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Lower Bounds for Howard's Algorithm for Finding Minimum Mean-Cost Cycles [chapter]

Thomas Dueholm Hansen, Uri Zwick
2010 Lecture Notes in Computer Science  
When applied to weighted directed graphs, which may be viewed as Deterministic MDPs (DMDPs), Howard's algorithm can be used to find Minimum Mean-Cost cycles (MMCC).  ...  Howard's algorithm also has the advantage that it can be applied to the more general problem of finding a cycle with a minimum cost-to-time ratio (see, e.g., Megiddo [14, 15]).  ...  We would also like to thank Daniel Andersson, Peter Bro Miltersen, as well as Omid Madani and Mike Paterson, for helpful discussions on policy iteration algorithms.  ... 
doi:10.1007/978-3-642-17517-6_37 fatcat:nv5ce77vpndkzar2ov2ywmpyje

An O(nm) time algorithm for finding the min length directed cycle in a graph

James B. Orlin, Antonio Sedeño-Noda
2017 Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms  
If the minimum mean cycle W ∗ has only two Proof.  ...  Our algorithm achieved the same time bound with real valued lengths, first determines the cycle with minimum mean length λ∗ in assuming that operations on real numbers take O(1) O(nm) time.  ... 
doi:10.1137/1.9781611974782.122 dblp:conf/soda/OrlinS17 fatcat:yaw3q46l75a4vjxdeg2sukzake

A robust basic cyclic scheduling problem

Idir Hamaz, Laurent Houssin, Sonia Cafieri
2018 EURO Journal on Computational Optimization  
We propose three exact algorithms for solving the problem. Two of them use a negative circuit detection algorithm as a subroutine and the last one is an Howard's algorithm adaptation.  ...  Results of numerical experiments on randomly generated instances show that the Howard's algorithm adaptation yields efficient results and opens perspectives on more difficult robust cyclic scheduling problems  ...  A pseudo-code of the procedure is presented in Algorithm 2. The algorithm starts with a lower bound α lb on the optimal cycle time.  ... 
doi:10.1007/s13675-018-0100-3 fatcat:2sskxthdhzgthlipokbsgvcy5y

Computing Optimal Cycle Mean in Parallel on CUDA

Jiří Barnat, Petr Bauch, Luboš Brim, Milan Češka
2011 Electronic Proceedings in Theoretical Computer Science  
In this paper we propose a data-parallel algorithmic solution to the problem and show how the computation of optimal cycle mean can be efficiently accelerated by means of CUDA technology.  ...  We show how the problem of computation of optimal cycle mean is decomposed into a sequence of data-parallel graph computation primitives and show how these primitives can be implemented and optimized for  ...  It maintains both upper and lower bound Λ 1 ≤ µ * ≤ Λ 2 together with a cycle C such that µ(C) = Λ 2 .  ... 
doi:10.4204/eptcs.72.8 fatcat:izyjvx6rlnhxdjqr2bit7ihs6y

Approximating the minimum cycle mean

Krishnendu Chatterjee, Monika Henzinger, Sebastian Krinninger, Veronika Loitzenbauer, Michael A. Raskin
2014 Theoretical Computer Science  
We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight.  ...  With an additional O(log(nW/ )) factor in space a cycle with approximately optimal weight can be computed within the same time bound.  ...  Lawler [22] gave a reduction for finding the minimum cycle mean that performs O(log(nW )) calls to a negative cycle detection algorithm.  ... 
doi:10.1016/j.tcs.2014.06.031 fatcat:soesmgat7rcanmnli7btsh2rwa

Experimental analysis of the fastest optimum cycle ratio and mean algorithms

Ali Dasdan
2004 ACM Transactions on Design Automation of Electronic Systems  
Some applications in the computer-aided design field include cycle time and slack optimization for circuits, retiming, timing separation analysis, and rate analysis.  ...  Optimum cycle ratio (OCR) algorithms are fundamental to the performance analysis of (digital or manufacturing) systems with cycles.  ...  Fig. 6 . 6 Howard's minimum cycle ratio algorithm (HOW). VAL excludes lines 8-11. BFS stands for the standard Breadth First Search algorithm.  ... 
doi:10.1145/1027084.1027085 fatcat:policwg3qbhy7m2bbs5f4iflyq

High-Level Synthesis of DSP Applications Using Adaptive Negative Cycle Detection

Nitin Chandrachoodan, Shuvra S. Bhattacharyya, K. J. Ray Liu
2002 EURASIP Journal on Advances in Signal Processing  
In terms of applications, the adaptive technique leads to a very fast implementation of Lawlers algorithm for the computation of the maximum cycle mean (MCM) of a graph, especially for a certain form of  ...  We present an algorithm for this problem, based on a novel extension of the well-known Bellman-Ford algorithm that allows us to adapt existing cycle information to the modified graph, and show by experiments  ...  to here as the RSJM algorithm), and (b) a modification of Howard's algorithm [10] , since it appears to be the fastest known algorithm to compute the cycle mean, and hence can also be used to check for  ... 
doi:10.1155/s1110865702205053 fatcat:ivstivlfynepzlmyw3xwp225q4

Approximating the minimum cycle mean

Krishnendu Chatterjee, Monika Henzinger, Sebastian Krinninger, Veronika Loitzenbauer
2013 Electronic Proceedings in Theoretical Computer Science  
We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight.  ...  where n is the number of vertices of the graph. (2) Second, when the weights are nonnegative, we present the first (1 + {\epsilon})-approximation algorithm for the problem and the running time of our algorithm  ...  It would be interesting to study whether there is a faster approximation algorithm for the minimum cycle mean problem, maybe at the cost of a worse approximation.  ... 
doi:10.4204/eptcs.119.13 fatcat:bc6e4ofepbf6bb2bthxkgrxrvi

Negative-cycle detection algorithms

Boris V. Cherkassky, Andrew V. Goldberg
1999 Mathematical programming  
We study the problem of finding a negative length cycle in a network. An algorithm for the negative cycle problem combines a shortest path algorithm and a cycle detection strategy.  ...  As a part of our study, we develop problem families for testing negative cycle algorithms.  ...  We also would like to thank Harold Stone for comments that improved our presentation. We thank Satish Rao for an insightful discussion of Howard's algorithm.  ... 
doi:10.1007/s101070050058 fatcat:fakfclxq3jbxfpfdyw5sy5v5um

Negative-cycle detection algorithms [chapter]

Boris V. Cherkassky, Andrew V. Goldberg
1996 Lecture Notes in Computer Science  
We study the problem of finding a negative length cycle in a network. An algorithm for the negative cycle problem combines a shortest path algorithm and a cycle detection strategy.  ...  As a part of our study, we develop problem families for testing negative cycle algorithms.  ...  We also would like to thank Harold Stone for comments that improved our presentation. We thank Satish Rao for an insightful discussion of Howard's algorithm.  ... 
doi:10.1007/3-540-61680-2_67 fatcat:zyssc6jivjfydlrg2osw6uint4

Multi-level clustering for clock skew optimization

Jonas Casanova, Jordi Cortadella
2009 Proceedings of the 2009 International Conference on Computer-Aided Design - ICCAD '09  
This new technique has been compared with previous work, showing the efficiency in the obtained performance and computational cost.  ...  However, this technique may become impractical if a different skew must be applied for each memory element.  ...  We would like to thank K.Ravindran and A.Kuehlmann for providing the benchmark suite used in [5] .  ... 
doi:10.1145/1687399.1687502 dblp:conf/iccad/CasanovaC09 fatcat:7333ujwhprd4perespx7lydexe

Efficient implementations of minimum-cost flow algorithms [article]

Z. Király, P. Kovács
2012 arXiv   pre-print
This paper presents efficient implementations of several algorithms for solving the minimum-cost network flow problem.  ...  A novel result of this work is the application of Goldberg's recent partial augment-relabel method in the cost-scaling algorithm.  ...  Löbel for developing CS2, RelaxIV, and MCF codes, respectively and for making these solvers available for academic use. We thank A. Frangioni and C.  ... 
arXiv:1207.6381v1 fatcat:al4z2akk6fbetcqzg2fwgt67hu

An Experimental Study of Minimum Mean Cycle Algorithms [chapter]

Loukas Georgiadis, Andrew V. Goldberg, Robert E. Tarjan, Renato F. Werneck
2009 2009 Proceedings of the Eleventh Workshop on Algorithm Engineering and Experiments (ALENEX)  
We study algorithms for the minimum mean cycle problem, a parametric version of shortest path feasibility (SPF).  ...  The three basic approaches to the problem are cycle-based, binary search, and tree-based. The first two use an SPF algorithm as a subroutine, while the latter uses a parametric approach.  ...  We thank Ali Dasdan for sharing his code with us and for giving us access to the IBM instances. We also thank Stephan Held for the BONN instances.  ... 
doi:10.1137/1.9781611972894.1 dblp:conf/alenex/GeorgiadisGTW09 fatcat:2n36z3iicvcktjeapcvqqzo27m

A practical method for multi-domain clock skew optimization

Yanling Zhi, Hai Zhou, Xuan Zeng
2011 16th Asia and South Pacific Design Automation Conference (ASP-DAC 2011)  
A framework based on branch-and-bound is carefully designed to search for the optimal clocking domain assignment, and a greedy clustering algorithm is developed to quickly estimate the upper bound of cycle  ...  period for a given branch.  ...  The authors would like to thank Jonas Casanova and Jordi Cortadella for providing the timing data for ISCAS89 benchmarks, and Wai-shing Luk for giving the important idea on how to determine the order of  ... 
doi:10.1109/aspdac.2011.5722245 dblp:conf/aspdac/ZhiZZ11 fatcat:xlgqrzqdsvevrffonsgweglj4i

Some Convergence Results for Howard's Algorithm

Olivier Bokanowski, Stefania Maroso, Hasnaa Zidani
2009 SIAM Journal on Numerical Analysis  
Extensions of Howard's algorithm for a max-min problem of the form max b∈B min a∈A (B a,b x − c a,b ) = 0 are also proposed.  ...  This paper deals with convergence results of Howard's algorithm for the resolution of min a∈A (B a x−c a ) = 0, where B a is a matrix, c a is a vector, and A is a compact set.  ...  Bonnans for interesting discussions and comments on the manuscript.  ... 
doi:10.1137/08073041x fatcat:7ac3qfox4rchzmt7gplt4z75ha
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