13915150
Deterministic P-RAM simulation with constant redundancy
In this paper, we show that distributing the memory of a parallel computer and, thereby, decreasing its granularity allows a reduction in the redundancy required to achieve polylog simulation time for each PRAM step. Previously, realistic models of parallel computation assigned one memory module to each processor and, as a result, insisted on relatively coarse-grain memory. We propose, on the other hand, a more flexible, but equally valid model of computation, the distributed-memory, bounded-degree network (DMBDN) model. This model allows the use of fine-grain memory while maintaining the realism of a bounded-degree interconnection network. We describe a P-RAM simulation scheme, which is admitted under the DMBDN model, that exploits the increased memory bandwidth provided by a two-dimensional mesh of trees (2DMOT) network to achieve an overhead in memory redundancy lower than that required by other fast, deterministic P-RAM simulations. Specifically, for a deterministic simulation of an n-processor P-RAM on a bounded-degree network, we are able to reduce the number of copies of each variable from O(logn/loglogn) to ®(1) and still simulate each P-RAM step in polylog time.
3240445
Computational Geometry&#8212;A Survey
We survey the state of the art of computational geometry, a discipline that deals with the complexity of geometric problems within the framework of the analysis of algorithms. This newly emerged area of activities has found numerous applications in various other disciplines, such as computer-aided design, computer graphics, operations research, pattern recognition, robotics, and statistics. Five major problem areas—convex hulls, intersections, searching, proximity, and combinatorial optimizations—are discussed. Seven algorithmic techniques—incremental construction, plane-sweep, locus, divide-and-conquer, geometric transformation, prune-and-search, and dynamization—are each illustrated with an example. A collection of problem transformations to establish lower bounds for geo-metric problems in the algebraic computation/decision model is also included.
215848405
The cube-connected cycles: a versatile network for parallel computation
An interconnection pattern of processing elements, the cube-connected cycles (CCC), is introduced which can be used as a general purpose parallel processor. Because its design complies with present...
10272212
A Simplified Technique for Hidden-Line Elimination in Terrains
In this paper we give a practical and efficient output-sensitive algorithm for constructing the display of a polyhedral terrain. It runs in O((d+n) log2 n) time and uses O(nα(n)) space, where d is the size of the final display, and α(n) is a (very slowly growing) functional inverse of Ackermann’s function. Our implementation is especially simple and practical, because we try to take full advantage of the specific geometrical properties of the terrain. The asymptotic speed of our algorithm has been improved upon theoretically by other authors, but at the cost of higher space usage and/or high overhead and complicated code. Our main data structure maintains an implicit representation of the convex hull of a set of points that can be dynamically updated in O(log2 n) time. It is especially simple and fast in our application since there are no rebalancing operations required in the tree.
206394014
Holographic dispersal and recovery of information
A simple scheme for dispersal and recovery of digital information based on the discrete Fourier transform is discussed. The author presents a different implementation of M.O. Rabin's (J. ACM, vol.36, no.2, p.335-48, Apr. 1989) scheme, whose recovery cost is O(log m+k) operations per character, assuming m= Theta (n); for example, when k= Theta (log n), this cost drops from O(m) to O(log m) per character. Since the implementation is based on the Fourier transform, it is termed holographic. >
53136
Optimal Reconstruction of a Sequence from its Probes
An important combinatorial problem, motivated by DNA sequencing in molecular biology, is the reconstruction of a sequence over a small finite alphabet from the collection of its probes (the sequence spectrum), obtained by sliding a fixed sampling pattern over the sequence. Such construction is required for Sequencing-by-Hybridization (SBH), a novel DNA sequencing technique based on an array (SBH chip) of short nucleotide sequences (probes). Once the sequence spectrum is biochemically obtained, a combinatorial method is used to reconstruct the DNA sequence from its spectrum. Since technology limits the number of probes on the SBH chip, a challenging combinatorial question is the design of a smallest set of probes that can sequence an arbitrary DNA string of a given length. We present in this work a novel probe design, crucially based on the use of universal bases [bases that bind to any nucleotide (Loakes and Brown, 1994)] that drastically improves the performance of the SBH process and asymptotically approaches the information-theoretic bound up to a constant factor. Furthermore, the sequencing algorithm we propose is substantially simpler than the Eulerian path method used in previous solutions of this problem.
