Results 1  10
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27
A simple lineartime modular decomposition algorithm for graphs, using order extension
, 2004
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A simpler lineartime recognition of circulararc graphs
 Freivalds (Eds.), Algorithm Theory  SWAT 2006, Proc. 10th Scandinavian Workshop on Algorithm Theory, Lecture
, 2006
"... Abstract. We give a linear time recognition algorithm for circulararc graphs. Our algorithm is much simpler than the linear time recognition algorithm of McConnell [10] (which is the only linear time recognition algorithm previously known). Our algorithm is a new and careful implementation of the a ..."
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Cited by 10 (1 self)
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Abstract. We give a linear time recognition algorithm for circulararc graphs. Our algorithm is much simpler than the linear time recognition algorithm of McConnell [10] (which is the only linear time recognition algorithm previously known). Our algorithm is a new and careful implementation of the algorithm of Eschen and Spinrad [4,5]. We also tighten the analysis of Eschen and Spinrad. 1
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.
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.
Algebraic Operations on PQ Trees and Modular Decomposition Trees
, 2005
"... Partitive set families are families of sets that can be quite large, but have a compact, recursive representation in the form of a tree. This tree is a common generalization of PQ trees, the modular decomposition of graphs, certain decompositions of boolean functions, and decompositions that arise o ..."
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Cited by 6 (1 self)
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Partitive set families are families of sets that can be quite large, but have a compact, recursive representation in the form of a tree. This tree is a common generalization of PQ trees, the modular decomposition of graphs, certain decompositions of boolean functions, and decompositions that arise on a variety of other combinatorial structures. We describe natural operators on partitive set families, give algebraic identities for manipulating them, and describe efficient algorithms for evaluating them. We use these results to obtain new time bounds for finding the common intervals of a set of permutations, finding the modular decomposition of an edgecolored graphs (also known as a twostructure), finding the PQ tree of a matrix when a consecutiveones arrangement is given, and finding the modular decomposition of a permutation graph when its permutation realizer is given.
Cplanarity of extrovert clustered graphs
 In Graph Drawing
, 2005
"... Abstract. A clustered graph has its vertices grouped into clusters in a hierarchical way via subset inclusion, thereby imposing a tree structure on the clustering relationship. The cplanarity problem is to determine if such a graph can be drawn in a planar way, with clusters drawn as nested regions ..."
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Cited by 6 (1 self)
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Abstract. A clustered graph has its vertices grouped into clusters in a hierarchical way via subset inclusion, thereby imposing a tree structure on the clustering relationship. The cplanarity problem is to determine if such a graph can be drawn in a planar way, with clusters drawn as nested regions and with each edge (drawn as a curve between vertex points) crossing the boundary of each region at most once. Unfortunately, as with the graph isomorphism problem, it is open as to whether the cplanarity problem is NPcomplete or in P. In this paper, we show how to solve the cplanarity problem in polynomial time for a new class of clustered graphs, which we call extrovert clustered graphs. This class is quite natural (we argue that it captures many clustering relationships that are likely to arise in practice) and includes the clustered graphs tested in previous work by Dahlhaus, as well as Feng, Eades, and Cohen. Interestingly, this class of graphs does not include, nor is it included by, a class studied recently by Gutwenger et al.; therefore, this paper offers an alternative advancement in our understanding of the efficient drawability of clustered graphs in a planar way. Our testing algorithm runs in O(n 3) time and implies an embedding algorithm with the same time complexity. 1
Unifying two Graph Decompositions with Modular Decomposition 0
, 2007
"... We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and 2−structures. We show that, under some axioms, a unique decomposition tree exists for umodules. Polynomialtime algorithms are provide ..."
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Cited by 3 (0 self)
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We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and 2−structures. We show that, under some axioms, a unique decomposition tree exists for umodules. Polynomialtime algorithms are provided for: nontrivial umodule test, maximal umodule computation, and decomposition tree computation when the tree exists. Our results unify many known decomposition like modular and bijoin decomposition of graphs, and a new decomposition of tournaments. 1
Testing Simultaneous Planarity when the Common Graph is 2Connected
, 2011
"... Two planar graphs G1 and G2 sharing some vertices and edges are simultaneously planar if they have planar drawings such that a shared vertex [edge] is represented by the same point [curve] in both drawings. It is an open problem whether simultaneous planarity can be tested efficiently. We give a lin ..."
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Cited by 3 (1 self)
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Two planar graphs G1 and G2 sharing some vertices and edges are simultaneously planar if they have planar drawings such that a shared vertex [edge] is represented by the same point [curve] in both drawings. It is an open problem whether simultaneous planarity can be tested efficiently. We give a lineartime algorithm to test simultaneous planarity when the two graphs share a 2connected subgraph. Our algorithm extends to the case of k planar graphs where each vertex [edge] is either common to all graphs or belongs to exactly one of them, and the common subgraph is 2connected.
A faster algorithm for finding minimum Tucker submatrices
"... Abstract. A binary matrix has the Consecutive Ones Property (C1P) if its columns can be ordered in such a way that all 1s on each row are consecutive. Algorithmic issues of the C1P are central in computational molecular biology, in particular for physical mapping and ancestral genome reconstruction. ..."
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Cited by 2 (1 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 1s on each row are consecutive. Algorithmic issues of the C1P are central in computational molecular biology, in particular for physical mapping and ancestral genome reconstruction. In 1972, Tucker gave a characterization of matrices that have the C1P by a set of forbidden submatrices, and a substantial amount of research has been devoted to the problem of efficiently finding such a minimum size forbidden submatrix. This paper presents a new O( ∆ 3 m 2 (m ∆ + n 3)) time algorithm for this particular task for a m×n binary matrix with at most ∆ 1entries per row, thereby improving the O( ∆ 3 m 2 (mn + n 3)) time algorithm of Dom et al. [17]. 1