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Efficient computation of representative sets with applications in parameterized and exact agorithms
 CORR
"... Let M = (E, I) be a matroid and let S = {S1,..., St} be a family of subsets of E of size p. A subfamily S ̂ ⊆ S is qrepresentative for S if for every set Y ⊆ E of size at most q, if there is a set X ∈ S disjoint from Y with X ∪ Y ∈ I, then there is a set X ̂ ∈ S ̂ disjoint from Y with X ̂ ∪ Y ∈ ..."
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Cited by 15 (3 self)
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Let M = (E, I) be a matroid and let S = {S1,..., St} be a family of subsets of E of size p. A subfamily S ̂ ⊆ S is qrepresentative for S if for every set Y ⊆ E of size at most q, if there is a set X ∈ S disjoint from Y with X ∪ Y ∈ I, then there is a set X ̂ ∈ S ̂ disjoint from Y with X ̂ ∪ Y ∈ I. By the classical result of Bollobás, in a uniform matroid, every family of sets of size p has a qrepresentative family with at most p+q
Probably Optimal Graph Motifs ∗
"... We show an O ∗ (2 k)time polynomial space algorithm for the ksized Graph Motif problem. We also introduce a new optimization variant of the problem, called Closest Graph Motif and solve it within the same time bound. The Closest Graph Motif problem encompasses several previously studied optimizati ..."
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Cited by 6 (2 self)
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We show an O ∗ (2 k)time polynomial space algorithm for the ksized Graph Motif problem. We also introduce a new optimization variant of the problem, called Closest Graph Motif and solve it within the same time bound. The Closest Graph Motif problem encompasses several previously studied optimization variants, like Maximum Graph Motif, MinSubstitute, and MinAdd. Moreover, we provide a piece of evidence that our result might be essentially tight: the existence of an O ∗ ((2−ɛ) k)time algorithm for the Graph Motif problem implies an O((2−ɛ ′ ) n)time algorithm for Set Cover.
Abusing the Tutte Matrix: An Algebraic Instance Compression for the Ksetcycle Problem
"... We give an algebraic, determinantbased algorithm for the KCycle problem, i.e., the problem of finding a cycle through a set of specified elements. Our approach gives a simple FPT algorithm for the problem, matching the O ∗ (2 K  ) running time of the algorithm of Björklund et al. (SODA, 2012). F ..."
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Cited by 4 (0 self)
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We give an algebraic, determinantbased algorithm for the KCycle problem, i.e., the problem of finding a cycle through a set of specified elements. Our approach gives a simple FPT algorithm for the problem, matching the O ∗ (2 K  ) running time of the algorithm of Björklund et al. (SODA, 2012). Furthermore, our approach is open for treatment by classical algebraic tools (e.g., Gaussian elimination), and we show that it leads to a polynomial compression of the problem, i.e., a polynomialtime reduction of the KCycle problem into an algebraic problem with coding size O(K  3). This is surprising, as several related problems (e.g., kCycle and the Disjoint Paths problem) are known not to admit such a reduction unless the polynomial hierarchy collapses. Furthermore, despite the result, we are not aware of any witness for the KCycle problem of size polynomial in K  + log n, which seems (for now) to separate the notions of polynomial compression and polynomial kernelization (as a polynomial kernelization for a problem in NP necessarily implies a small witness).
Z.: Faster deterministic algorithms for packing, matching and tdominating set problems
 CoRR
, 2013
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"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: