K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms. J. Comp. Syst. Sc., 13:335--379, 1976. Home/Search Document Not in Database Summary Related Articles Check |
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A Spectral Algorithm for Seriation and the Consecutive.. - Atkins, Boman.. (1998) (11 citations) (Correct)
....of problems. Unlike traditional combinatorial methods, our approach uses an eigenvector of a matrix to order the elements. Our main result is that this approach correctly solves an important ordering problem we call the seriation problem which includes the wellknown consecutive ones problem (C1P) [5] as a special case. More formally, we are given a set of n elements to sequence; that is, we wish to bijectively map the elements to the integers 1, n. We also have a symmetric, real valued correlation function (sometimes called a similarity function) that reflects the desire for elements ....
.... so that the correlations are consistent; that is, if # is our permutation of elements and #(i) #(j) #(k) then f(i, j) f(i, k) and f(j, k) f(i, k) Although there may be an exponential number of such orderings, they can all be described in a compact data structure known as a PQ tree [5], which we review in the next section. Not all correlation functions allow for a consistent sequencing. If a consistent ordering is possible we will say the problem is well posed. # Received by the editors May 8, 1995; accepted for publication (in revised form) January 8, 1997; published ....
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K. S. Booth and G. S. Lueker, Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, J. Comput. System Sci., 13 (1976), pp. 333--379.
Uniform Sampling from Phylogenetic Trees - Phillips (2002) (Correct)
....to a left to right drawing of the tree. Since rotations do not a ect the topology of the tree (see Figure 3.1) the ordering need not be the actual left to right ordering in the given phylogenetic tree. There appears to be a strong connection to the integer permutation problem for which PQ trees [6] were developed, so a similar data structure may be appropriate for our problem. If S is not supplied with such an ordering, we can simply label each leaf in the tree with a left to right index during the preprocessing phase and then sort S based on these labelings in (m lg m) time. ....
K.S. Booth and G.S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13:335-379, 1976.
Simpler Projective Plane Embedding - Jianping Roth Creo (Correct)
....linear time should be interpreted as time in O(n) There are several linear time algorithms for nding a planar embedding of a graph. The rst of these was developed in 1974 by Hopcroft and Tarjan [21] Booth and Lueker derived another approach which uses a data structure called a PQ tree [6]. Other algorithms include those of de Fraysseix and Rosentiehl [11] and Williamson [35, 36] More recently, Boyer and Myrvold have proposed a new approach [7] All of these algorithms are fairly complex. Two slower approaches to planarity testing that are easier to program are the O(n ) ....
K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ{tree algorithms. J. Comput. Sys. Sci., 13:335-379, 1976.
Fragments of Order - Gionis, Kujala, Mannila (2003) (1 citation) (Correct)
....connections to the consequtive ones property. A matrix of 0s and 1s has the consequtive ones property, if there is a way of permuting the attributes so that for each row all the 1s are consequtive. Testing whether a matrix has the consequtive ones property can be done in linear time using PQ trees [4, 5, 11]. The relationship of spectral methods and the consequtive ones property is studied in more detail in [3] The relationship between spectral clustering and finding fragments of order is interesting. Consider the case when the input data has the consequtive ones property. Then by the results of ....
K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using P-Q tree algorithms. J. of Comp. and Syst. Sci., 13:335--379, 1976.
Coarse Grained Parallel Graph Planarity Testing - Cáceres, Chan, Dehne, Song (2000) (1 citation) (Correct)
....Pronex. 1 Introduction In this paper, we consider the problem of detecting whether a graph G is planar and, if so, reporting a planar embedding of G. The rst sequential linear time algorithm for planarity testing and planar embedding was presented by Hopcroft and Tarjan [7] Booth and Lueker [1] described another linear time algorithm which is based on a previous version by Lempel, Even and Cederbaum [12] but uses PQ trees and st numbering. J aJ a and Simon [8] showed that the problem is in NC. Using [1, 12] Klein and Reif [11] presented an ecient PRAM algorithm which requires n) time ....
