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47
Approximation and FixedParameter Algorithms for Consecutive Ones Submatrix Problems
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
"... We develop an algorithmically useful refinement of a forbidden submatrix characterization of 0/1matrices fulfilling the Consecutive Ones Property (C1P). This characterization finds applications in new polynomialtime approximation algorithms and fixedparameter tractability results for the NPhard ..."
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Cited by 10 (0 self)
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We develop an algorithmically useful refinement of a forbidden submatrix characterization of 0/1matrices fulfilling the Consecutive Ones Property (C1P). This characterization finds applications in new polynomialtime approximation algorithms and fixedparameter tractability results for the NPhard problem to delete a minimum number of rows or columns from a 0/1matrix such that the remaining submatrix has the C1P.
Minimal Conflicting Sets for the Consecutive Ones Property in ancestral genome reconstruction
, 912
"... 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 ..."
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Cited by 9 (4 self)
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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. Version of December 21, 2009. 1
Approximability and parameterized complexity of consecutive ones submatrix problems
 IN PROC. 4TH TAMC, VOLUME 4484 OF LNCS
, 2007
"... We develop a refinement of a forbidden submatrix characterization of 0/1matrices fulfilling the Consecutive Ones Property (C1P). This novel characterization finds applications in new polynomialtime approximation algorithms and fixedparameter tractability results for the problem to find a maximum ..."
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Cited by 8 (4 self)
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We develop a refinement of a forbidden submatrix characterization of 0/1matrices fulfilling the Consecutive Ones Property (C1P). This novel characterization finds applications in new polynomialtime approximation algorithms and fixedparameter tractability results for the problem to find a maximumsize submatrix of a 0/1matrix such that the submatrix has the C1P. Moreover, we achieve a problem kernelization based on simple data reduction rules and provide several search tree algorithms. Finally, we derive inapproximability results.
Algorithmic Aspects of the ConsecutiveOnes Property
, 2009
"... We survey the consecutiveones property of binary matrices. Herein, a binary matrix has the consecutiveones property (C1P) if there is a permutation of its columns that places the 1s consecutively in every row. We provide an overview over connections to graph theory, characterizations, recognition ..."
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Cited by 8 (1 self)
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We survey the consecutiveones property of binary matrices. Herein, a binary matrix has the consecutiveones property (C1P) if there is a permutation of its columns that places the 1s consecutively in every row. We provide an overview over connections to graph theory, characterizations, recognition algorithms, and applications such as integer linear programming and solving Set Cover.
A simple linear time algorithm for cograph recognition
 Discrete Applied Mathematics
, 2005
"... www.elsevier.com/locate/dam ..."
Minimal proper interval completions
 In Proceedings of WG 2006  32nd International Workshop on GraphTheoretic Concepts in Computer Science
, 2006
"... Abstract. Given an arbitrary graph G = (V, E) and a proper interval graph H = (V, F) with E ⊆ F we say that H is a proper interval completion of G. The graph H is called a minimal proper interval completion of G if, for any sandwich graph H ′ = (V, F ′ ) with E ⊆ F ′ ⊂ F, H ′ is not a proper inter ..."
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Cited by 6 (1 self)
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Abstract. Given an arbitrary graph G = (V, E) and a proper interval graph H = (V, F) with E ⊆ F we say that H is a proper interval completion of G. The graph H is called a minimal proper interval completion of G if, for any sandwich graph H ′ = (V, F ′ ) with E ⊆ F ′ ⊂ F, H ′ is not a proper interval graph. In this paper we give a O(n + m) time algorithm computing a minimal proper interval completion of an arbitrary graph. The output is a proper interval model of the completion. 1
A Synthesis on Partition Refinement: a useful Routine for Strings, Graphs, Boolean Matrices and Automata
 In Proc. Fifteenth STACS
, 1998
"... Partition refinement techniques are used in many algorithms. This tool allows efficient computation of equivalence relations and is somehow dual to unionfind algorithms. The goal of this paper is to propose a single routine to quickly implement all these already known algorithms and to solve a ..."
