshes. Our first algorithm computes the convex hull of an arbitrary set ofn points in the plane inO (logn) time on a mesh with multiple broadcasting of sizen×n. The second algorithm shows that the same problem can be solved inO (1) time on a reconfigurable mesh of sizen×n. Both algorithms achieve time lower bounds for their respective model of computation.
IEEE Transactions on Parallel and Distributed Systems, 1992
A family of intervals on the real line provides a natural model for a vast number of scheduling a... more A family of intervals on the real line provides a natural model for a vast number of scheduling and VLSI problems. Recently, a number of parallel algorithms to solve a variety of practical problems on such a family of intervals have been proposed in the literature. The authors develop computational tools and show how they can be used for the
Journal of Parallel and Distributed Computing, 1995
The purpose of this work is to present simple time-optimal algorithms for a number of convexity-r... more The purpose of this work is to present simple time-optimal algorithms for a number of convexity-related problems on meshes with multiple broadcasting. More speci cally, we show that with an nvertex convex polygon P as input, the tasks of computing the perimeter, the area, the diameter, the width, the modality, the smallest-area enclosing rectangle, and the largest-area inscribed triangle sharing an edge with P , can be solved in O(log n) time on a mesh with multiple broadcasting of size n n. Furthermore, this is proved time-optimal in this model of computation. Similarly, we show that with two n-vertex convex polygons P and Q as input, the tasks of detecting whether P lies inside Q and of computing the maximum distance between P and Q can be solved in O(log n) time, which turns out to be time-optimal. We further show that in case P and Q are separable, task of computing the minimum distance between P and Q can be performed in O(1) time on a mesh with multiple broadcasting of size n n.
International Journal of Foundations of Computer Science, 1992
Encoding the shape of a binary tree is a basic step in a number of algorithms in integrated circu... more Encoding the shape of a binary tree is a basic step in a number of algorithms in integrated circuit design, automated theorem proving, and game playing. We propose cost-optimal parallel algorithms to solve the binary tree encoding/decoding problem. Specifically, we encode the relevant shape information of an n-node binary tree in a 2n bitstring. Conversely, given an arbitrary 2n bitstring we reconstruct the shape of the corresponding binary tree, if such a tree exists. All our algorithms run in O(log n) time using O(n/log n) processors in the EREW-PRAM model of computation.
IEEE Transactions on Parallel and Distributed Systems, 1994
A U.S.A. bstract e One of the fundamental algorithmic problems in computer science involves selec... more A U.S.A. bstract e One of the fundamental algorithmic problems in computer science involves selecting th -th smallest element in a collection of elements. We propose an algorithm design m k A n ethodology to solve the selection problem on meshes with multiple broadcasting. Our methodology leads to a selection algorithm that runs in O( ) time on a mesh n (log n ) 4 n 3/8 1/4 5/8 1/4 1/8 3/ (log n ) n /(log n ) a l with multiple broadcasting of size ×
One of the fundamental algorithmic problems in computer science involves selecting thekth smalles... more One of the fundamental algorithmic problems in computer science involves selecting thekth smallest element in a setS ofn elements. In this paper we present a fast selection algorithm which runs inO(n 1/8 logn) time on a mesh with multiple broadcasting of sizen 3/8 ×n 5/8. Our result shows that, just like semigroup computations, selection can be done much faster on a suitably chosen rectangular mesh than on square meshes. We also show that if every processor can storen 1/9 items, then our selection algorithm runs inO(n 1/9 logn) time on a mesh with multiple broadcasting of sizen 1/3 ×n 5/9.
run in O(logn) time and O(log" n) time, respectively. In fact, our convex hull algorithm applies ... more run in O(logn) time and O(log" n) time, respectively. In fact, our convex hull algorithm applies to ordered points in the plane as well: with an ordered set S of n such points stored one of size VS X tp er processor in a reconfigurable mesh n, our algorithm computes the convex hull of S in 0 (log2 n).
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Papers by Jingyuan Zhang