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Odd minimum cut sets and b-matchings revisited
[article]

2006
*
arXiv
*
pre-print

The famous Padberg-Rao separation algorithm for

arXiv:math/0607088v1
fatcat:mqbe4tmvnbb67jd6wmzh7gev7a
*b*-*matching*polyhedra can be implemented to run in O(n^2m log(n^2/m)) time in the uncapacitated case,*and*in O(nm^2 log(n^2/m)) time in the capacitated case ... (where n is the number of vertices*and*m is the number of edges of the underlying graph). ... Finally, we define T as the*set*of all vertices u for which the value*b*u is*odd*,*and*we let v ∈ T iff u*b*u is*odd*. ...##
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Odd Minimum Cut Sets and b-Matchings Revisited

2008
*
SIAM Journal on Discrete Mathematics
*

The famous Padberg-Rao separation algorithm for

doi:10.1137/060664793
fatcat:5tcjmkpgmzfmnjjpltic3kukge
*b*-*matching*polyhedra can be implemented to run in O(|V | 2 |E| log(|V | 2 /|E|)) time in the uncapacitated case,*and*in O(|V ||E| 2 log (|V | 2 /|E|)) time ... We give a new*and*simple algorithm for the capacitated case which can be implemented to run in O(|V | 2 |E| log(|V | 2 /|E|)) time. ... One of the T -*odd*edges of the*cut*-tree induces a*minimum**odd**cut*in G. Proof. Let U ⊂ V be an*odd**set*such that δ(U ) is a*minimum**odd**cut*in G. ...##
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Dawn of computer-aided design

2013
*
Proceedings of the 2013 ACM international symposium on International symposium on physical design - ISPD '13
*

cycle = No

doi:10.1145/2451916.2451930
dblp:conf/ispd/Takahashi13
fatcat:2tna2zt5uzdyrouavcwc57mpba
*odd*face ⇔ No*odd*vertex degree (Euler Graph) a*b*d e f c g h i C A*B*E F D Maximum*Cut*of Planar Graph Min Via Problem ⇔ Max*Cut*Problem of Planar Graph ⇔ Min ... CAS 1969 -Most Distant (Reliable) Pair of Sub-trees -Unique Graph Partition, Sparse, Dense,*and*Other -The*minimum**set*of voltages*and*currents that describes all variables in a circuit 2013/3/25 ... #via = #conflict edges in 2-coloring = #edge that needed to be removed to make the graph bipartite ⇔ #edge in*cut*...##
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Strongly Connected Spanning Subgraph for Almost Symmetric Networks

2017
*
International journal of computational geometry and applications
*

Given a

doi:10.1142/s0218195917500042
fatcat:b46qqrmiyzge3cvngxrizs5ngi
*set*V of points in the plane such that each point u ∈ V has a radius r u , the symmetric disk graph of V is a directed graph G = (V, E), such that E = {(u, v) : |uv| ≤ r u*and*|uv| ≤ r v }. ... Given a constant t ≥ 1, a directed graph G is a t-spanner of a*set*of points V if, for every two points u*and*v in V , there exists a directed path from u to v in G of length at most t · |uv|, where |uv ... in V*odd*),*and*let M denote a*minimum*weight perfect*matching*of G*odd*. ...##
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Page 1241 of Mathematical Reviews Vol. , Issue 96b
[page]

1996
*
Mathematical Reviews
*

{Pi,---,P,} where P; = P((/;,h;),(fj,4;41)), such that: (a) s(P;) = S(P), for i=1,---,t,

*and*(*b*) the P; are disjoint. If no such*set*exists, stop. Every*matching*by 7 is a maximum*matching*of G. ... A*cut*D treated as a*set*of edges is called a T-*cut*if each of two components of the graph G \ D contains an*odd*number of ver- tices from 7. ...##
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Revisiting a Cutting-Plane Method for Perfect Matchings

2020
*
Open Journal of Mathematical Optimization
*

In 2016, Chandrasekaran, Végh,

doi:10.5802/ojmo.2
fatcat:tqqthnhgprhn7d62kldpextowe
*and*Vempala (Mathematics of Operations Research, 41(1):23-48) published a method to solve the*minimum*-cost perfect*matching*problem on an arbitrary graph by solving a strictly ... We then give an explicit algorithm that exploits our method,*and*show that this new algorithm still runs in strongly polynomial time. ... Huang, Michael McCulloch,*and*the Fields Institute*and*Fields Centre for Quantitative Analysis*and*Modelling (Fields CQAM) -without whom this research would not have been possible. ...##
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Double Digest Revisited: Complexity and Approximability in the Presence of Noisy Data
[chapter]

2003
*
Lecture Notes in Computer Science
*

We

doi:10.1007/3-540-45071-8_52
fatcat:mwhnq5dpu5aufnl5rszpok5ofm
*revisit*the double digest problem, which occurs in sequencing of large DNA strings*and*consists of reconstructing the relative positions of*cut*sites from two different enzymes: we rst show that double ... In a third part, we investigate these variations with the additional restriction that conincident*cut*sites are disallowed*and*we show that it is NP-hard to even nd feasible solutions in this case, thus ... On the other hand, in P*B*each point except the rst*and*the last is the sum of a multiple of h*and*an*odd*multiple of t. Thus,*sets*P A*and*P*B*are disjoint except for the rst*and*the last point. ...##
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DCJ-Indel sorting revisited

