2017
DOI: 10.1007/s00453-017-0319-z
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Edge Bipartization Faster than $$2^k$$ 2 k

Abstract: In the Edge Bipartization problem one is given an undirected graph G and an integer k, and the question is whether k edges can be deleted from G so that it becomes bipartite. Guo et al. (J Comput Syst Sci 72(8):1386-1396, 2006 proposed an algorithm solving this problem in time O(2 k · m 2 ); today, this algorithm is a textbook example of an application of the iterative compression technique. Despite extensive progress in the understanding of the parameterized complexity of graph separation problems in the rece… Show more

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Cited by 9 publications
(7 citation statements)
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“…For example, covering cycles by deleting minimum number of edges (feedback edge set problem) in undirected graphs is polynomial time solvable, while the related feedback vertex set problem is NP-Complete. Also, covering odd cycles by deleting edges in undirected graphs admits a more efficient FPT algorithm [23] although both the problems are NP-Complete. Covering cycles by minimum number of arcs (feedback arc set) in tournaments has a sub-exponential algorithm [1] while the vertex version of the problem (feedback vertex set) in tournaments is unlikely to admit sub-exponential algorithms under Exponential Time Hypothesis [8,11,14].…”
Section: Resultsmentioning
confidence: 99%
“…For example, covering cycles by deleting minimum number of edges (feedback edge set problem) in undirected graphs is polynomial time solvable, while the related feedback vertex set problem is NP-Complete. Also, covering odd cycles by deleting edges in undirected graphs admits a more efficient FPT algorithm [23] although both the problems are NP-Complete. Covering cycles by minimum number of arcs (feedback arc set) in tournaments has a sub-exponential algorithm [1] while the vertex version of the problem (feedback vertex set) in tournaments is unlikely to admit sub-exponential algorithms under Exponential Time Hypothesis [8,11,14].…”
Section: Resultsmentioning
confidence: 99%
“…Faster Algorithm for Finite Fields Let F p be a finite p-element field with p ≥ 3. For Min-2-Lin(F 2 ) a O * (1.977 k ) time algorithm can be obtained using the approach of [36]. Every finite field obviously has an effective representation so we assume without loss of generality that F p is effective.…”
Section: Evenmentioning
confidence: 99%
“…Let F p be a finite p-element field with p ≥ 3. For Min-2-Lin(F 2 ) a O * (1.977 k ) time algorithm can be obtained using the approach of [32]. Every finite field obviously has an effective representation so we assume without loss of generality that F p is effective.…”
Section: Even Faster Algorithm For Finite Fieldsmentioning
confidence: 99%