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### Computing Cycle Covers without Short Cycles [chapter]

Markus Bläser, Bodo Siebert
2001 Lecture Notes in Computer Science
A cycle cover of a graph is a spanning subgraph where each node is part of exactly one simple cycle. A k-cycle cover is a cycle cover where each cycle has length at least k.  ...  Output: a k-cycle cover of G.  ...  A k-restricted cycle cover (or k-cycle cover for short) is a cycle cover in which each cycle has length at least k.  ...

### Tolerance Based Contract-or-Patch Heuristic for the Asymmetric TSP [chapter]

Boris Goldengorin, Gerold Jäger, Paul Molitor
2006 Lecture Notes in Computer Science
arc from a short cycle in an OAPS with the largest upper tolerance with respect to one of the relaxed ATSP.  ...  Our improvement is based on replacing the selection of each path to be contracted after deleting a heaviest arc from each short cycle in an Optimal Assignment Problem Solution (OAPS) by contracting a single  ...  Algorithm 3 (COP/KSP and COP/GKS) 1 Choose a threshold t. 2 Solve the AP with a minimum cycle cover F . 3 If there is a cycle with length at most t (a short cycle), delete a heaviest arc in every short  ...

### Page 310 of Welding Journal Vol. 30, Issue 3 [page]

1951 Welding Journal
The fatigue strength at 100,000 cycles, designated as F 100,000, was then computed by means of an empirical equation, from tests in which the actual number of cycles of stress to produce failure was less  ...  The fatigue strength at 2,000,000 cycles, designated as Fatigue Tests of Beams F 2,000,000, was computed from tests in which the actual number of cycles of stress to produce failure was greater than 300,000  ...

### Approximation Algorithms for Restricted Cycle Covers Based on Cycle Decompositions [chapter]

Bodo Manthey
2006 Lecture Notes in Computer Science
For most sets L, the problem of computing L-cycle covers of maximum weight is NP-hard and APX-hard. We devise polynomial-time approximation algorithms for L-cycle covers.  ...  A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An L-cycle cover is a cycle cover in which the length of every cycle is in the set L ⊆ N.  ...  Thus, we are interested in computing cycle covers that do not contain short cycles.  ...

### Page 144 of Astronomy and Astrophysics Vol. 193, Issue 1-2 [page]

1988 Astronomy and Astrophysics
This difference is due to the short-period variation: when we compute the phases in the short-period cycle, we find that the deeper eclipses correspond to lower light levels in the short-period variation  ...  Allowing for the short-period variation, and since the mean brightness outside eclipse is m, = 3.333, we can compute the depths of both eclipses.  ...

### Shortest Non-trivial Cycles in Directed and Undirected Surface Graphs [chapter]

Kyle Fox
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
We also describe an algorithm to compute a shortest non-null-homologous cycle in G in O((g 2 + g b)n log n) time, extending a known algorithm of Erickson to compute a shortest non-separating cycle.  ...  In order to achieve this time bound, we use a restriction of the infinite cyclic cover that may be useful in other contexts.  ...  In short, we compute the cyclic double cover Σ 2 λ as described in Appendix A. The lift of G = (V, E) to Σ 2 λ contains the vertex set V × {0, 1}.  ...

### Shortest Non-trivial Cycles in Directed and Undirected Surface Graphs [article]

Kyle Fox
2012 arXiv   pre-print
We also describe an algorithm to compute a shortest non-null-homologous cycle in G in O((g^2 + g b)n log n) time, extending a known algorithm of Erickson to compute a shortest non-separating cycle.  ...  If G is undirected, then we give an algorithm to compute a shortest non-separating cycle in 2^O(g) n log log n time.  ...  In short, we compute the cyclic double cover Σ 2 λ as described in Appendix A. The lift of G = (V, E) to Σ 2 λ contains the vertex set V × {0, 1}.  ...