2013
*
Algorithms for Molecular Biology
*

The introduction of the double

doi:10.1186/1748-7188-8-6
pmid:23452758
pmcid:PMC3655023
fatcat:5z3fwpjkibcszjf3k372lzbnxa
*cut**and*join operation (DCJ) caused a flurry of research into the study of multichromosomal rearrangements. ... There is still room for research in this area, most notably the problem of sorting when the cost of indels is allowed to vary with respect to the cost of a DCJ*and*we demand a*minimum*cost transformation ... Assume without loss of generality that p π*odd*− p π even ≥ p γ*odd*− p γ even ,*and**set*m = min {p π,γ , p γ*odd*− p γ even }. ...##
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Revisiting a Cutting Plane Method for Perfect Matchings
[article]

2019
*
arXiv
*
pre-print

In 2016, Chandrasekaran, Végh,

arXiv:1908.10989v1
fatcat:g7ky5oxvhbhwzib6sva4t75hem
*and*Vempala published a method to solve the*minimum*-cost perfect*matching*problem on an arbitrary graph by solving a strictly polynomial number of linear programs. ... We then give an explicit algorithm that exploits are method,*and*show that this new algorithm still runs in strongly polynomial time. ... Huang, Michael McCulloch,*and*the Fields Institute*and*Fields Centre for Quantitative Analysis*and*Modelling (Fields CQAM) -without whom this research would not have been possible. ...##
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Near Linear Time Approximation Schemes for Uncapacitated and Capacitated b--Matching Problems in Nonbipartite Graphs
[article]

2018
*
arXiv
*
pre-print

We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated)

arXiv:1307.4355v4
fatcat:4yo3mojimfbehlb2xv22fvciam
*b*--*matching*problems for non-bipartite graphs that run in time (near) linear in the number ... First, even though the dual of these problems have exponentially many variables*and*an efficient exact computation of dual weights is infeasible, we show that we can efficiently compute*and*use a sparse ... That approach is the "*minimum**odd*-*cut*" approach of Padberg*and*Rao [27] . ...##
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Survey of local algorithms

2013
*
ACM Computing Surveys
*

For more general packing

doi:10.1145/2431211.2431223
fatcat:zlnxn57wunh6jl5om2lagbfvim
*and*covering problems (such as the*set*cover problem or packing LPs) there is more freedom. ... Being highly scalable*and*fault-tolerant, such algorithms are ideal in the operation of large-scale distributed systems. ... Edge dominating*sets*are closely related to*matchings*: a maximal*matching*is an edge dominating*set*,*and*a*minimum*-size maximal*matching*is a*minimum*-size edge dominating*set*[2, 151] . ...##
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Brane blobology in the large D effective theory
[article]

2020
*
arXiv
*
pre-print

Highly deformed black dumbbells

arXiv:2009.11823v2
fatcat:z2njgub2dbh4bef3owynw4jcoe
*and*ripples are also found to be tractable in the same approximation. ... In this article, we demonstrate the blob approximation has a wider range of applicability by formulating the interaction between blobs*and*subsequent dynamics. ... Acknowledgments The author would like to thank Roberto Emparan for useful comments*and*discussion. ...##
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AliquotG: An Improved Heuristic Algorithm for Genome Aliquoting

2013
*
PLoS ONE
*

We also compared the performance of our method with an earlier method using simulation data

doi:10.1371/journal.pone.0064279
pmid:23691189
pmcid:PMC3653901
fatcat:bymxrgzicbeurmsrxofm6x4g3a
*sets**and*found that our algorithm has higher accuracy. ... Though several heuristic algorithms have been published, here, we sought improved algorithms for the problem with respect to the double*cut**and*join (DCJ) distance. ... Acknowledgments We thank Robert Warren*and*David Sankoff for supplying their program. Author Contributions Conceived*and*designed the experiments: ZL SH AX. Analyzed the data: ZC SH. ...##
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Fast marching methods for the continuous traveling salesman problem

2007
*
Proceedings of the National Academy of Sciences of the United States of America
*

APPLIED MATHEMATICS AQ: A AQ:

doi:10.1073/pnas.0609910104
pmid:17220271
pmcid:PMC1783106
fatcat:r2uuitrvivgytetutznik3dml4
*B*Fn1 balt4/zpq-pnas/zpq-pnas/zpq-orig/zpq4642-06a flemingj S21؍ 1/7/07 15:05 Art: 06-09910 Input-JL Cadmus: 4642 Research Article • Applied Mathematics Andrews*and*Sethian ... We describe algorithms for both a heuristic*and*an optimal solution to this problem. ... Then comes the calculation of a perfect*matching*among the cities of the*minimum*spanning tree with an*odd*number of edges in the*minimum*spanning tree. ...##
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LP can be a cure for Parameterized Problems

2012
*
Symposium on Theoretical Aspects of Computer Science
*

Then, using known

doi:10.4230/lipics.stacs.2012.338
dblp:conf/stacs/NarayanaswamyRRS12
fatcat:3ing2rm3mjar7ljqroq35jd4sm
*and*new reductions, we give O * (2.6181 k ) algorithms for the parameterized versions of Above Guarantee Vertex Cover,*Odd*Cycle Transversal, Split Vertex Deletion*and*Almost 2-SAT,*and*... The notable improvement is the bound for*Odd*Cycle Transversal for which this is the first major improvement after the first algorithm that showed it fixed-parameter tractable in 2003. ... Conclusion*and*Further Work We have demonstrated that using the drop in LP values to analyze branching algorithms can give powerful results for parameterized complexity. ...
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