We address the problem of optimizing the distribution of partially replicated databases over a computer network. Replication is used to increase data availability in the presence of site or communication failures and to decrease retrieval costs by local access if possible. We present a new bio-inspired replication management approach which is adaptive, completely decentralized, and based on swarm intelligence. Each node has the autonomy to start at any time, depending on the internal state of its stored data objects, a redistribution process. "Redistribution" means replicate, create, delete, update, or move data objects to other nodes of the network. The redistribution process is a dynamic load-balancing scheme which runs with lower priority in the background. The system is event-driven, but the learning process is not synchronized with the events.

The main contribution of this work is to show that a number of fundamental and seemingly unrelated problems in database design, pattern recognition, robotics, computational geometry, and image processing can be solved simply and elegantly by stating them as instances of a unifying algorithmic framework that we call the multiple query problem. The multiple query problem (MQ, for short) is a 5-tuple (Q, A, D, /spl phi/, /spl oplus/), where Q is a set of queries, A is a set of items, D is a set of solutions, /spl phi/: Q/spl times/A/spl rarr/D is a function, and /spl oplus/ is a commutative and associative binary operator over D. The input to the MQ problem consists of a sequence Q=of m queries from Q and of a sequence A=of n items from A. The goal is to compute, for every query q/sub i/ (1/spl les/i/spl les/m) its solution defined as /spl phi/(q/sub i/,A)=/spl phi/(q/sub i/,a/sub 1/)/spl oplus//spl phi/(q/sub i/,a/sub 2/)/spl oplus//spl middot//spl middot//spl middot//spl oplus//spl phi/(q/sub i/,a/sub n/). We begin by discussing a generic algorithm that solves a large class of MQ problems in O(/spl radic/m+f(n)) time on a reconfigurable mesh of size /spl radic/n/spl times//spl radic/n, where f(n) is the time necessary to compute the expression d/sub 1/ /spl oplus/ d/sub 2/ /spl oplus//spl middot//spl middot//spl middot//spl oplus/ d/sub n/ with d/sub i/ /spl isin/ D on such a platform. We then go on to show that the MQ framework affords us an optimal algorithm for the multiple point location problem on a reconfigurable mesh of size /spl radic/n/spl times//spl radic/n. Given a set A of n points and a set Q of m (m/spl les/n) points in the plane, our algorithm reports, in O(/spl radic/m+log log n) time, all points of Q that lie inside the convex hull of A. Quite surprisingly, our algorithm solves the multiple point location problem without computing the convex hull of A which, in itself, takes /spl Omega/(/spl radic/n) time on a reconfigurable mesh of size /spl radic/n/spl times//spl radic/n. Finally, we prove an /spl Omega/(/spl radic/m+g(n)) time lower bound for nontrivial MQ problems, where g(n) is the lower bound for evaluating the expression d/sub 1/ /spl oplus/ d/sub 2/ /spl oplus//spl middot//spl middot//spl middot//spl oplus/ d/sub n/ with d/sub i/ /spl isin/ D, on a reconfigurable mesh of size /spl radic/n/spl times//spl radic/n.

We address the problem of designing efficient and scalable hardware-algorithms for computing the sum and prefix sums of a w/sup k/-bit, (k/spl ges/2), sequence using as basic building blocks linear arrays of at most w/sup 2/ shift switches, where w is a small power of 2. An immediate consequence of this feature is that in our designs broadcasts are limited to buses of length at most w/sup 2/. We adopt a VLSI delay model where the "length" of a bus is proportional with the number of devices on the bus. We begin by discussing a hardware-algorithm that computes the sum of a w/sup k/-bit binary sequence in the time of 2k-2 broadcasts, while the corresponding prefix sums can be computed in the time of 3k-4 broadcasts. Quite remarkably, in spite of the fact that our hardware-algorithm uses only linear arrays of size at most w/sup 2/, the total number of broadcasts involved is less than three times the number required by an "ideal" design. We then go on to propose a second hardware-algorithm, operating in pipelined fashion, that computes the sum of a kw/sup 2/-bit binary sequence in the time of 3k+[log/sub w/ k]=3 broadcasts. Using this design, the corresponding prefix sums can be computed in the time of 4k+[log/sub w/ k]-5 broadcasts.