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Cited by 5 (4 self)
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Partition refinement techniques are used in many algorithms. This tool allows efficient computation of equivalence relations and is somehow dual to unionfind algorithms. The goal of this paper is to propose a single routine to quickly implement all these already known algorithms and to solve a large class of potentially new problems. Our framework yields to a unique scheme for correctness proofs and complexity analysis. Various examples are presented to show the different ways of using this routine. 1 Introduction A partition of a finite set E is a collection of disjoint subsets of E called classes whose union is E. Refining a partition consists in splitting its classes into smaller classes. Partition refinement techniques have been studied in four main papers [7, 15, 13, 6]. Hopcroft [7] may be the very first designer of such a technique. He used it in order to minimize the number of states of a deterministic finite automaton. Spinrad [15] investigated the graph partitioning ...
Linear time recognition of Helly circulararc models and graphs
 manuscript, 2007 (Presented at COCOON’06 and SIAM DM’06 Confs
, 2007
"... Abstract. A circulararc model (C, A) is a circle C together with a collection A of arcs of C. If A satisfies the Helly Property then (C, A) is a Helly circulararc model. A (Helly) circulararc graph is the intersection graph of a (Helly) circulararc model. Circulararc graphs and their subclasses ..."
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Cited by 5 (2 self)
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Abstract. A circulararc model (C, A) is a circle C together with a collection A of arcs of C. If A satisfies the Helly Property then (C, A) is a Helly circulararc model. A (Helly) circulararc graph is the intersection graph of a (Helly) circulararc model. Circulararc graphs and their subclasses have been the object of a great deal of attention, in the literature. Linear time recognition algorithm have been described both for the general class and for some of its subclasses. However, for Helly circulararc graphs, the best recognition algorithm is that by Gavril, whose complexity is O(n 3). In this article, we describe different characterizations for Helly circulararc graphs, including a characterization by forbidden induced subgraphs for the class. The characterizations lead to a linear time recognition algorithm for recognizing graphs of this class. The algorithm also produces certificates for a negative answer, by exhibiting a forbidden subgraph of it, within this same bound.
Capturing polynomial time on interval graphs
 in Proceedings of the 25th IEEE Symposium on Logic in Computer Science, 2010, this volume
"... The present paper proves a characterization of all polynomialtime computable queries on the class of interval graphs by sentences of fixedpoint logic with counting. The result is one of the first establishing the capturing of polynomial time on a graph class which is defined by forbidden induced s ..."
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The present paper proves a characterization of all polynomialtime computable queries on the class of interval graphs by sentences of fixedpoint logic with counting. The result is one of the first establishing the capturing of polynomial time on a graph class which is defined by forbidden induced subgraphs. More precisely, it is shown that on the class of unordered interval graphs, any query is polynomialtime computable if and only if it is definable in fixedpoint logic with counting. Furthermore, it is shown that fixedpoint logic is not expressive enough to capture polynomial time on the classes of chordal graphs or incomparability graphs. 1
Collective Tree Spanners in Graphs with Bounded Parameters
 ALGORITHMICA
, 2006
"... In this paper we study collective additive tree spanners for special families of graphs including planar graphs, graphs with bounded genus, graphs with bounded treewidth, graphs with bounded cliquewidth, and graphs with bounded chordality. We say that a graph G = (V, E) admits a system of μ colle ..."
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Cited by 4 (4 self)
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In this paper we study collective additive tree spanners for special families of graphs including planar graphs, graphs with bounded genus, graphs with bounded treewidth, graphs with bounded cliquewidth, and graphs with bounded chordality. We say that a graph G = (V, E) admits a system of μ collective additive tree rspanners if there is a system T (G) of at most μ spanning trees of G such that for any two vertices x,y of G a spanning tree T ∈ T (G) exists such that dT (x, y) ≤ dG(x, y) + r. We describe a general method for constructing a “small” system of collective additive tree rspanners with small values of r for “well ” decomposable graphs, and as a byproduct show (among other results) that any weighted planar graph admits a system of O ( √ n) collective additive tree 0spanners, any weighted graph with treewidth at most k − 1 admits a system of k log 2 n collective additive tree 0spanners, any weighted graph with cliquewidth at most k admits a system of k log 3/2 n collective additive tree (2w)spanners, and any weighted graph with size of largest induced cycle at most c admits a system of log 2 n collective additive tree (2⌊c/2⌋w)spanners and a system of 4 log 2 n collective additive tree (2(⌊c/3⌋+1)w)spanners (here, w is the maximum edge weight in G). The latter result is refined for weighted weakly chordal graphs: any such graph admits a system of 4 log 2 n collective additive tree (2w)spanners. Furthermore, based on this collection of trees, we derive a compact and efficient routing scheme for those families of graphs. Results of this paper were partially presented at the ISAAC’05 conference [14].