Algorithm Engineering for Optimal Graph Bipartization

Hüffner, Falk

doi:10.7155/jgaa.00177

Cited by 44 publications

(40 citation statements)

References 45 publications

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“…For instances from Odd Cycle Transversal, we also include the results of the algorithm for directly solving Odd Cycle Transversal by Hüffner [9].…”

Section: Methodsmentioning

confidence: 99%

“…Hüffner: This is the state-of-the-art algorithm by Hüffner for directly solving Odd Cycle Transversal [9]. This algorithm is based on an FPT algorithm by Reed, Smith and Vetta [18] using the iterative compression technique.…”

Section: Mcs: Mcsmentioning

confidence: 99%

“…We used real Odd Cycle Transversal instances from bioinformatics, which formulates the Minimum Site Removal problem 7 [9].…”

Section: Real Sparse Networkmentioning

confidence: 99%

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Branch-and-reduce exponential/FPT algorithms in practice: A case study of vertex cover

Akiba

Iwata

2016

Theoretical Computer Science

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We investigate the gap between theory and practice for exact branching algorithms. In theory, branch-and-reduce algorithms currently have the best time complexity for numerous important problems. On the other hand, in practice, state-of-the-art methods are based on different approaches, and the empirical efficiency of such theoretical algorithms have seldom been investigated probably because they are seemingly inefficient because of the plethora of complex reduction rules. In this paper, we design a branch-and-reduce algorithm for the vertex cover problem using the techniques developed for theoretical algorithms and compare its practical performance with other state-of-the-art empirical methods. The results indicate that branch-and-reduce algorithms are actually quite practical and competitive with other state-ofthe-art approaches for several kinds of instances, thus showing the practical impact of theoretical research on branching algorithms.

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“…For instances from Odd Cycle Transversal, we also include the results of the algorithm for directly solving Odd Cycle Transversal by Hüffner [9].…”

Section: Methodsmentioning

confidence: 99%

Section: Mcs: Mcsmentioning

confidence: 99%

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Branch-and-reduce exponential/FPT algorithms in practice: A case study of vertex cover

Akiba

Iwata

2016

Theoretical Computer Science

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“…In an attempt to remedy this, Hüffner [5] provided an alternative algorithm for the problem. In this paper we give yet another algorithm for OCT. We believe that our algorithm is simpler and more intuitive than the previous versions.…”

Section: Introductionmentioning

confidence: 99%

Simpler Parameterized Algorithm for OCT

Lokshtanov

Saurabh

Sikdar

2009

Lecture Notes in Computer Science

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“…This technique has been useful in resolving several other open problems in the area of parameterized complexity, including Directed Feedback Vertex Set, Almost 2-SAT, Multicut [3,32,26]. However, the algorithm for OCT had seen no further improvements in the last 9 years, though reinterpretations of the algorithm have been published [13,20]. Only recently, Lokshtanov et al [18] obtained an algorithm with an improved dependence on the parameter k. This algorithm is based on a branching guided by linear programming and runs in time O(2.32 k n O(1) ).…”

Section: Introductionmentioning

confidence: 99%

Linear Time Parameterized Algorithms via Skew-Symmetric Multicuts

Ramanujan¹,

Saurabh²

2013

Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms

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A skew-symmetric graph (D = (V, A), σ) is a directed graph D with an involution σ on the set of vertices and arcs. Flows on skew-symmetric graphs have been used to generalize maximum flow and maximum matching problems on graphs, initially by Tutte [1967], and later by Goldberg and Karzanov [1994, 1995]. In this paper, we introduce a separation problem, d-SkewSymmetric Multicut, where we are given a skewsymmetric graph D, a family of T of d-sized subsets of vertices and an integer k. The objective is to decide if there is a set X ⊆ A of k arcs such that every set J in the family has a vertex v such that v and σ(v) are in different strongly connected components of D = (V, A \ (X ∪ σ(X)). In this paper, we give an algorithm for d-Skew-Symmetric Multicut which runs in time O((4d) k (m+n+ )), where m is the number of arcs in the graph, n the number of vertices and the length of the family given in the input.This problem, apart from being independently interesting, also abstracts out and captures the main combinatorial obstacles towards solving numerous classical problems. Our algorithm for d-Skew-Symmetric Multicut paves the way for the first linear time parameterized algorithms for several problems. We demonstrate its utility by obtaining the following linear time parameterized algorithms.• We show that Almost 2-SAT is a special case of 1-Skew-Symmetric Multicut, resulting in an algorithm for Almost 2-SAT which runs in time O(4 k k 4 ) where k is the size of the solution and is the length of the input formula. Then, using linear time parameter preserving reductions to Almost 2-SAT, we obtain algorithms for Odd Cycle Transversal and Edge Bipartization which run in time O(4 k k 4 (m+n)) and O(4 k k 5 (m+ n)) respectively where k is size of the solution, * Supported by Parameterized Approximation, ERC Starting Grant 306992.

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Algorithm Engineering for Optimal Graph Bipartization

Cited by 44 publications

References 45 publications

Branch-and-reduce exponential/FPT algorithms in practice: A case study of vertex cover

Branch-and-reduce exponential/FPT algorithms in practice: A case study of vertex cover

Simpler Parameterized Algorithm for OCT

Linear Time Parameterized Algorithms via Skew-Symmetric Multicuts

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