The first main contribution of this work is to propose an efficient VLSI architecture obtained by augmenting the Mesh with Multiple Broadcasting (MMB) with precharged 1-bit row and column buses. The new architecture, which we call Mesh with Hybrid Buses (MHB for short), is realizable in VLSI with no increase in the area or the wiring complexity of the MMB chip. Our second main contribution is to show that the MHB is extremely well-suited for solving an entire slew of digital geometry tasks. The MHB is not a reconfigurable architecture. Yet, quite remarkably, for a large number of fundamental digital geometry tasks, the MHB offers a level of performance previously attained only by reconfigurable architectures. Specifically, with a digital image pretiled onto a MHB of size /spl radic/n/spl times//spl radic/n one pixel per processor, we show that the problems of computing the convex hull of the image, computing the diameter and the width of the image, deciding whether a set of digital points is a digital line, computing the maximum distance between two images, deciding whether two images are linearly separable, computing several moments and low-level descriptors of the image, including the perimeter, area, center, and median row of its convex hull, can be solved in O(log n) time. By contrast, the fastest possible algorithms for the problems above on the MMB run in /spl Theta/(n/sup 1/6/) time. Finally, we go on to show that, with minor changes, our algorithms can be implemented to run within cost-optimality on a MHB of size /spl radic/n/log n/spl times//spl radic/n/log n.

The main contribution of this work is to present elegant broadcast-efficient protocols for permutation routing, ranking, and sorting on single-hop Mobile Radio Networks with p stations and k radio channels, denoted by MRN(p,k). Clearly, any protocol performing these tasks on n items must perform /sup n///sub k/ broadcast rounds because each item must be broadcast at least once. We begin by presenting an optimal off-line permutation routing protocol using /sup n///sub k/ broadcast rounds for arbitrary k, p, and n. Further, we show that optimal on-line routing can be performed in /sup n///sub k/ broadcast rounds, provided that either k=1 or p=n. We then go on to develop an online routing protocol that takes 2/sup n///sub k/+k-1 broadcast rounds on the MRN(p,k), whenever k/spl les//spl radic//sup p///sub 2/. Using these routing protocols as basic building blocks, we develop a ranking protocol that takes 2/sup n///sub k/+o(/sup n///sub k/) broadcast rounds as well as a sorting protocol that takes 3/sup n///sub k/+o(/sup n///sub k/) broadcast rounds, provided that k /spl epsiv/ o(/spl radic/n) and p=n. Finally, we develop a ranking protocol that takes 3/sup n///sub k/+o(/sup n///sub k/) broadcast rounds, as well as a sorting protocol that takes 4/sup n///sub k/+o(/sup n///sub k/) broadcast rounds on the MRN(p,k), provided that k/spl les//spl radic//sup p///sub 2/ and p /spl epsiv/ o(n). Featuring very low proportionality constants, our protocols offer a vast improvement over the state of the art.

Sorting is a fundamental problem with applications in all areas of computer science and engineering. In this work, we address the problem of sorting on mesh connected computers enhanced by endowing each row and each column with its own dedicated high-speed bus. This architecture, commonly referred to as a mesh with multiple broadcasting, is commercially available and has been adopted by the DAP family of multiprocessors. Somewhat surprisingly, the problem of sorting m, (m/spl les/n), elements on a mesh with multiple broadcasting of size /spl radic/n/spl times//spl radic/n has been studied, thus far, only in the sparse case, where m/spl isin//spl Theta/(/spl radic/n) and in the dense case, where m/spl isin//spl Theta/O(/spl radic/n). Yet, many applications require using an existing platform of size /spl radic/n/spl times//spl radic/n for sorting m elements, with /spl radic/n<m/spl les/n. Our main contribution is to present the first known adaptive time- and VLSI-optimal sorting algorithm for meshes with multiple broadcasting. Specifically we show that, for every choice of a constant 0

A number of applications in computer-aided manufacturing, CAD, and computer-aided geometric design ask for triangulating pieces of material with defects. These tasks are known collectively as constrained triangulations. Recently, a powerful architecture called the reconfigurable mesh has been proposed: In essence, a reconfigurable mesh consists of a mesh-connected architecture augmented by a dynamically reconfigurable bus system. The main contribution of this paper is to show that the flexibility of the reconfigurable mesh can be exploited for the purpose of obtaining constant-time algorithms for a number of constrained triangulation problems. These include triangulating a convex planar region containing any constant number of convex holes, triangulating a convex planar region in the presence of a collection of rectangular holes, and triangulating a set of ordered line segments. Specifically with a collection of O(n) such objects as input, our algorithms run in O(1) time on a reconfigurable mesh of size n/spl times/n. To the best of our knowledge, this is the first time constant time solutions to constrained triangulations are reported on this architecture.

