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An improved optimal algorithm for bubble-sorting-based non-Manhattan channel routing

IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS 1999年第2期18卷 163-171页

作者： Yan, JT Natl Chiao Tung Univ Comp Syst Res Ctr Hsinchu 30050 Taiwan

It is well known that a non-Manhattan channel router always uses fewer routing tracks than a Manhattan router in a channel, To our knowledge, for a bubble-sorting-based non-Manhattan channel routing (BSNMCR) problem, Chaudhary's O(kn(2)) heuristic algorithm [8] and Chen's O(k(2)n) optimal algorithm [9] have been, respectively, proposed, where n is the number of terminals and k is the number of routing tracks in a channel. However, the time complexity of the two algorithms is in O(n(3)) time in the worst case. In this paper, based on optimality-oriented swap-direction selection in an optimal bubble-sorting solution, an improved optimal algorithm for a BSNMCR problem is proposed, and the time complexity of the proposed algorithm is proven to be in O(kn) time and in O(n(2)) time in the worst case.

关键词： bubble sorting channel routing optimal algorithm physical design

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A fast optimal non-continuous slot reuse scheme for CRMA high-speed networks

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JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 2001年第2期17卷 217-228页

作者： Sheu, PR Lin, CM Natl Yunlin Univ Sci & Technol Dept Elect Engn Yunlin 640 Taiwan

Cyclic-Reservation Multiple-Access (CRMA) is an effective access scheme for hi h speed networks. In CRMA? the headend periodically generates reserve commands. If necessary, each station may reserve a number of empty slots in each reserve command. For each reserve command, the headend generates a cycle of length equal to the total number of empty slots which al e reserved to serve the reservations. Generally speaking, a longer cycle length means a longer access delay and a lower throughput. Therefore, it is desirable to study how to reduce the cycle length. However, it has been shown that the problem is NP-complete if all the empty slots used by a station in a cycle ne required to be consecutive [1]. In this paper, we remove the slot-contiguity constraint and propose a fast, optimal non-continuous slot reuse scheme with low time complexity O(M-2), where M denotes the number of stations. Experimental results demonstrate that our new scheme has much shorter cycle lengths, much higher throughput, and much shorter MAC (Medium Access Control) delay than the original CRMA scheme.

关键词： cyclic-reservation multiple-access dual-bus network high-speed network optimal algorithm slot reuse

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optimal conditional estimation: Average case setting

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2001年第3期109卷 649-666页

作者： Kacewicz, B Univ Min & Met Dept Appl Math Krakow Poland

We consider an estimation problem which appears in the identification of systems by means of restricted complexity models: find the optimal approximation to an element of a linear normed space (a system) based on noisy information, subject to the restriction that approximations (models) can be selected from a prescribed subspace;M of the problem element space. In contrast to the worst-case optimization criterion, which may be pessimistic, in this paper the quality of an identification algorithm is measured by its local average performance. Two types of local average errors are considered: for a given information (measurement) y and for a given unknown element x, the latter in two versions. For a wide spectrum of norms in the measurement space, we define an optimal algorithm and give expressions for its average errors which show the dependence on information, information errors, unmodelled dynamics, and norm in the measurement space.

关键词： local average error conditional identification optimal algorithm optimal information

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A generalized framework for iterative source-channel decoding

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ANNALS OF TELECOMMUNICATIONS 2001年第7-8期56卷 435-446页

作者： Görtz, N Tech Univ Munich Inst Commun Engn D-80290 Munich Germany

Joint source-channel decoding is considered for a transmission system, in which the quantizer indices of several autocorrelated source signals are bit-interleaved, commonly channel encoded, and transmitted in parallel. Since the optimal decoding algorithm is not feasible in most practical situations, iterative source-channel decoding has been introduced. The latter is generalized in the present paper Furthermore, it is shown in detail, that iterative source-channel decoding can be derived by insertion of appropriate approximations into the optimal joint decoding algorithm. The approximations allow the decomposition of the optimal decoder into two parts, which can be identified as the constituent decoders for the channel-code and the source-code redundancies. Similar as in other concatenated coding systems, the constituent decoders are applied in an iterative decoding scheme. Its performance is analyzed by simulation results.

关键词： source coding channel coding decoding iteration optimal algorithm approximation

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Matrix multiplication on the OTIS-Mesh optoelectronic computer

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IEEE TRANSACTIONS ON COMPUTERS 2001年第7期50卷 635-646页

作者： Wang, CF Sahni, S So Illinois Univ Dept Comp Sci Carbondale IL 62901 USA Univ Florida Dept Comp & Informat Sci & Engn Gainesville FL 32611 USA

We develop algorithms to multiply two vectors, a vector and a matrix, and two matrices on an OTIS-Mesh optoelectronic computer. Two mappings, group row and group submesh [25], of a matrix onto an OTIS-Mesh are considered and the relative merits of each compared. We show that our algorithms to multiply a column and row vector use an optimal number of data moves for both the group row and group submesh mappings, our algorithm to multiply a row vector and a column vector is optimal for the group row mapping, and our algorithm to multiply a matrix by a column vector is optimal for the group row mapping.

