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26
PC trees and circularones arrangements
 Theoretical Computer Science
"... A 01 matrix has the consecutiveones property if its columns can be ordered so that the ones in every row are consecutive. It has the circularones property if its columns can be ordered so that, in every row, either the ones or the zeros are consecutive. PQ trees are used for representing all cons ..."
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Cited by 35 (4 self)
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A 01 matrix has the consecutiveones property if its columns can be ordered so that the ones in every row are consecutive. It has the circularones property if its columns can be ordered so that, in every row, either the ones or the zeros are consecutive. PQ trees are used for representing all consecutiveones orderings of the columns of a matrix that has the consecutiveones property. We give an analogous structure, called a PC tree, for representing all circularones orderings of the columns of a matrix that has the circularones property. No such representation has been given previously. In contrast to PQ trees, PC trees are unrooted. We obtain a much simpler algorithm for computing PQ trees that those that were previously available, by adding a zero column, x, to a matrix, computing the PC tree, and then picking the PC tree up by x to root it. 1
Interval bigraphs and circular arc graphs
 J. Graph Theory
"... Abstract We prove that the complements of interval bigraphs are precisely those circular arc graphs of clique covering number two which admit a representation without two arcs covering the whole circle. We give another characterization of interval bigraphs, in terms of a vertex ordering, that we hop ..."
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Cited by 19 (5 self)
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Abstract We prove that the complements of interval bigraphs are precisely those circular arc graphs of clique covering number two which admit a representation without two arcs covering the whole circle. We give another characterization of interval bigraphs, in terms of a vertex ordering, that we hope may prove helpful in finding a more efficient recognition algorithm than presently known. We use these results to show equality, amongst bipartite graphs, of several classes of structured graphs (proper interval bigraphs, complements of proper circular arc graphs, asteroidaltriplefree graphs, permutation graphs, and cocomparability graphs). Our results verify a conjecture of Lundgren and disprove a conjecture of M"uller. 1 Background A graph H is an interval graph if it is the intersection graph of a family of intervals Iv, v 2 V (H). (Two vertices v; v 0 are adjacent in H if and only if Iv and Iv0 intersect.) If the
Fragments of Order
, 2003
"... Highdimensional collections of 01 data occur in many applications. The attributes in such data sets are typically considered to be unordered. However, in many cases there is a natural total or partial order # underlying the variables of the data set. Examples of variables for which such orders exi ..."
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Cited by 12 (2 self)
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Highdimensional collections of 01 data occur in many applications. The attributes in such data sets are typically considered to be unordered. However, in many cases there is a natural total or partial order # underlying the variables of the data set. Examples of variables for which such orders exist include terms in documents, courses in enrollment data, and paleontological sites in fossil data collections. The observations in such applications are flat, unordered sets; however, the data sets respect the underlying ordering of the variables. By this we mean that if A # B # C are three variables respecting the underlying ordering #, and both of variables A and C appear in an observation, then, up to noise levels, variable B also appears in this observation. Similarly, if A1 # A2 # # A l1 # A l is a longer sequence of variables, we do not expect to see many observations for which there are indices i < j < k such that A i and Ak occur in the observation but A j does not.
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 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 ...
On Planar Supports for Hypergraphs
"... A graph G is a support for a hypergraph H = (V, S) if the vertices of G correspond to the vertices of H such that for each hyperedge Si ∈ S the subgraph of G induced by Si is connected. G is a planar support if it is a support and planar. Johnson and Pollak [9] proved that it is NPcomplete to decide ..."
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Cited by 5 (0 self)
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A graph G is a support for a hypergraph H = (V, S) if the vertices of G correspond to the vertices of H such that for each hyperedge Si ∈ S the subgraph of G induced by Si is connected. G is a planar support if it is a support and planar. Johnson and Pollak [9] proved that it is NPcomplete to decide if a given hypergraph has a planar support. In contrast, there are polynomial time algorithms to test whether a given hypergraph has a planar support that is a path, cycle, or tree. In this paper we present an algorithm which tests in polynomial time if a given hypergraph has a planar support that is a tree where the maximal degree of each vertex is bounded. Our algorithm is constructive and computes a support if it exists. Furthermore, we prove that it is already NPhard to decide if a hypergraph has a 2outerplanar support. 1
Four Lessons in Versatility or How Query Languages Adapt to the Web
"... Exposing not only humancentered information, but machineprocessable data on the Web is one of the commonalities of recent Web trends. It has enabled a new kind of applications and businesses where the data is used in ways not foreseen by the data providers. Yet this exposition has fractured the W ..."
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Cited by 3 (3 self)
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Exposing not only humancentered information, but machineprocessable data on the Web is one of the commonalities of recent Web trends. It has enabled a new kind of applications and businesses where the data is used in ways not foreseen by the data providers. Yet this exposition has fractured the Web into islands of data, each in different Web formats: Some providers choose XML, others RDF, again others JSON or OWL, for their data, even in similar domains. This fracturing stifles innovation as application builders have to cope not only with one Web stack (e.g., XML technology) but with several ones, each of considerable complexity. With Xcerpt we have developed a rule and pattern based query language that aims to give shield application builders from much of this complexity: In a single query language XML and RDF data can be accessed, processed, combined, and republished. Though the need for combined access to XML and RDF data has been recognized in previous work (including the W3C’s GRDDL), our approach differs in four main aspects: (1) We provide a single language (rather than two separate or embedded languages), thus minimizing the conceptual overhead of dealing with disparate data formats. (2) Both the declarative (logicbased) and the operational semantics are unified in that they apply for querying XML and RDF in the same way. (3) We show that the resulting query language can be implemented reusing traditional database technology, if desirable. Nevertheless, we also give a unified evaluation approach based on interval labelings of graphs that is at least as fast as existing approaches for treeshaped XML data, yet provides linear time and space querying also for many RDF graphs. We believe that Web query languages are the right tool for declarative data access in Web applications and that Xcerpt is a significant step towards a more convenient, yet highly efficient data access in a “Web of Data”.