We present simple and broadcast-efficient ranking and sorting algorithms on the broadcast communication model (BCM, for short) with few communication channels. At the heart of our algorithms is a new and elegant sampling and bucketing scheme whose main feature is that the resulting buckets are well balanced, making costly rebalancing unnecessary. The resulting ranking algorithm uses only 2 n/k+o(n/k) broadcast rounds, while 3 n/k+o(n/k) broadcast rounds are needed for sorting on a L-channel, n-processor BCM whenever k/spl les//spl radic/(n/log n). These bounds are fairly tight, when compared with the trivial lower bound of n/k broadcast rounds necessary to permute n items using k communication channels.

The main contribution of this paper is to present simple and elegant podality-based algorithms for a variety of computational tasks motivated by, and finding applications to, pattern recognition, computer graphics, computational morphology, image processing, robotics, computer vision, and VLSI design. The problems that we address involve computing the convex hull, the diameter, the width, and the smallest area enclosing rectangle of a set of points in the plane, as well as the problems of finding the maximum Euclidian distance between two planar sets of points, and of constructing the Minkowski sum of two convex polygons. Specifically, we show that once we fix a positive constant /spl epsiv/, all instances of size m, (n/sup 1/2 +/spl epsiv///spl les/m/spl les/n) of the problems above, stored in the first [m//spl radic/n] columns of a mesh with multiple broadcasting of size /spl radic/n/spl times//spl radic/n can be solved time-optimally in /spl Theta/(m//spl radic/n) time.

Query processing is a crucial component of various application domains including information retrieval, database design and management, pattern recognition, robotics, and VLSI. Many of these applications involve data stored in a matrix satisfying a number of properties. One property that occurs time and again specifies that the rows and the columns of the matrix are independently sorted. It is customary to refer to such a matrix as sorted. An instance of the batched searching and ranking problem (BSR) involves a sorted matrix A of items from a totally ordered universe, along with a collection Q of queries. Q is an arbitrary mix of the following query types: for a search query q/sub j/, one is interested in an item of A that is closest to q/sub j/; for a rank query q/sub j/ one is interested in the number of items of A that are strictly smaller than q/sub j/. The BSR problem asks for solving all queries in Q. The authors consider the BSR problem in the following context: the matrix A is pretiled, one item per processor, onto an enhanced mesh of size /spl radic/n/spl times//spl radic/n; the m queries are stored, one per processor, in the first m//spl radic/n~ columns of the platform. Their main contribution is twofold. First, they show that any algorithm that solves the BSR problem must take at least /spl Omega/(max{logn, /spl radic/m}) time in the worst case. Second, they show that this time lower bound is tight on meshes of size /spl radic/n/spl times//spl radic/n enhanced with multiple broadcasting, by exhibiting an algorithm solving the BSR problem in /spl Theta/(max{logn, /spl radic/m}) time on such a platform.

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 the paper is to provide yet another example of a fundamental problem for which this phenomenon occurs. Specifically, we show that the problem of computing the convex hull of a set of n sorted points in the plane can be solved in O(n/sup 1/8/ log /sup 3/4/) time on a rectangular mesh with multiple broadcasting of size n/sup 3/8/ log/sup 1/4/ n/spl times/n/sup 5/8//log/sup 1/4/n. The fastest previously known algorithms on a square mesh of size /spl radic/n/spl times//spl radic/n run in O(n/sup 1/6/) time in case the n points are pixels in a binary image, and in O(n/sup 1/6/log/sup 3/2/ n) time for sorted points in the plane.

Answering rank queries is a recurring operation in various application domains including geographic data processing, information retrieval, database design, information management, and medical image processing. Many of these applications involve data stored in a matrix satisfying a number of properties. One property that occurs time and again in applications specifies that the rows and the columns of the matrix are independently sorted. It is customary to refer to such a matrix as sorted. An instance of the Batched Ranking problem, (BR, for short) involves a sorted matrix A of items from a totally ordered universe, along with a collection Q of queries of the following type: for a query q/sub j/ one is interested in the number of items in A that are smaller than q/sub j/. The BR problem asks for solving all queries in Q. In this work, we consider the BR problem in the following context: the matrix A is pretiled, one item per processor, onto an enhanced mesh of size /spl radic/n/spl times//spl radic/n; the m queries are stored, one per processor, in the first m//spl radic/n columns of the platform. Our main contribution is twofold. First, we show that any algorithm that solves the BR problem must take at least /spl Omega/(log n+/spl radic/m) time in the worst case. Second, we show that this time lower bound is tight on meshes of size /spl radic/n/spl times//spl radic/n enhanced with multiple broadcasting, by exhibiting an algorithm solving the BR problem in O(log n+/spl radic/m) time on such a platform.

