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## Minimum membership set covering and the consecutive ones property (2006)

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Venue: | IN PROC. 10TH SWAT, VOLUME 4059 OF LNCS |

Citations: | 3 - 1 self |

### Citations

10431 | Introduction to Algorithms
- Cormen, Leiserson, et al.
- 1990
(Show Context)
Citation Context ...on, a number of interesting challenges for future research is exhibited. 1 Introduction Set Cover (and, equivalently, Hitting Set [1]) is a core problem of algorithmics and combinatorial optimization =-=[2, 3]-=-. The basic task is, given a collection C of subsets of a base set S, to select as few sets in C as possible such that their union is the base set. This models many resource allocation problems and ge... |

2792 | Computational complexity
- Papadimitriou
- 1994
(Show Context)
Citation Context ... the following instance (S, Cred, Cblue,k) of RBHS: 2 Note that it is essential for the NP-completeness of R3-Sat that the Boolean formula F may contain size-2 clauses, otherwise, the problem is in P =-=[15]-=-. 5sProc. 10th SWAT-06, Vol. 4059 in LNCS, pp. 339-350, Springer, 2006 F = ( x1 ∨ x2 ∨ ¬x3 ) ∧ ( ¬x2 ∨ x3 ∨ x4 ) ∧ ( ¬x1 ∨ ¬x2 ∨ ¬x4 ) ∧ ( ¬x1 ∨ x3 ∨ ¬x4 ) s 1 1 s 2 1 s 3 1 s2 s 2 1 2 s3 2 s2 s 3 1 3... |

1365 |
Integer and Combinatorial Optimization
- Nemhauser, Wolsey
- 1988
(Show Context)
Citation Context ...tains only whole “chunks” of that arrangement, that is, without any gaps. 1 Set Cover instances with c.o.p. are solvable in polynomial time, a fact which is made use of in many practical applications =-=[11, 13, 16, 17]-=-. Thus, the question naturally arises whether such results can be transferred to MMSC. This is what we study here, arriving at a much more colorful scenario than in the classical case. In order to tho... |

1190 | Parameterized Complexity
- Downey, Fellows
- 1999
(Show Context)
Citation Context ... Cover is NP-complete and only allows for a logarithmic-factor polynomial-time approximation [7]. It is parameterized intractable (that is, W[2]complete) with respect to the parameter “solution size” =-=[5, 14]-=-. Numerous variants of set covering are known and have been studied [2, 4, 8, 9, 11, 16]. Motivated by applications concerning interference reduction in cellular networks, Kuhn et al. [10] very recent... |

767 | A Threshold of ln n for Approximating Set Cover
- Feige
- 1998
(Show Context)
Citation Context ...allocation problems and generalizes fundamental graph problems such as Vertex Cover and Dominating Set. Set Cover is NP-complete and only allows for a logarithmic-factor polynomial-time approximation =-=[7]-=-. It is parameterized intractable (that is, W[2]complete) with respect to the parameter “solution size” [5, 14]. Numerous variants of set covering are known and have been studied [2, 4, 8, 9, 11, 16].... |

433 | Invitation to Fixed-Parameter Algorithms
- Niedermeier
- 2006
(Show Context)
Citation Context ... Cover is NP-complete and only allows for a logarithmic-factor polynomial-time approximation [7]. It is parameterized intractable (that is, W[2]complete) with respect to the parameter “solution size” =-=[5, 14]-=-. Numerous variants of set covering are known and have been studied [2, 4, 8, 9, 11, 16]. Motivated by applications concerning interference reduction in cellular networks, Kuhn et al. [10] very recent... |

291 |
On the complexity of timetable and multi-commodity flow problems
- Even, Itai, et al.
- 1976
(Show Context)
Citation Context ...ed have cardinality at most 2. Proof. We prove the theorem by showing how the restricted RBHS instance can equivalently be stated as a 2-Sat problem; 2-Sat is well-known to be solvable in linear time =-=[6]-=-. For our reduction, we construct the following instance F of 2-Sat for a given instance (S, Cred, Cblue,1) of RBHS: – For each element si ∈ S, where 1 ≤ i ≤ n, F contains the variable xi. – For each ... |