1765683
The Role of Arithmetic in Fast Parallel Matrix Inversion
Abstract. In the last two decades several NC algorithms for solving basic linear algebraic problems have appeared in the literature. This interest was clearly motivated by the emergence of a parallel computing technology and by the wide applicability of matrix computations. The traditionally adopted computation model, however, ignores the arithmetic aspects of the applications, and no analysis is currently available demonstrating the concrete feasibility of many of the known fast methods. In this paper we give strong evidence to the contrary, on the sole basis of the issue of robustness, indicating that some theoretically brilliant solutions fail the severe test of the ``Engineering of Algorithms.'' We perform a comparative analysis of several well-known numerical matrix inversion algorithms under both fixed- and variable-precision models of arithmetic. We show that, for most methods investigated, a typical input leads to poor numerical performance, and that in the exact-arithmetic setting no benefit derives from conditions usually deemed favorable in standard scientific computing. Under these circumstances, the only algorithm admitting sufficiently accurate NC implementations is Newton's iterative method, and the word size required to guarantee worst-case correctness appears to be the critical complexity measure. Our analysis also accounts for the observed instability of the considered superfast methods when implemented with the same floating-point arithmetic that is perfectly adequate for the fixed-precision approach.
37382391
Horizons of Parallel Computation
This paper considers the ultimate impact of fundamental physical limitations---notably, speed of light and device size---on parallel computing machines. Although we fully expect an innovative and very gradual evolution to the limiting situation, here we take the provocative view of exploring the consequences of the accomplished attainment of the physical bounds. The main result is that scalability holds only for neighborly interconnections, such as the square mesh, of bounded-size synchronous modules, presumably of the area-universal type. We also discuss the ultimate infeasibility of latency-hiding, the violation of intuitive maximal speedups, and the emerging novel processor-time tradeoffs.
45504051
Horizons of Parallel Computation
This paper considers the ultimate impact of fundamental physical limitations—notably, speed of light and device size—on parallel computing machines. Although we fully expect an innovative and very gradual evolution to the limiting situation, we take here the provocative view of exploring the consequences of the accomplished attainment of the physical bounds. The main result is that scalability holds only for neighborly interconnections, such as the square mesh, of bounded-size synchronous modules, presumably of the area-universal type. We also discuss the ultimate infeasibility of latency-hiding, the violation of intuitive maximal speedups, and the emerging novel processor-time tradeoffs.
18686062
Sequencing-by-hybridization revisited: the analog-spectrum proposal
All published approaches to DNA sequencing by hybridization (SBH) consist of the biochemical acquisition of the spectrum of a target sequence (the set of its subsequences conforming to a given probing pattern) followed by the algorithmic reconstruction of the sequence from its spectrum. In the "standard" or "uniform" approach, the probing pattern is a string of length L and the length of reliably reconstructible sequences is known to be m/sub len/ = O(2/sup L/). For a fixed microarray area, higher sequencing performance can be achieved by inserting nonprobing gaps ("wild-cards") in the probing pattern. The reconstruction, however, must cope with the emergence of fooling probes due to the gaps and algorithmic failure occurs when the spectrum becomes too densely populated, although we can achieve m/sub comp/ = O(4/sup L/). Despite the combinatorial success of gapped probing, all current approaches are based on a biochemically unrealistic spectrum-acquisition model (digital-spectrum). The reality of hybridization is much more complex. Departing from the conventional model, in this paper, we propose an alternative, called the analog-spectrum model, which more closely reflects the biochemical process. This novel modeling reestablishes probe length as the performance-governing factor, adopting "semidegenerate bases" as suitable emulators of currently inadequate universal bases. One important conclusion is that accurate biochemical measurements are pivotal to the success of SBH. The theoretical proposal presented in this paper should be a convincing stimulus for the needed biotechnological work.