The main contribution of this work is to show that a number of digital geometry problems can be solved elegantly on meshes with multiple broadcasting by using a time-optimal solution to the leftmost one problem as a basic subroutine. Consider a binary image pretiled onto a mesh with multiple broadcasting of size [Formula: see text] one pixel per processor. Our first contribution is to prove an Ω(n1/6) time lower bound for the problem of deciding whether the image contains at least one black pixel. We then obtain time lower bounds for many other digital geometry problems by reducing this fundamental problem to all the other problems of interest. Specifically, the problems that we address are: detecting whether an image contains at least one black pixel, computing the convex hull of the image, computing the diameter of an image, deciding whether a set of digital points is a digital line, computing the minimum distance between two images, deciding whether two images are linearly separable, computing the perimeter, area and width of a given image. Our second contribution is to show that the time lower bounds obtained are tight by exhibiting simple O(n1/6) time algorithms for these problems. As previously mentioned, an interesting feature of these algorithms is that they use, directly or indirectly, an algorithm for the leftmost one problem recently developed by one of the authors.

A graph G is an interval graph if there is a one-one correspondence between its vertices and a family I of intervals, such that two vertices in G are adjacent if and only if their corresponding intervals overlap. In this context, the family I of intervals is referred to as an interval model of G. Recently, a powerful architecture called the reconfigurable mesh has been proposed: in essence, a reconfigurable mesh consists of a mesh-connected architecture augmented by a dynamically reconfigurable bus system. In this paper, we exploit the reconfigurable mesh architecture for the purpose of obtaining constant-time algorithms for a number of computational problems on interval graphs. These problems include finding a maximum size independent set, a minimum clique cover, a minimum size dominating set, a shortest path between any two vertices in G, the diameter and the center of G, as well as Breadth-First Search and Depth-First Search trees for G. Specifically, with an n-vertex interval graph specified by its interval model as input, all our algorithms run in constant time on a reconfigurable mesh of size n × n. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Given a collection of objects in the plane along with a viewpoint /spl omega/, the visibility problem involves determining the portion of each object that is visible to an observer positioned at /spl omega/. The visibility problem is central to various application areas including computer graphics, image processing, VLSI design, and robot navigation, among many others. The main contribution of this work is to provide time-optimal solutions to this problem for several classes of objects, namely ordered line segments, disks, and iso-oriented rectangles in the plane. In addition, our visibility algorithm for line segments is at the heart of time-optimal solutions for determining, for each element in a given sequence of real numbers, the position of the nearest larger element within that sequence, triangulating a set of points in the plane, determining the visibility pairs among a set of vertical line segments, and constructing the dominance and visibility graphs of a set of iso-oriented rectangles in the plane. All the algorithms in this paper involve an input of size n and run in O(log n) time on a mesh with multiple broadcasting of size n/spl times/n. This is the first instance of time-optimal solutions for these problems on this architecture.>

Triangulating a set of points in the plane is a central theme in computer-aided manufacturing, robotics, CAD, VLSI design, geographic data processing, and computer graphics. Even more challenging are constrained triangulations, where a triangulation is sought in the presence of a number of constraints such as prescribed edges and/or forbidden areas. In this paper, we show that the flexibility of the reconfigurable mesh architecture can be exploited to obtain constant-time algorithms for a number of triangulation problems. These include triangulating an arbitrary set of points in the plane, a convex planar region with a convex hole, and a convex planar region in the presence of rectangular holes. Specifically, with a collection of O(n) such constraints as input, our algorithms run in O(1) time on a reconfigurable mesh of size n/spl times/n. To the best of our knowledge, these are the first constant time solutions to constrained triangulations reported on this architecture.>

The main contribution of this work is to show that a number of fundamental digital geometry tasks can be solved fast on a novel VLSI architecture obtained by augmenting the mesh with multiple broadcast architecture (MMB) with precharged 1-bit row and column buses. The new architecture that we call mesh with hybrid buses (MHB) is readily implementable in VLSI with no increase in the area or the wiring complexity of the MMB chip. More importantly, the new architecture affords us an exponential gain in the running time when compared with the MMB. Specifically, with a digital image pretiled onto an MHB of size /spl radic/n/spl times//spl radic/n one pixel per processor we show that the problems of computing the convex hull of the image, computing the diameter and the width of the image, deciding whether two images are linearly separable, computing several moments and low-level descriptors of the image including the perimeter, area, center, and median row of its convex hull can be solved in O(log n) time. The fastest possible algorithms for the problems above on the MMB run in /spl Theta/(n/sup 1/6/).>

Consider arbitrary collections A = a_1,a_2,.. .,a_n of items and Q = q_1,q_2,...,q_m (1 leqslant mn leqslant n) of queries from a totally ordered universe. The multiple rank problem involves computing for every query qi the number of items in A that have a lesser value. Our contribution is to show that the problem at hand can be solved time-optimally on meshes with multiple broadcasting. More specifically, if the collection A is siored in some order one item per processor and if Q is stored one query per processor in the leftmost frac{m} {{sqrt n }} columns of a mesh with multiple broadcasting of size sqrt n x /sqrt n, the corresponding instance of the multiple rank problem can be solved in Theta left( {m^{frac{1} {3}} n^{frac{1} {6}} } right) time. As an application we present a time-optimal algorithm to compute the histogram of a m-level gray image of size sqrt n x sqrt n in Theta left( {m^{frac{1} {3}} n^{frac{1} {6}} } right) time.

