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Odd minimum cut sets and b-matchings revisited
[article]
2006
arXiv
pre-print
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The famous Padberg-Rao separation algorithm for 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. ...
arXiv:math/0607088v1
fatcat:mqbe4tmvnbb67jd6wmzh7gev7a
Odd Minimum Cut Sets and b-Matchings Revisited
2008
SIAM Journal on Discrete Mathematics
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The famous Padberg-Rao separation algorithm for 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. ...
doi:10.1137/060664793
fatcat:5tcjmkpgmzfmnjjpltic3kukge
Dawn of computer-aided design
2013
Proceedings of the 2013 ACM international symposium on International symposium on physical design - ISPD '13
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cycle = No odd face
⇔ No odd vertex degree (Euler Graph)
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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 ...
doi:10.1145/2451916.2451930
dblp:conf/ispd/Takahashi13
fatcat:2tna2zt5uzdyrouavcwc57mpba
Strongly Connected Spanning Subgraph for Almost Symmetric Networks
2017
International journal of computational geometry and applications
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Given a 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 . ...
doi:10.1142/s0218195917500042
fatcat:b46qqrmiyzge3cvngxrizs5ngi
Page 1241 of Mathematical Reviews Vol. , Issue 96b
[page]
1996
Mathematical Reviews
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{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. ...
Revisiting a Cutting-Plane Method for Perfect Matchings
2020
Open Journal of Mathematical Optimization
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In 2016, Chandrasekaran, Végh, 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. ...
doi:10.5802/ojmo.2
fatcat:tqqthnhgprhn7d62kldpextowe
Double Digest Revisited: Complexity and Approximability in the Presence of Noisy Data
[chapter]
2003
Lecture Notes in Computer Science
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We 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. ...
doi:10.1007/3-540-45071-8_52
fatcat:mwhnq5dpu5aufnl5rszpok5ofm
DCJ-Indel sorting revisited
2013
Algorithms for Molecular Biology
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The introduction of the double 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 }. ...
doi:10.1186/1748-7188-8-6
pmid:23452758
pmcid:PMC3655023
fatcat:5z3fwpjkibcszjf3k372lzbnxa
Revisiting a Cutting Plane Method for Perfect Matchings
[article]
2019
arXiv
pre-print
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In 2016, Chandrasekaran, Végh, 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. ...
arXiv:1908.10989v1
fatcat:g7ky5oxvhbhwzib6sva4t75hem
Near Linear Time Approximation Schemes for Uncapacitated and Capacitated b--Matching Problems in Nonbipartite Graphs
[article]
2018
arXiv
pre-print
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We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) 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] . ...
arXiv:1307.4355v4
fatcat:4yo3mojimfbehlb2xv22fvciam
Survey of local algorithms
2013
ACM Computing Surveys
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For more general packing 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] . ...
doi:10.1145/2431211.2431223
fatcat:zlnxn57wunh6jl5om2lagbfvim
Brane blobology in the large D effective theory
[article]
2020
arXiv
pre-print
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Highly deformed black dumbbells 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. ...
arXiv:2009.11823v2
fatcat:z2njgub2dbh4bef3owynw4jcoe
AliquotG: An Improved Heuristic Algorithm for Genome Aliquoting
2013
PLoS ONE
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We also compared the performance of our method with an earlier method using simulation data 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. ...
doi:10.1371/journal.pone.0064279
pmid:23691189
pmcid:PMC3653901
fatcat:bymxrgzicbeurmsrxofm6x4g3a
Fast marching methods for the continuous traveling salesman problem
2007
Proceedings of the National Academy of Sciences of the United States of America
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APPLIED MATHEMATICS AQ: A AQ: 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. ...
doi:10.1073/pnas.0609910104
pmid:17220271
pmcid:PMC1783106
fatcat:r2uuitrvivgytetutznik3dml4
LP can be a cure for Parameterized Problems
2012
Symposium on Theoretical Aspects of Computer Science
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Then, using known 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. ...
doi:10.4230/lipics.stacs.2012.338
dblp:conf/stacs/NarayanaswamyRRS12
fatcat:3ing2rm3mjar7ljqroq35jd4sm
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