146 |
Primal-dual approximation algorithms for integral flow and multicuts in trees
- Garg, Yannakakis, et al.
- 1997
(Show Context)
Citation Context ...ime approximation [7]. It is parameterized intractable (that is, W[2]complete) with respect to the parameter “solution size” [5, 14]. Numerous variants of set covering are known and have been studied =-=[2, 4, 8, 9, 11, 16]-=-. Motivated by applications concerning interference reduction in cellular networks, Kuhn et al. [10] very recently introduced and investigated the Minimum Membership Set Cover problem. Minimum Members... |

90 | Algorithms for the set covering problem
- Caprara, Toth, et al.
- 2000
(Show Context)
Citation Context ...on, a number of interesting challenges for future research is exhibited. 1 Introduction Set Cover (and, equivalently, Hitting Set [1]) is a core problem of algorithmics and combinatorial optimization =-=[2, 3]-=-. The basic task is, given a collection C of subsets of a base set S, to select as few sets in C as possible such that their union is the base set. This models many resource allocation problems and ge... |

80 |
Structure Preserving Reductions among Convex Optimization Problems
- Ausiello, D'Atri, et al.
- 1980
(Show Context)
Citation Context ...eteness, and approximability results for various cases here. In addition, a number of interesting challenges for future research is exhibited. 1 Introduction Set Cover (and, equivalently, Hitting Set =-=[1]-=-) is a core problem of algorithmics and combinatorial optimization [2, 3]. The basic task is, given a collection C of subsets of a base set S, to select as few sets in C as possible such that their un... |

77 | Combination can be hard: Approximability of the unique coverage problem
- Demaine, Feige, et al.
(Show Context)
Citation Context ...ime approximation [7]. It is parameterized intractable (that is, W[2]complete) with respect to the parameter “solution size” [5, 14]. Numerous variants of set covering are known and have been studied =-=[2, 4, 8, 9, 11, 16]-=-. Motivated by applications concerning interference reduction in cellular networks, Kuhn et al. [10] very recently introduced and investigated the Minimum Membership Set Cover problem. Minimum Members... |

35 | On the consecutive ones property - Meidanis, Porto, et al. - 1998 |

22 |
Optimal capacity scheduling
- Veinott, Wagner
- 1962
(Show Context)
Citation Context ...tains only whole “chunks” of that arrangement, that is, without any gaps. 1 Set Cover instances with c.o.p. are solvable in polynomial time, a fact which is made use of in many practical applications =-=[11, 13, 16, 17]-=-. Thus, the question naturally arises whether such results can be transferred to MMSC. This is what we study here, arriving at a much more colorful scenario than in the classical case. In order to tho... |

17 | Solving geometric covering problems by data reduction
- Mecke, Wagner
- 2004
(Show Context)
Citation Context ...ime approximation [7]. It is parameterized intractable (that is, W[2]complete) with respect to the parameter “solution size” [5, 14]. Numerous variants of set covering are known and have been studied =-=[2, 4, 8, 9, 11, 16]-=-. Motivated by applications concerning interference reduction in cellular networks, Kuhn et al. [10] very recently introduced and investigated the Minimum Membership Set Cover problem. Minimum Members... |

12 | Set covering with almost consecutive ones property
- Ruf, Schöbel
(Show Context)
Citation Context |

11 | Exact algorithms and applications for Tree-Like Weighted Set Cover
- Guo, Niedermeier
(Show Context)
Citation Context |

5 | Interference in cellular networks: The minimum membership set cover problem
- Kuhn, Rickenbach, et al.
- 2005
(Show Context)
Citation Context ...on size” [5, 14]. Numerous variants of set covering are known and have been studied [2, 4, 8, 9, 11, 16]. Motivated by applications concerning interference reduction in cellular networks, Kuhn et al. =-=[10]-=- very recently introduced and investigated the Minimum Membership Set Cover problem. Minimum Membership Set Cover (MMSC) Input: A set S, a collection C of subsets of S, and a nonnegative integer k. Ta... |