Recently the authors have shown that the versatility of the reconfigurable mesh can be exploited to devise 0(1) time algorithms for a number of important computational tasks relevant to image processing, computer graphics, and computer vision. Specifically, we have shown that if one or two n-vertex (convex) polygons are pretiled, one vertex per processor, onto a reconfigurable mesh of size sqrt n X sqrt n, then a number of geometric problems can be solved in 0(1) time. These include testing an arbitrary polygon for convexity, the point location problem, the supporting lines problem, the stabbing problem, constructing the common tangents of two separable convex polygons, deciding whether two convex polygons intersect, and computing the smallest distance between the boundaries of two convex polygons. The novelty of these algorithms is that the problems are solved in the dense case. The purpose of this paper is to add to the list of problems that can be solved in 0(1) time in the dense case. The problems that we address are: determining the minimum area corner triangle for a convex polygon, determining the k-maximal vertices of a restricted class of convex polygons, updating the convex hull of a convex polygon in the presence of a set of query points, and determining a point that belongs to exactly one of two given convex polygons.

One of the fundamental algorithmic problems in computer science involves selecting the kth smallest element in a collection A of n elements. We propose an algorithm design methodology to solve the selection problem on meshes with multiple broadcasting. Our methodology leads to a selection algorithm that runs in O(n/sup 1/8/(log n)/sup 3/4/)) time on a mesh with multiple broadcasting of size n/sup 3/8/(log n)/sup 1/4//spl times/n/sup 5/8//(log n)/sup 1/4/. This result is optimal over a large class of selection algorithms. Our result shows that just as for semigroup computations, selection can be done faster on suitably chosen rectangular meshes than on square meshes.>

The compaction step of integrated circuit design motivates the study of various visibility problems among vertical segments in the plane. One popular variant is referred to as the Vertical Segment Visibility problem (VSV, for short) and is stated as follows. Given a collection S of n disjoint vertical line segments in the plane, for every endpoint of a segment in S determine the first line segment, if any, interacted by a horizontal ray to the right (resp. left) originating from that endpoint. The contribution of this paper is to propose a time-optimal algorithm for the VSP problem on meshes with multiple broadcasting. The authors then use this algorithm to derive time-optimal solutions for two related problems. All the algorithms run in O(log n) time on a mesh with multiple broadcasting of size n /spl times/ n. This is the first instance of time-optimal solutions for these problems known to us.>

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 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 \left\lceil {\frac{m} {{\sqrt n }}} \right\rceil columns of a mesh with multiple broadcasting of size \sqrt {n} x \sqrt {n} can be sorted in O({\frac{m} {{\sqrt n }}}) time.

Interval graphs provide a natural model for a vast number of scheduling and VLSI problems. A variety of interval graph problems have been solved on the PRAM family. Recently, a powerful architecture called the reconfigurable mesh has been proposed: in essence, a reconfigurable mesh consists of a mesh-connected architecture augmented by a dynamically reconfigurable bus system. It has been argued that the regular structure of the reconfigurable mesh is suitable for VLSI implementation. The authors develop a set of tools and show how they can be used to devise constant time algorithms to solve a number of interval-related problem on reconfigurable meshes. These problems include finding a maximum independent set, a minimum clique cover, a minimum dominating set, a minimum coloring, along with algorithms to compute the shortest path between a pair of intervals and, based on the shortest path, an algorithm to find the center of an interval graph. More precisely, with an arbitrary family of n intervals as input, all their algorithms run in constant time on a reconfigurable mesh of size n*n.>

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 purpose of devising cost-optimal parallel algorithms for a number of interval-related problems, including finding a largest subset of pairwise nonoverlapping intervals, a minimum dominating subset of intervals, along with algorithms to compute the shortest path between a pair of intervals and, based on the shortest path, a parallel algorithm to find the center of the family of intervals. More precisely, with an arbitrary family of n intervals as input, all the algorithms run in O(log n) time using O(n) processors in the EREW-PRAM model of computation.>