....and planar embedding was presented by Hopcroft and Tarjan [7] Booth and Lueker [1] described another linear time algorithm which is based on a previous version by Lempel, Even and Cederbaum [12] but uses PQ trees and st numbering. J aJ a and Simon [8] showed that the problem is in NC. Using [1, 12], Klein and Reif [11] presented an ecient PRAM algorithm which requires n) time using a linear number of processors. Using open ear decomposition and st numbering, Ramachandran and Reif [15] presented a PRAM algorithm with linear work. Unfortunately, theoretical results from PRAM algorithms do ....
[Article contains additional citation context not shown here]
K.S. Booth and G.S. Lueker. Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity Using PQ- Tree Algorithms. Journal of Computer and Systems Sciences, 13:335-379, 1976.
A Note on the Consecutive Ones Submatrix Problem - Hajiaghayi, Ganjali (2002) (1 citation) (Correct)
....to know whether there exists a submatrix B consisting of K of the columns of A that satisfies C1P. Fulkerson and Gross introduced C1P and gave the first polynomial time sequential algorithm for it [2] The classic algorithm for solving C1P is a lineartime sequential algorithm of Booth and Lueker [3] based on PQ trees which is quite complicated. Simpler algorithms were found by Meidanis et al. 1] and Habib et al. 9] Nevertheless, the generalized COS problem is NP complete. This NP completeness result as well as the ones for many variants of this problem are used to show the ....
K.S. Booth, G.S. Lueker, Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, J. Comput. Systems Sci. 13 (3) (1976) 335--379.
Testing Superperfection of k-trees - Kloks, Bodlaender (1992) (Correct)
....for constant k ( 12] 3] 14] 17] Of theoretical great importance is the work of Robertson and Seymour (see [18] who showed that, for each k, there exists a finite set of forbidden minors for partial k trees. Most classes of perfect graphs can be recognized in polynomial time ( 19] [5], 11] 16] 10] An exception seems to be the class of superperfect graphs. Determining the interval chromatic number of a weighted interval graph with weights 1 and 2 is NP complete. When restricted to weighted partial k trees, for some constant k, and with weights bounded by some constant, ....
K.S. Booth and G.S. Lueker, Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, Journal of Computer and System Sciences 13, 335 - 379, 1976.
A fast linear time embedding algorithm based on the.. - Mutzel (1992) (Correct)
....the problem of testing planarity of a graph. Lempel, Even and Cederbaum [LEC] presented the vertex addition based algorithm using PQ trees, a very complicated data structure. It was proved to have a linear time implementation in 1976 partly by Even and Tarjan [ET] and partly by Booth and Lueker [BL], by introducing an st numbering of a graph. The first linear time algorithm was given by Hopcroft and Tarjan [HT] in 1974 using depth first search trees. This algorithm, which is path addition based, is generally considered to be more complicated than the PQ tree approach. Many applications ....
Booth, K.S. and G.S. Leuker, Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity Using PQ-tree Algorithms, J. of Comp. and Sys. Sci., vol. 13, pp. 335-379, 1976. 25
Certifying Algorithms for Recognizing Interval Graphs and.. - Graphs Dieter Kratsch Self-citation (Graphs) (Correct)
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K. S. Booth and G. S. Lueker, Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, JCSS, 13 (1976), pp. 335--379.
Crossings in Clustered Level Graphs - Forster (2004) Self-citation (Graphs) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13:335--379, 1976.
Planar Graphs with Topological Constraints - Dornheim (2002) (1 citation) Self-citation (Graphs) (Correct)
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K. Booth, G. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J. Comput. Syst. Sci., 13: 335--379, 1976
Kayles on Special Classes of Graphs - An application of.. - Bodlaender (1991) Self-citation (Graphs) (Correct)
.... can associate with each vertex v 2 V an interval on the real line [b v ; e v ] R, such that for all v; w 2 V , v 6= w: v; w) 2 E , b v ; e v ] b w ; e w ] 6= Interval graphs can be recognized in O(n e) time, and in the same order of time, the corresponding interval model can be built [2]. As only the order of the endpoints of the intervals matters, one can assume that all b v ; e v 2 f1; 2; 2ng. A generalization of the interval graphs are the circular arc graphs. They can be defined as follows: Definition 2.3 A graph G = V; E) is a circular arc graph, iff one can ....
