How to Find Long Paths Efficiently

Monien, Burkhard

doi:10.1016/s0304-0208(08)73110-4

Cited by 107 publications

(106 citation statements)

References 4 publications

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“…The approximability of the associated optimization problems is very much open despite considerable efforts in recent years. Monien [10] gave an algorithm to find a path of length k in time O(k! · n · m) where n and m are respectively the number of vertices and the number of edges of the graph.…”

Section: Introductionmentioning

confidence: 99%

On the Approximation of Finding A(nother) Hamiltonian Cycle in Cubic Hamiltonian Graphs

Bazgan

Sántha

Tuza

1999

Journal of Algorithms

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Section: Introductionmentioning

confidence: 99%

On the Approximation of Finding A(nother) Hamiltonian Cycle in Cubic Hamiltonian Graphs

Bazgan

Sántha

Tuza

1999

Journal of Algorithms

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“…For Minimum-Weight Path, the length of the path is a natural parameter. Monien [21] gave the first fixed-parameter algorithm with a running time of O(k!· nm). Bodlaender [2] gave an algorithm running in O(2 k k!·n) time using dynamic programming.…”

Section: Introductionmentioning

confidence: 99%

Algorithm Engineering for Color-Coding with Applications to Signaling Pathway Detection

2007

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Color-coding is a technique to design fixed-parameter algorithms for several NP-complete subgraph isomorphism problems. Somewhat surprisingly, not much work has so far been spent on the actual implementation of algorithms that are based on color-coding, despite the elegance of this technique and its wide range of applicability to practically important problems. This work gives various novel algorithmic improvements for color-coding, both from a worst-case perspective as well as under practical considerations. We apply the resulting implementation to the identification of signaling pathways in protein interaction networks, demonstrating that our improvements speed up the color-coding algorithm by orders of magnitude over previous implementations. This allows more complex and larger structures to be identified in reasonable time; many biologically relevant instances can even be solved in seconds where, previously, hours were required.

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“…We are not aware of any parameterized investigations of the last three problems. The algorithm behind the main result is inspired by the technique of representative systems introduced by Monien [6] (see also [8,5] and [1,Section 8.2]). Iteratively for i = 1, 2, .…”

Section: Introductionmentioning

confidence: 99%

A Parameterized View on Matroid Optimization Problems

Marx

2006

Automata, Languages and Programming

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Abstract. Matroid theory gives us powerful techniques for understanding combinatorial optimization problems and for designing polynomialtime algorithms. However, several natural matroid problems, such as 3-matroid intersection, are NP-hard. Here we investigate these problems from the parameterized complexity point of view: instead of the trivial O(n k ) time brute force algorithm for finding a k-element solution, we try to give algorithms with uniformly polynomial (i.e., f (k) · n O(1) ) running time. The main result is that if the ground set of a represented matroid is partitioned into blocks of size ℓ, then we can determine in f (k, ℓ)·n O(1) randomized time whether there is an independent set that is the union of k blocks. As consequence, algorithms with similar running time are obtained for other problems such as finding a k-set in the intersection of ℓ matroids, or finding k terminals in a network such that each of them can be connected simultaneously to the source by ℓ disjoint paths.

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How to Find Long Paths Efficiently

Cited by 107 publications

References 4 publications

On the Approximation of Finding A(nother) Hamiltonian Cycle in Cubic Hamiltonian Graphs

On the Approximation of Finding A(nother) Hamiltonian Cycle in Cubic Hamiltonian Graphs

Algorithm Engineering for Color-Coding with Applications to Signaling Pathway Detection

A Parameterized View on Matroid Optimization Problems

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