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15
Applying parallel computation algorithms in the design of serial algorithms
 J. ACM
, 1983
"... Abstract. The goal of this paper is to point out that analyses of parallelism in computational problems have practical implications even when multiprocessor machines are not available. This is true because, in many cases, a good parallel algorithm for one problem may turn out to be useful for design ..."
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Cited by 234 (7 self)
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Abstract. The goal of this paper is to point out that analyses of parallelism in computational problems have practical implications even when multiprocessor machines are not available. This is true because, in many cases, a good parallel algorithm for one problem may turn out to be useful for designing an efficient serial algorithm for another problem. A d ~ eframework d for cases like this is presented. Particular cases, which are discussed in this paper, provide motivation for examining parallelism in sorting, selection, minimumspanningtree, shortest route, maxflow, and matrix multiplication problems, as well as in scheduling and locational problems.
Globally optimal regions and boundaries as minimum ratio weight cycles
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... Abstract. We describe a new form of energy functional for the modelling and identification of regions in images. The energy is defined on the space of boundaries in the image domain, and can incorporate very general combinations of modelling information both from the boundary (intensity gradients,.. ..."
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Cited by 72 (2 self)
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Abstract. We describe a new form of energy functional for the modelling and identification of regions in images. The energy is defined on the space of boundaries in the image domain, and can incorporate very general combinations of modelling information both from the boundary (intensity gradients,...), and from the interior of the region (texture, homogeneity,. We describe two polynomialtime digraph algorithms for finding the global minima of this energy. One of the algorithms is completely general, minimizing the functional for any choice of modelling information. It runs in a few seconds on a 256 × 256 image. The other algorithm applies to a subclass of functionals, but has the advantage of being extremely parallelizable. Neither algorithm requires initialization. 1.
Optimizing TwoPhase, LevelClocked Circuitry (Extended Abstract)
"... We investigate two strategies for reducing the clock period of a twophase, levelclocked circuit: clock tuning, which adjusts the waveforms that clock the circuit, and retiming, which relocates circuit latches. These methods can be used to convert a circuit with edgetriggered latches into a faster ..."
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Cited by 55 (16 self)
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We investigate two strategies for reducing the clock period of a twophase, levelclocked circuit: clock tuning, which adjusts the waveforms that clock the circuit, and retiming, which relocates circuit latches. These methods can be used to convert a circuit with edgetriggered latches into a faster levelclocked one. We model a twophase circuit as a graph whose vertex set V is a collection of combinational logic blocks, and whose edge set E is a set of interconnections. Each interconnection passes through 0 or more latches, where each latch is clocked by one of two periodic, nonoverlapping waveforms, or phases. We give efficient polynomialtime algorithms for problems involving the timing verification and optimization of twophase circuitry. Included are algorithms for ffl verifyi...
Beamlets and Multiscale Image Analysis
 in Multiscale and Multiresolution Methods
, 2001
"... We describe a framework for multiscale image analysis in which line segments play a role analogous to the role played by points in wavelet analysis. ..."
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Cited by 54 (16 self)
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We describe a framework for multiscale image analysis in which line segments play a role analogous to the role played by points in wavelet analysis.
Globally Optimal Regions and Boundaries
, 1999
"... We propose a new form of energy functional for the segmentation of regions in images, and an efficient method for finding its global optima. The energy can have contributions from both the region and its boundary, thus combining the best features of region and boundarybased approaches to segmentat ..."
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Cited by 33 (2 self)
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We propose a new form of energy functional for the segmentation of regions in images, and an efficient method for finding its global optima. The energy can have contributions from both the region and its boundary, thus combining the best features of region and boundarybased approaches to segmentation. By transforming the region energy into a boundary energy, we can treat both contributions on an equal footing, and solve the global optimization problem as a minimum mean weight cycle problem on a directed graph. The simple, polynomialtime algorithm requires no initialization and is highly parallelizable.
Inverse optimization
 OPERATIONS RESEARCH
, 2001
"... In this paper, we study inverse optimization problems defined as follows. Let S denote the set of feasible solutions of an optimization problem P, let c be a specified cost vector, and x 0 be a given feasible solution. The solution x 0 may or may not be an optimal solution of P with respect to the c ..."
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Cited by 25 (2 self)
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In this paper, we study inverse optimization problems defined as follows. Let S denote the set of feasible solutions of an optimization problem P, let c be a specified cost vector, and x 0 be a given feasible solution. The solution x 0 may or may not be an optimal solution of P with respect to the cost vector c. The inverse optimization problem is to perturb the cost vector c to d so that x 0 is an optimal solution of P with respect to d and �d − c � p is minimum, where �d − c � p is some selected L p norm. In this paper, we consider the inverse linear programming problem under L 1 norm (where �d − c � p = ∑ i∈J w j�d j − c j�, with J denoting the index set of variables x j and w j denoting the weight of the variable j) and under L � norm (where �d −c � p = max j∈J �w j�d j −c j���. We prove the following results: (i) If the problem P is a linear programming problem, then its inverse problem under the L 1 as well as L � norm is also a linear programming problem. (ii) If the problem P is a shortest path, assignment or minimum cut problem, then its inverse problem under the L 1 norm and unit weights can be solved by solving a problem of the same kind. For the nonunit weight case, the inverse problem reduces to solving a minimum cost flow problem. (iii) If the problem P is a minimum cost flowproblem, then its inverse problem under the L 1 norm and unit weights reduces to solving a unitcapacity minimum cost flowproblem. For the nonunit weight case, the inverse problem reduces to solving a minimum cost flowproblem. (iv) If the problem P is a minimum cost flowproblem, then its inverse problem under the L � norm and unit weights reduces to solving a minimum mean cycle problem. For the nonunit weight case, the inverse problem reduces to solving a minimum costtotime ratio cycle problem. (v) If the problem P is polynomially solvable for linear cost functions, then inverse versions of P under the L 1 and L � norms are also polynomially solvable.