K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms. J. Comp. Syst. Sc., 13:335--379, 1976.
Treewidth and Minimum Fill-in on D-Trapezoid Graphs - Bodlaender, Kloks, al. (1995) Self-citation (Graphs) (Correct)
....is much better for d 2 f1; 2g. The 1 trapezoid graphs are exactly the interval graphs and the 2 trapezoid graphs are exactly the trapezoid graphs by Theorem 3.1. There is a linear time recognition algorithm for interval graphs computing an interval model if the input graph is an interval graph [11]. There is an O(n ) recognition algorithm for trapezoid graphs computing a trapezoid model if the input graph is a trapezoid graph [28] Moreover, Theorem 3.1 shows that for any fixed d the d trapezoid graphs form a subclass of the cocomparability graphs. Hence the class of d trapezoid graphs ....
K.S. Booth and G.S. Lueker, Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, Journal of Computer and System Sciences 13, 335 \Gamma 379, 1976.
Thomas Wolle - Arie Koster Hans (2004) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms. J. Comp. Syst. Sc., 13:335--379, 1976.
Visualizing Related Metabolic Pathways - In Two And (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13(3):335--379, 1976.
Clone-Array Pooled Shotgun Mapping and Sequencing: - Design And Analysis (Correct)
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Booth, K. S. and G. S. Lueker. Testing for the Consecutive Ones Property, interval graphs, and graph planarity using PQ-tree algorithms. J. Comp. Sys. Sci., 13:335--379, 1976.
Improved Symmetric Lists - Bachmaier, Raitner (2004) (2 citations) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms. Journal of Computers and System Sciences, 12:335--379, 1976.
Radial Level Planarity Testing and Embedding in.. - Bachmaier.. (2004) (2 citations) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13:335--379, 1976.
Radial Level Planarity Testing and Embedding in Linear Time - Bachmaier, Brandenburg.. (2005) (2 citations) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13:335--379, 1976.
Radial Level Planarity Testing and Embedding in Linear Time - Bachmaier, Brandenburg.. (2003) (2 citations) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13:335--379, 1976.
Clustered Level Planarity - Forster, Bachmaier (2004) (Correct)
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Booth, K.S., Lueker, G.S.: Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity Using PQ-Tree Algorithms. Journal of Computer and System Sciences 13 (1976) 335--379
Track Planarity Testing and Embedding - Bachmaier, Brandenburg, Forster (2004) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13:335--379, 1976.
Approximation Algorithms for the Consecutive Ones Submatrix.. - Tan, Zhang (Correct)
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K. S. Booth and G. S. Lueker. Test for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J. Comput. Systems Sci., 13 (1976), 335-379.
A Branch-and-Cut Approach to Physical Mapping with.. - Christof, Jünger.. (1997) (2 citations) (Correct)
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K. Booth and G. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J. of Computer and System Sciences, 13:335--379, 1976.
Improved Symmetric Lists - Bachmaier (2004) (2 citations) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms. Journal of Computers and System Sciences, 12:335--379, 1976.
Improved Symmetric Lists - Bachmaier, Raitner (2004) (2 citations) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms. Journal of Computers and System Sciences, 12:335--379, 1976.
Visualizing Related Metabolic Pathways in Two and a Half.. - Brandes, Dwyer, Schreiber (2003) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13(3):335--379, 1976.
Hierarchical Decompositions for Visualizing Large Graphs - Finocchi (2002) (Correct)
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Booth, K., and Lueker, G. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences 13 (1976), 335--379.
