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164
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.
A Survey of Computational Complexity Results in Systems and Control
, 2000
"... The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fi ..."
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Cited by 116 (21 self)
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The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fields. We begin with a brief introduction to models of computation, the concepts of undecidability, polynomial time algorithms, NPcompleteness, and the implications of intractability results. We then survey a number of problems that arise in systems and control theory, some of them classical, some of them related to current research. We discuss them from the point of view of computational complexity and also point out many open problems. In particular, we consider problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, timevarying linear systems, nonlinear and hybrid systems, and stochastic optimal control.
An Accurate Worst Case Timing Analysis for RISC Processors
 IN IEEE REALTIME SYSTEMS SYMPOSIUM
, 1995
"... An accurate and safe estimation of a task's worst case execution time (WCET) is crucial for reasoning about the timing properties of realtime systems. In RISC processors, the execution time of a program construct (e.g., a statement) is affected by various factors such as cache hits/misses and pi ..."
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Cited by 99 (3 self)
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An accurate and safe estimation of a task's worst case execution time (WCET) is crucial for reasoning about the timing properties of realtime systems. In RISC processors, the execution time of a program construct (e.g., a statement) is affected by various factors such as cache hits/misses and pipeline hazards, and these factors impose serious problems in analyzing the WCETs of tasks. To analyze the timing effects of RISC's pipelined execution and cache memory, we propose extensions to the original timing schema where the timing information associated with each program construct is a simple timebound. In our approach, associated with each program construct is what we call a WCTA (Worst Case Timing Abstraction), which contains detailed timing information of every execution path that might be the worst case execution path of the program construct. This extension leads to a revised timing schema that is similar to the original timing schema except that concatenation and pruning...
The Complexity of Mean Payoff Games on Graphs
 Theoretical Computer Science
, 1996
"... We study the complexity of finding the values and optimal strategies of mean payoff games on graphs, a family of perfect information games introduced by Ehrenfeucht and Mycielski and considered by Gurvich, Karzanov and Khachiyan. We describe a pseudopolynomial time algorithm for the solution of suc ..."
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Cited by 96 (3 self)
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We study the complexity of finding the values and optimal strategies of mean payoff games on graphs, a family of perfect information games introduced by Ehrenfeucht and Mycielski and considered by Gurvich, Karzanov and Khachiyan. We describe a pseudopolynomial time algorithm for the solution of such games, the decision problem for which is in NP " coNP. Finally, we describe a polynomial reduction from mean payoff games to the simple stochastic games studied by Condon. These games are also known to be in NP " coNP, but no polynomial or pseudopolynomial time algorithm is known for them. 1 Introduction Let G = (V; E)be a finite directed graph in which each vertex has at least one edge going out of it. Let w : E ! f\GammaW; : : : ; 0; : : : ; Wg be a function that assigns an integral weight to each edge of G. Ehrenfeucht and Mycielski [EM79] studied the following infinite twoperson game played on such a graph. The game starts at a vertex a 0 2 V . The first player chooses an edge e...
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.
MARKOV PAGING
, 2000
"... This paper considers the problemof paging under the assumption that the sequence of pages accessed is generated by a Markov chain. We use this model to study the faultrate of paging algorithms. We first draw on the theory of Markov decision processes to characterize the paging algorithmthat achieve ..."
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Cited by 61 (4 self)
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This paper considers the problemof paging under the assumption that the sequence of pages accessed is generated by a Markov chain. We use this model to study the faultrate of paging algorithms. We first draw on the theory of Markov decision processes to characterize the paging algorithmthat achieves optimal faultrate on any Markov chain. Next, we address the problemof devising a paging strategy with low faultrate for a given Markov chain. We show that a number of intuitive approaches fail. Our main result is a polynomialtime procedure that, on any Markov chain, will give a paging algorithm with faultrate at most a constant times optimal. Our techniques show also that some algorithms that do poorly in practice fail in the Markov setting, despite known (good) performance guarantees when the requests are generated independently from a probability distribution.
Exact and Approximate Distances in Graphs  a survey
 In ESA
, 2001
"... We survey recent and not so recent results related to the computation of exact and approximate distances, and corresponding shortest, or almost shortest, paths in graphs. We consider many different settings and models and try to identify some remaining open problems. ..."
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Cited by 57 (0 self)
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We survey recent and not so recent results related to the computation of exact and approximate distances, and corresponding shortest, or almost shortest, paths in graphs. We consider many different settings and models and try to identify some remaining open problems.
Faster Maximum and Minimum Mean Cycle Algorithms for System Performance Analysis
 IEEE TRANSACTIONS ON COMPUTERAIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS
, 1997
"... Maximum and minimum mean cycle problems are important problems with many applications in performance analysis of synchronous and asynchronous digital systems including rate analysis of embedded systems, in discreteevent systems, and in graph theory. Karp's algorithm is one of the fastest and common ..."
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Cited by 56 (6 self)
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Maximum and minimum mean cycle problems are important problems with many applications in performance analysis of synchronous and asynchronous digital systems including rate analysis of embedded systems, in discreteevent systems, and in graph theory. Karp's algorithm is one of the fastest and commonest algorithms for both of these problems. We present this paper mainly in the context of the maximum mean cycle problem. We show that Karp's algorithm processes more vertices and arcs than needed to find the maximum cycle mean of a digraph. This observation motivated us to propose a new graph unfolding scheme that remedies this deficiency and leads to three faster algorithms with different characteristics. Asymptotic analysis tells us that our algorithms always run faster than Karp's algorithm. Experiments on benchmark graphs confirm this fact for most of the graphs. Like Karp's algorithm, they are also applicable to both the maximum and minimum mean cycle problems. Moreover, one of them is...
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.
New scaling algorithms for the assignment and minimum mean cycle problems
, 1992
"... In this paper we suggest new scaling algorithms for the assignment and minimum mean cycle problems. Our assignment algorithm is based on applying scaling to a hybrid version of the recent auction algorithm of Bertsekas and the successive shortest path algorithm. The algorithm proceeds by relaxing th ..."
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Cited by 50 (4 self)
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In this paper we suggest new scaling algorithms for the assignment and minimum mean cycle problems. Our assignment algorithm is based on applying scaling to a hybrid version of the recent auction algorithm of Bertsekas and the successive shortest path algorithm. The algorithm proceeds by relaxing the optimality conditions, and the amount of relaxation is successively reduced to zero. On a network with 2n nodes, m arcs, and integer arc costs bounded by C, the algorithm runs in O(,/n m log(nC)) time and uses very simple data structures. This time bound is comparable to the time taken by Gabow and Tarjan's scaling algorithm, and is better than all other time bounds under the similarity assumption, i.e., C = O(n k) for some k. We next consider the minimum mean cycle problem. The mean cost of a cycle is defined as the cost of the cycle divided by the number of arcs it contains. The minimum mean cycle problem is to identify a cycle whose mean cost is minimum. We show that by using ideas of the assignment algorithm in an approximate binary search procedure, the minimum mean cycle problem can also be solved in O(~/n m log nC) time. Under the similarity assumption, this is the best available time bound to solve the minimum mean cycle problem.