### On the Sound Covering Cycle Problem in Paired de Bruijn Graphs [chapter]

2015 Lecture Notes in Computer Science
We study the NP-hard Sound Covering Cycle problem which has as input a paired de Bruijn graph G and two integers d and , and the task is to find a length-cycle C containing all arcs of G such that for  ...  Without loss of generality assume i < j. We transform C into a new cycle C in which q + q i=1 |W i | is smaller. This contradicts our choice of C.  ...  Theorem 4 . 4 Approximately Sound Covering Cycle can be solved in O(8 n·∆ · 2 n·∆ d ) · poly(n · ∆ d + log ) time.Finally, we consider the combination of finding a short and approximately sound cycle.  ...

### Approximating Maximum Weight Cycle Covers in Directed Graphs with Weights Zero and One

Markus Bläser, Bodo Manthey
2005 Algorithmica
A cycle cover of a graph is a spanning subgraph each node of which is part of exactly one simple cycle. A k-cycle cover is a cycle cover where each cycle has length at least k.  ...  The goal is to find a k-cycle cover with minimum weight.  ...  Computing an Initial Cycle Cover We start by computing an initial cycle cover (2-cycle cover) C of G with maximum weight.  ...

### Transforming Curves on Surfaces Redux [chapter]

Jeff Erickson, Kim Whittlesey
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
Almost exactly 100 years ago, Max Dehn described an algorithm to determine whether two given cycles on a compact surface are homotopic, meaning one cycle can be continuously deformed into the other without  ...  Our algorithm combines components of these earlier algorithms, classical results in small cancellation theory by Gersten and Short [Inventiones 1990], and simple run-length encoding.  ...  can be performed directly on the cycle without constructing or searching any portion of the universal cover.  ...

### Seasonal Sensitivity on COBEL-ISBA Local Forecast System for Fog and Low Clouds

Stevie Roquelaure, Thierry Bergot
2007 Pure and Applied Geophysics
The reference cycle and the perturbed cycles are done with the clear sky hypothesis (without cloud cover) and without advection.  ...  Forecast Sensitivity to Mesoscale Forecast sensitivity to cloud cover The impact of cloud cover is evaluated for three different cycles: the Aladin cloud cover cycle, which takes into account the cloud  ...

### Approximation Algorithms for Restricted Cycle Covers Based on Cycle Decompositions [article]

Bodo Manthey
2006 arXiv   pre-print
The weight of a cycle cover of an edge-weighted graph is the sum of the weights of its edges. We come close to settling the complexity and approximability of computing L-cycle covers.  ...  A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An L-cycle cover is a cycle cover in which the length of every cycle is in the set L.  ...  Thus, we are interested in computing cycle covers that do not contain short cycles.  ...

### Aviation-induced cirrus and radiation changes at diurnal timescales

Ulrich Schumann, Kaspar Graf
2013 Journal of Geophysical Research - Atmospheres
One model computes a ratio of 0.6, implying an estimate of global net RF of about 50 mW m À2 (40-80 mW m À2 ).  ...  The same "aviation fingerprint" is found in 8 years (2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011) of Meteosat observations of cirrus cover and OLR.  ...  The computed LW RF corresponds to the observable negative change in OLR due to aviation at short time scales. Therefore, we will compare CoCiP-computed LW RF with negative OLR changes.  ...

### Better approximations for max TSP

Refael Hassin, Shlomi Rubinstein
2000 Information Processing Letters
It treats differently short cycles, such that |C i | ε −1 , and long cycles. For each short cycle it computes a maximum Hamiltonian path on its vertices.  ...  A cycle cover C. 3.  ...

### Combining Problems on RAC Drawings and Simultaneous Graph Drawings [chapter]

Evmorfia N. Argyriou, Michael A. Bekos, Michael Kaufmann, Antonios Symvonis
2012 Lecture Notes in Computer Science
The drawing can be computed in linear time. We can extend the algorithm that produces a GRacSim drawing of a path and a matching to also cover the case of a cycle C and a matching M.  ...  A cycle and a matching always admit a GRacSim drawing on an (n + 2) × (n + 2) integer grid. The drawing can be computed in linear time. Corollary 1.  ...
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