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

2010
*
Lecture Notes in Computer Science
*

When applied to weighted directed graphs, which may be viewed as Deterministic MDPs (DMDPs),

doi:10.1007/978-3-642-17517-6_37
fatcat:nv5ce77vpndkzar2ov2ywmpyje
*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*. ...##
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An O(nm) time algorithm for finding the min length directed cycle in a graph

2017
*
Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms
*

If the

doi:10.1137/1.9781611974782.122
dblp:conf/soda/OrlinS17
fatcat:yaw3q46l75a4vjxdeg2sukzake
*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. ...##
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A robust basic cyclic scheduling problem

2018
*
EURO Journal on Computational Optimization
*

We propose three exact

doi:10.1007/s13675-018-0100-3
fatcat:2sskxthdhzgthlipokbsgvcy5y
*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. ...##
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Computing Optimal Cycle Mean in Parallel on CUDA

2011
*
Electronic Proceedings in Theoretical Computer Science
*

In this paper we propose a data-parallel

doi:10.4204/eptcs.72.8
fatcat:izyjvx6rlnhxdjqr2bit7ihs6y
*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 . ...##
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Approximating the minimum cycle mean

2014
*
Theoretical Computer Science
*

We consider directed graphs where each edge is labeled with an integer weight and study the fundamental

doi:10.1016/j.tcs.2014.06.031
fatcat:soesmgat7rcanmnli7btsh2rwa
*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*. ...##
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Experimental analysis of the fastest optimum cycle ratio and mean algorithms

2004
*
ACM Transactions on Design Automation of Electronic Systems
*

Some applications in the computer-aided design field include

doi:10.1145/1027084.1027085
fatcat:policwg3qbhy7m2bbs5f4iflyq
*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*. ...##
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High-Level Synthesis of DSP Applications Using Adaptive Negative Cycle Detection

2002
*
EURASIP Journal on Advances in Signal Processing
*

In terms of applications, the adaptive technique leads to a very fast implementation of Lawlers

doi:10.1155/s1110865702205053
fatcat:ivstivlfynepzlmyw3xwp225q4
*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*...##
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Approximating the minimum cycle mean

2013
*
Electronic Proceedings in Theoretical Computer Science
*

We consider directed graphs where each edge is labeled with an integer weight and study the fundamental

doi:10.4204/eptcs.119.13
fatcat:bc6e4ofepbf6bb2bthxkgrxrvi
*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. ...##
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Negative-cycle detection algorithms

1999
*
Mathematical programming
*

We study the problem of

doi:10.1007/s101070050058
fatcat:fakfclxq3jbxfpfdyw5sy5v5um
*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*. ...##
###
Negative-cycle detection algorithms
[chapter]

1996
*
Lecture Notes in Computer Science
*

We study the problem of

doi:10.1007/3-540-61680-2_67
fatcat:zyssc6jivjfydlrg2osw6uint4
*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*. ...##
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Multi-level clustering for clock skew optimization

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

doi:10.1145/1687399.1687502
dblp:conf/iccad/CasanovaC09
fatcat:7333ujwhprd4perespx7lydexe
*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] . ...##
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Efficient implementations of minimum-cost flow algorithms
[article]

2012
*
arXiv
*
pre-print

This paper presents efficient implementations of several

arXiv:1207.6381v1
fatcat:al4z2akk6fbetcqzg2fwgt67hu
*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. ...##
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An Experimental Study of Minimum Mean Cycle Algorithms
[chapter]

2009
*
2009 Proceedings of the Eleventh Workshop on Algorithm Engineering and Experiments (ALENEX)
*

We study

doi:10.1137/1.9781611972894.1
dblp:conf/alenex/GeorgiadisGTW09
fatcat:2n36z3iicvcktjeapcvqqzo27m
*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. ...##
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A practical method for multi-domain clock skew optimization

2011
*
16th Asia and South Pacific Design Automation Conference (ASP-DAC 2011)
*

A framework based on branch-and-

doi:10.1109/aspdac.2011.5722245
dblp:conf/aspdac/ZhiZZ11
fatcat:xlgqrzqdsvevrffonsgweglj4i
*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 ...##
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Some Convergence Results for Howard's Algorithm

2009
*
SIAM Journal on Numerical Analysis
*

Extensions of

doi:10.1137/08073041x
fatcat:7ac3qfox4rchzmt7gplt4z75ha
*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. ...
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