Finding minimum cost to time ratio cycles with small integral transit times
 NETWORKS
, 1993
"... Let D = (V, E) be a digraph with n vertices and m arcs. For each e E E there is an associated cost ce and a transit time te; Ce can be arbitrary, but we require t to be a nonnegative integer. The cost to time ratio of a cycle C is X(C) = 3 ec ceCeec t. Let E ' c E denote the set of arcs e with te> ..."
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Cited by 23 (1 self)
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Let D = (V, E) be a digraph with n vertices and m arcs. For each e E E there is an associated cost ce and a transit time te; Ce can be arbitrary, but we require t to be a nonnegative integer. The cost to time ratio of a cycle C is X(C) = 3 ec ceCeec t. Let E ' c E denote the set of arcs e with te> 0, let T = max{tv: (u, v) E} for each vertex u, and let T = uev T. We give a new algorithm for finding a cycle C with the minimum cost to time ratio X(C). The algorithm's (T(m + n log n)) running time is dominated by O(T) shortest paths calculations on a digraph with nonnegative arc lengths. Further, we consider early termination of the algorithm and a faster O(Tm) algorithm in case E E ' is acyclic, i.e., in case each cycle has a strictly positive transit time, which gives an O(n²) algorithm for a class of cyclic staffing problems considered by Bartholdi et al. The algorithm can be seen to be an extension of the O(nm) algorithm of Karp for the case in which t = 1 for all e E E, which is the problem of calculating a minimum mean cycle. Our algorithm can also be modified to solve the related parametric shortest paths problem in O(T(m + n log n)) time.
Determining Asynchronous Pipeline Execution Times
 Proc. 9th Workshop on Languages and Compilers for Parallel Computing
, 1996
"... Asynchronous pipelining is a form of parallelism in which processors execute different loop tasks (loop statements) as opposed to different loop iterations. An asynchronous pipeline schedule for a loop is an assignment of loop tasks to processors, plus an order on instances of tasks assigned to the ..."
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Cited by 3 (1 self)
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Asynchronous pipelining is a form of parallelism in which processors execute different loop tasks (loop statements) as opposed to different loop iterations. An asynchronous pipeline schedule for a loop is an assignment of loop tasks to processors, plus an order on instances of tasks assigned to the same processor. This variant of pipelining is particularly relevant in distributed memory systems (since pipeline control may be distributed across processors), but may also be used in shared memory systems. Accurate estimation of the execution time of a pipeline schedule is needed to determine if pipelining is appropriate for a loop, and to compare alternative schedules. Pipeline execution of n iterations of a loop requires time at most a + bn, for some constants a and b. The coefficient b is the iteration interval of the pipeline schedule, and is the primary measure of the performance of a schedule. The startup time a is a secondary performance measure. We generalize previous work on det...
The Complexity of Dynamic/Periodic Languages and Optimization Problems
 in Proc. 13th ACM Annual Symposium on Theory of Computing (STOC
, 1985
"... 2 Deterministic dynamic/periodic optimization problems arise naturally in various quantitative disciplines including Computer Science, Economics, and Operations Research. These periodic models may be applied to longrange ..."
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Cited by 3 (0 self)
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2 Deterministic dynamic/periodic optimization problems arise naturally in various quantitative disciplines including Computer Science, Economics, and Operations Research. These periodic models may be applied to longrange
The Basic Cyclic Scheduling Problem with Linear Precedence Constraints
 Rapport MASI 91/34, Institut Blaise Pascal
, 1991
"... In this paper, we consider a finite set of generic tasks that we execute a large number of times. We introduce the linear constraints between two generic tasks : the difference of iteration indices between the execution of two tasks subject to a precedence constraint is a linear function of these in ..."
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Cited by 3 (1 self)
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In this paper, we consider a finite set of generic tasks that we execute a large number of times. We introduce the linear constraints between two generic tasks : the difference of iteration indices between the execution of two tasks subject to a precedence constraint is a linear function of these indices. These constraints are modeled by a linear graph G. Moreover, we consider no resource constraints. We aim at characterizing the optimal frequencies of the generic tasks. Since the executions of the generic tasks are only subject to precedence constraints, the maximum frequencies are achieved in the earliest schedule. The study of its asymptotic behavior allows us to develop an algorithm to compute the maximum frequencies of the generic tasks : it is based on a particular decomposition of the linear graph and on the expansion of its components. We construct a valued graph by contracting these components and we show that the longest paths of that graph provide the maximum values of the f...