关键词： matrix multiplication OTIS-Mesh optical interconnect optoelectronic computer optimal algorithm

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optimal average case estimation in Hilbert norms

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MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS 2000年第4期13卷 347-359页

作者： Kacewicz, B Stanislaw Staszic Univ Min & Met Dept Appl Math PL-30059 Krakow Poland

In contrast to the worst case approach, the average case setting provides less conservative insight into the quality of estimation algorithms. In this paper we consider two local average case error measures of algorithms based on noisy information, in Hilbert norms in the problem element and information spaces. We define the optimal algorithm and provide formulas for its two local errors, which explicitly exhibit the influence of factors such as information, information (measurement) errors, norms in the considered spaces, a subset where approximations are allowed, and "unmodeled dynamics." Based on the error expression, we formulate in algebraic language the problem of selecting the optimal approximating subspace. The solution is given along with the specific formula for the error, which depends on the eigenvalues of a certain matrix defined by information and norms under consideration.

关键词： identification algorithms average case setting local errors optimal algorithm optimal subspace

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Hierarchical bubble-sorting-based non-Manhattan channel routing

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IEE PROCEEDINGS-COMPUTERS AND DIGITAL TECHNIQUES 2000年第4期147卷 215-220页

作者： Yan, JT Chung Hua Univ Dept Comp Sci & Informat Engn Hsinchu Taiwan

For a bubble-sorting-based non-Manhattan channel routing (BSNMCR) problem, Chen's O(k(2)n) optimal algorithm and Yan's O(kn) optimal algorithm have been proposed respectively where n is the number of terminals and k is the number of routing tracks in a channel. For the sorting process of a given vector, these two optimal algorithms consider that a left-swap pass or a right-swap pass is an overall pass. As the distribution of most of the routing nets in a channel has a local property a vector may be divided into several smaller subvectors, and each subvector can be sorted by a left-swap pass or a right-swap pass to further optimise the number of tracks in a channel. In the paper, based on an optimality-oriented swap-direction selection and a 'divide-and-conquer' technology, a hierarchical BSNMCR (HBSNMCR) problem is formulated and an O(hn) optimal algorithm is proposed, where h is the number of routing tracks in a HBSNMCR solution, for h less than or equal to k.

关键词： Electronic engineering computing Computer-aided circuit analysis and design divide-and-conquer technology network routing optimal algorithm routing tracks optimality-oriented swap-direction selection Digital circuit design, modelling and testing hierarchical bubble-sorting-based non-Manhattan channel routing sorting circuit layout CAD sorting process

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An optimal algorithm for certain boundary value problem

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 1997年第2期83卷 195-203页

作者： Stys, K Stys, T UNIV BOTSWANA & SWAZILAND DEPT MATHPRIVATE BAG 0022GABORONEBOTSWANA

The O(h(4)) finite-difference scheme for the second derivative u ''(x) leads to a coherent pentadiagonal matrix which is factorized into two tridiagonal matrices. This factorization is used to derive an optimal algorithm for solving a linear system of equations with the pentadiagonal matrix. As an application, a nonlinear system of ordinary differential equations is approximated by an O(h(4)) convergent finite-difference scheme. This scheme is solved by the implicit iterative method applying the algorithm at each iteration. A Mathematica module designed for the purpose of testing and using the method is attached.

关键词： optimal algorithm boundary problem sparse matrices

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An optimal algorithm for scanning all spanning trees of undirected graphs

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SIAM JOURNAL ON COMPUTING 1997年第3期26卷 678-692页

作者： Shioura, A Tamura, A Uno, T UNIV ELECTROCOMMUN DEPT COMP SCI & INFORMAT MATHCHOFUTOKYO 182JAPAN TOKYO INST TECHNOL DEPT SYST SCIMEGURO KUTOKYO 152JAPAN

Let G be an undirected graph with V vertices and E edges. Many algorithms have been developed for enumerating all spanning trees in G. Most of the early algorithms use a technique called ''backtracking.'' Recently, several algorithms using a different technique have been proposed by Kapoor and Ramesh (1992), Matsui (1993), and Shioura and Tamura (1993). They find a new spanning tree by exchanging one edge of a current one. This technique has the merit of enabling us to compress the whole output of all spanning trees by outputting only relative changes of edges. Kapoor and Ramesh first proposed an O(N + V + E)-time algorithm by adopting such a ''compact'' output, where N is the number of spanning trees. Another algorithm with the same time complexity was constructed by Shioura and Tamura. These are optimal in the sense of time complexity but not in terms of space complexity because they take O(VE) space. We refine Shioura and Tamura's algorithm and decrease the space complexity from O(VE) to O(V + E) while preserving the time complexity. Therefore, our algorithm is optimal in the sense of both time and space complexities.

关键词： optimal algorithm spanning trees undirected graphs

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An algorithm of global optimization for solving layout problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1999年第2期114卷 430-436页

作者： Feng, EM Wang, XL Wang, XM Teng, HF Dalian Univ Technol Dept Appl Math Dalian 116024 Peoples R China

The two-dimensional layout problem is known to be NP-complete, and the current research work is basically in the heuristic way. In this paper, we mainly discuss the methods for solving layout problem about the artificial satellite module by virtue of graph theory and group theory. Also, an algorithm of global optimization is presented first time. The method given here can be extended to solve other type of layout problems. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： packing optimal algorithm symmetry group equivalent relation isomorphism

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