Compressing Large Boolean Matrices Using Reordering.. - Johnson, Krishnan.. (2004) (1 citation) (Correct)
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Booth, K. S., and Lueker, G. S. Testing for the consecutive ones property, interval graphs, and graph planarity using P-Q tree algorithms. J. of Comp. and Syst. Sci. 13 (1976), 335--379.
On the Minimality and Global Consistency of Row-Convex.. - van Beek, Dechter (13 citations) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms. J. Comput. Syst. Sci., 13:335--379, 1976.
Clone-Array Pooled Shotgun Mapping and Sequencing.. - Csuros, Li.. (2003) (Correct)
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Booth, K.S. and Lueker, G.S., Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, J. Comp. Sys. Sci., 13:335--379, 1976.
Common Intervals in Permutations - Corteel, Louchard, Pemantle (2004) (Correct)
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K. S. Booth and G. S. Lueker, Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity Using PQ-Tree Algorithms. J. Comput. Syst. Sci. 13(3): 335-379 (1976)
Towards the Visualization of Overlapping Sets - Boyen, Mishra, O'Callaghan (Correct)
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Booth and Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms. JCSS, 13:335--379, 1976.
Improved Symmetric Lists - Bachmaier, Raitner (2004) (2 citations) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms. Journal of Computers and System Sciences, 12:335--379, 1976.
Clustered Level Planarity - Forster, Bachmaier (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13:335--379, 1976.
Radial Level Planarity Testing - And Embedding In (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13:335--379, 1976.
Radial Level Planarity Testing and Embedding - In Linear Time (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13:335-379, 1976.
Hierarchical Decompositions for Visualizing Large Graphs - Finocchi (2002) (Correct)
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Booth, K., and Lueker, G. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences 13 (1976), 335--379.
Visualizing Related Metabolic Pathways in Two and a Half.. - Brandes, Dwyer, Schreiber (2004) (Correct)
No context found.
K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13(3):335--379, 1976.
The Haplotyping Problem: An Overview of Computational.. - Bonizzoni, Vedova.. (2003) (2 citations) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms. Journal of Computer and System Sciences, 13(3):335--379, 1976.
Radial Level Planarity Testing and Embedding in Linear Time - Bachmaier, Brandenburg.. (2005) (2 citations) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13:335--379, 1976.
Efficient Subtyping Tests with PQ-Encoding - Zibin, Gil (2001) (1 citation) (Correct)
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K. S. Booth and G. S. Leuker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J. Comput. Sys. Sci., 13(3):335--379, Dec. 1976.
Track Planarity Testing and Embedding - Bachmaier, Brandenburg, Forster (2004) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13:335--379, 1976.
A New Parallel Algorithm for Planarity Testing - Bader, Sreshta (2003) (Correct)
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K.S. Booth and G.S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J. Computer and System Sciences, 13(3):335--379, 1976.
Building PQR Trees in Almost-Linear Time - Telles, Meidanis (2003) (Correct)
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K.S. Booth and G.S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13(3):335-379, 1976.
The Complexity of Planarity Testing - Allender, Mahajan (2003) (1 citation) (Correct)
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K Booth and G Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms. Journal of Computer and System Sciences, 13:335--379, 1976.
Correcting and Implementing the PC-tree Planarity Algorithm - John Boyer Cristina (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ{tree algorithms. Journal of Computer and Systems Sciences, 13:335-379, 1976.
Radial Level Planarity Testing and Embedding in Linear Time - Bachmaier, Brandenburg.. (2003) (2 citations) (Correct)
No context found.
K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13:335--379, 1976.
Simplified O(n) Planarity Algorithms - Boyer, Myrvold (2001) (Correct)
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K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ{tree algorithms. Journal of Computer and Systems Sciences, 13:335-379, 1976.
The Haplotyping Problem: An Overview of Computational.. - Bonizzoni, Vedova.. (2003) (2 citations) (Correct)
No context found.
K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms. Journal of Computer and System Sciences, 13(3):335--379, 1976.
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