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59
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 149 (4 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.
Optimal Paths in Weighted Timed Automata
 HSCC
, 2001
"... We consider an optimalreachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to a (parametric) shortestpath problem for a finite directed graph. The directed gr ..."
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Cited by 122 (5 self)
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We consider an optimalreachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to a (parametric) shortestpath problem for a finite directed graph. The directed graph we construct is a refinement of the region automaton due to Alur and Dill. We present an exponential time algorithm to solve the shortestpath problem for weighted timed automata starting from a single state, and a doublyexponential time algorithm to solve this problem starting from a zone of the state space.
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 c ..."
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Cited by 74 (4 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...
Throughput analysis of synchronous data flow graphs
 In ACSD’06, Proc. (2006), IEEE
, 2006
"... Synchronous Data Flow Graphs (SDFGs) are a useful tool for modeling and analyzing embedded data flow applications, both in a single processor and a multiprocessing context or for application mapping on platforms. Throughput analysis of these SDFGs is an important step for verifying throughput requir ..."
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Cited by 41 (16 self)
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Synchronous Data Flow Graphs (SDFGs) are a useful tool for modeling and analyzing embedded data flow applications, both in a single processor and a multiprocessing context or for application mapping on platforms. Throughput analysis of these SDFGs is an important step for verifying throughput requirements of concurrent realtime applications, for instance within designspace exploration activities. Analysis of SDFGs can be hard, since the worstcase complexity of analysis algorithms is often high. This is also true for throughput analysis. In particular, many algorithms involve a conversion to another kind of data flow graph, the size of which can be exponentially larger than the size of the original graph. In this paper, we present a method for throughput analysis of SDFGs, based on explicit statespace exploration and we show that the method, despite its worstcase complexity, works well in practice, while existing methods often fail. We demonstrate this by comparing the method with stateoftheart cycle mean computation algorithms. Moreover, since the statespace exploration method is essentially the same as simulation of the graph, the results of this paper can be easily obtained as a byproduct in existing simulation tools. 1
The data broadcast problem with nonuniform time
 In Proc. of the 10th Symp. on Discrete Algorithms (SODA ’99
, 1999
"... Abstract. The Data Broadcast Problem consists of finding an infinite schedule to broadcast a given set of messages so as to minimize a linear combination of the average service time to clients requesting messages, and of the cost of the broadcast. This problem also models the Maintenance Scheduling ..."
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Cited by 40 (4 self)
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Abstract. The Data Broadcast Problem consists of finding an infinite schedule to broadcast a given set of messages so as to minimize a linear combination of the average service time to clients requesting messages, and of the cost of the broadcast. This problem also models the Maintenance Scheduling Problem and the MultiItem Replenishment Problem. Previous work concentrated on a discretetime restriction where all messages have transmission time equal to 1. Here, we study a generalization of the model to a setting of continuous time and messages of nonuniform transmission times. We prove that the Data Broadcast Problem is strongly NPhard, even if the broadcast costs are all zero, and give 3approximation algorithms. Key Words. broadcasting.
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 wit ..."
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Cited by 26 (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.
Performance analysis based on timing simulation
, 1993
"... Abstract — Determining the cycle time and a critical cycle is a fundamental problem in the analysis of concurrent systems. We solve this problem using timing simulation of an underlying Signal Graph (an extension of Marked Graphs). For a Signal Graph with n vertices and m arcs our algorithm has the ..."
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Cited by 18 (0 self)
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Abstract — Determining the cycle time and a critical cycle is a fundamental problem in the analysis of concurrent systems. We solve this problem using timing simulation of an underlying Signal Graph (an extension of Marked Graphs). For a Signal Graph with n vertices and m arcs our algorithm has the polynomial time complexity O(b 2 m), wherebis the number of vertices with initially marked inarcs (typically b n). The algorithm has a clear semantic and a low descriptive complexity. We illustrate the use of the algorithm by applying it to performance analysis of asynchronous circuits. I
An Experimental Study of Minimum Mean Cycle Algorithms
, 1998
"... We present a comprehensive experimental study of ten leading algorithms for the minimum mean cycle problem. For most of these algorithms, there has not been a clear understanding of their performance in practice although theoretical bounds have been proved for their running times. Only an experiment ..."
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Cited by 17 (1 self)
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We present a comprehensive experimental study of ten leading algorithms for the minimum mean cycle problem. For most of these algorithms, there has not been a clear understanding of their performance in practice although theoretical bounds have been proved for their running times. Only an experimental study can shed light on whether changes in an algorithm that make its running time theoretically more efficient are worth the overhead in terms of their payoff in practice. To this end, our experimental study provides a great deal of insight. In our evaluation, we programmed these algorithms uniformly and efficiently. We systematically compared them on a test suite composed of random graphs as well as benchmark circuits. Above all, our experimental results provide important insights into the individual performance as well as relative performance of these algorithms in practice. One of the most surprising results of this study is that Howard's algorithm, a well known algorithm to the stoch...
Maximum Flows and Parametric Shortest Paths in Planar Graphs
"... We observe that the classical maximum flow problem in any directed planar graph G can be reformulated as a parametric shortest path problem in the oriented dual graph G ∗. This reformulation immediately suggests an algorithm to compute maximum flows, which runs in O(n log n) time. As we continuously ..."
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Cited by 16 (1 self)
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We observe that the classical maximum flow problem in any directed planar graph G can be reformulated as a parametric shortest path problem in the oriented dual graph G ∗. This reformulation immediately suggests an algorithm to compute maximum flows, which runs in O(n log n) time. As we continuously increase the parameter, each change in the shortest path tree can be effected in O(log n) time using standard dynamic tree data structures, and the special structure of the parametrization implies that each directed edge enters the evolving shortest path tree at most once. The resulting maximumflow algorithm is identical to the recent algorithm of Borradaile and Klein [J. ACM 2009], but our new formulation allows a simpler presentation and analysis. On the other hand, we demonstrate that for a similarly structured parametric shortest path problem on the torus, the shortest path tree can change Ω(n²) times in the worst case, suggesting that a different method may be required to efficiently compute maximum flows in highergenus graphs.
Setting Parameters by Example
, 1999
"... We introduce a class of “inverse parametric optimization” problems, in which one is given both a parametric optimization problem and a desired optimal solution; the task is to determine parameter values that lead to the given solution. We describe algorithms for solving such problems for minimum spa ..."
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Cited by 16 (5 self)
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We introduce a class of “inverse parametric optimization” problems, in which one is given both a parametric optimization problem and a desired optimal solution; the task is to determine parameter values that lead to the given solution. We describe algorithms for solving such problems for minimum spanning trees, shortest paths, and other “optimal subgraph” problems, and discuss applications in multicast routing, vehicle path planning, resource allocation, and board game programming.