On the consecutive ones property

Meidânis, João; Porto, Oscar; Telles, Guilherme P.

doi:10.1016/s0166-218x(98)00078-x

Cited by 69 publications

(64 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…First, we applied it to the unit-cost set covering problems arising from the incidence matrices of Steiner triple systems. These problems were introduced by Fulkerson, Nemhauser, and Trotter in 1974 [1] (see also [11]), who suggest using them as test cases for set covering algorithms. This is motivated by the fact that they are hard to solve despite their relatively small size.…”

Section: Numerical Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Set covering with almost consecutive ones property

Ruf

Schöbel

2004

Discrete Optimization

View full text Add to dashboard Cite

In this paper, we consider set covering problems with a coefficient matrix almost having the consecutive ones property, i.e., in most rows of the coefficient matrix, the ones appear consecutively and only a few blocks of consecutive ones appear in the remaining rows. If this property holds for all rows it is well known that the set covering problem can be solved efficiently. For our case of almost consecutive ones we present a reformulation exploiting the consecutive ones structure to develop bounds and a branching scheme. Our approach has been tested on real-world data as well as on theoretical problem instances.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

“…If a matrix has the consecutive ones property, the permutation of the columns making the ones appear consecutively can be found by using the algorithm of Booth and Lueker [1]; Meidanis and Telles [11]. This algorithm can be performed in O(MN).…”

Section: Definitionmentioning

confidence: 99%

Set covering with almost consecutive ones property

Ruf

Schöbel

2004

Discrete Optimization

View full text Add to dashboard Cite

show abstract

“…Figure 2 shows examples of different classes of convex bipartite graphs. For convex, biconvex, and bipartite permutation graphs, there are linear-time recognition algorithms that output the corresponding orderings on the vertex sets in linear time [4,19,24]. Throughout this paper, we assume that in the input graph, vertices of A and B are labeled with integers 1, 2, .…”

Section: Preliminariesmentioning

confidence: 99%

Finding Maximum Edge Bicliques in Convex Bipartite Graphs

Nussbaum

Sack

et al. 2011

Algorithmica

View full text Add to dashboard Cite

A bipartite graph G = (A, B, E) is convex on B if there exists an ordering of the vertices of B such that for any vertex v ∈ A, vertices adjacent to v are consecutive in B. A complete bipartite subgraph of a graph G is called a biclique of G. Motivated by an application to analyzing DNA microarray data, we study the problem of finding maximum edge bicliques in convex bipartite graphs. Given a bipartite graph G = (A, B, E) which is convex on B, we present a new algorithm that computes a maximum edge biclique of G in O(n log 3 n log log n) time and O(n) space, where n = |A|. This improves the current O(n 2 ) time bound available for the problem. We also show that for two special subclasses of convex bipartite graphs, namely 312 Algorithmica (2012) 64:311-325 for biconvex graphs and bipartite permutation graphs, a maximum edge biclique can be computed in O(nα(n)) and O(n) time, respectively, where n = min(|A|, |B|) and α(n) is the slowly growing inverse of the Ackermann function.

show abstract

“…groups of markers that were co-localized in the ancestral genome of interest), then it has the C1P, which can be decided in linear-time and space [5,17,20,24,25]. However, with most real datasets, M contains errors.…”

Section: Such Ordering Of the Markers Define Chromosomal Segments Calmentioning

confidence: 99%

Minimal Conflicting Sets for the Consecutive Ones Property in Ancestral Genome Reconstruction

Chauve

Haus

Stephen

et al. 2009

Comparative Genomics

View full text Add to dashboard Cite

Abstract. A binary matrix has the Consecutive Ones Property (C1P) if its columns can be ordered in such a way that all 1's on each row are consecutive. A Minimal Conflicting Set is a set of rows that does not have the C1P, but every proper subset has the C1P. Such submatrices have been considered in comparative genomics applications, but very little is known about their combinatorial structure and efficient algorithms to compute them. We first describe an algorithm that detects rows that belong to Minimal Conflicting Sets. This algorithm has a polynomial time complexity when the number of 1s in each row of the considered matrix is bounded by a constant. Next, we show that the problem of computing all Minimal Conflicting Sets can be reduced to the joint generation of all minimal true clauses and maximal false clauses for some monotone boolean function. We use these methods on simulated data related to ancestral genome reconstruction to show that computing Minimal Conflicting Set is useful in discriminating between true positive and false positive ancestral syntenies. We also study a dataset of yeast genomes and address the reliability of an ancestral genome proposal of the Saccahromycetaceae yeasts.Draft, do not distribute.

show abstract

On the consecutive ones property

Cited by 69 publications

References 7 publications

Set covering with almost consecutive ones property

Set covering with almost consecutive ones property

Finding Maximum Edge Bicliques in Convex Bipartite Graphs

Minimal Conflicting Sets for the Consecutive Ones Property in Ancestral Genome Reconstruction

Contact Info

Product

Resources

About