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@String{PSB = {Proceedings of the Pacific Symposium on Biocomputing}}
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@String{C = {Combinatorica}}
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@String{JDM = {SIAM Journal on Discrete Mathematics}}
@String{JAM = {SIAM Journal on Applied Mathematics}}
@String{JOC = {SIAM Journal on Computing}}
@String{JGT = {Journal of Graph Theory}}
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, lien v\'erifi\'e le 20/03/2006
%+ section 1 : introduction
%+ section 2 : motivation : alignement ADN
%+ section 3 : NP complétude de independent set de rectangles par réduction de 3 sat
%+ section 4 : MIS & ((d+1)-claw)-free graphs : algo t-opt heuristique d'amélioration gloutonne,
%+ ratio d'approximation < d/2+epsilon, pas mieux que d/2
%+ MWIS : ratio de t-opt < d-1+1/d, pas mieux que d-1-epsilon
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, lien v\'erifi\'e le 19/04/2006
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, lien v\'erifi\'e le 13/03/2006
%+ section 1 : Exemples d'applis des t-int graphs : transmission media data, linear ressource alloc
%+ des t-uni graphs : multiseq similarity
%+
%+ MWIS APX-hard sur les (2,2) union graphs
@article{bekt2001,
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, lien v\'erifi\'e le 13/03/2006
%+ 1|(1,h,1), \textrm{coupled, strict, prec, exact gap}|C_{\max}
%+ NP complet par réduction de coloration équilibrée
%+ Coloration équilibrée NP-complet par réduction de 3-PARTITION
%+ Rapport avec les graphes 2-intervallaires ??
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, lien v\'erifi\'e le 15/03/2006
% chapitre 3.2 : Approximabilité de 2IP (pp44-49)
% chapitre 6, idem que bfv2004
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, lien v\'erifi\'e le 13/03/2006
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, lien v\'erifi\'e le 16/03/2006
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, lien v\'erifi\'e le 21/03/2006
% Exo 5 : faire le graphe d'intervalles en réunissant dans le mm coin
% les sommets avec le même chiffre, et tenter de trouver une
% k-coloration sur le graphe formé en recollant les sommets
% de même chiffre par paires
% Exo 6 : considérer chaque 2 intervalle comme deux sommets, il y a un
% seul graphe de degré 2 exactement (il n'y avait pas 3 gens en
% mm temps à la bibli) or ce n'est pas un graphe d'intervalles,
% c'est un vieux cycle.
%
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pages = {571-584},
publisher = {North-Holland, Amsterdam},
year = 1970,
}
% relations between matching number \nu and transversal number \tau
@article{gw1995,
author = {Andr\'as Gy{\'a}rf{\'a}s and Douglas B. West},
title = {Multitrack Interval Graphs},
journal = CG,
year = 1995,
volume = 109,
pages = {109-116},
note = {\url{http://www.math.uiuc.edu/~west/pubs/tracks.ps}}
}
, lien v\'erifi\'e le 21/03/2006
@inproceedings{jmt1992,
author = {Deborah Joseph and Joao Meidanis and Prasoon Tiwari},
title = {Determining DNA Sequence Similarity Using Maximum Independent Set Algorithms for Interval Graphs},
journal = {3rd Scandinavian Workshop on Algorithm Theory},
pages = {326-337},
booktitle = {Lecture Notes in Computer Science},
volume = 621,
year = 1992,
}
@article{kaiser1997,
author = {Tom{\'a}s Kaiser},
title = {Transversals of d-Intervals},
journal = {Discrete and Computational Geometry},
volume = 18,
number = 2,
year = 1997,
note = {\url{http://www.springerlink.com/link.asp?id = gn67lv27h5jacx4q}}
}
, lien v\'erifi\'e le 16/03/2006
@unpublished{karlsson2005,
author = {Ragnar Karlsson},
title = {A Survey of Split Intervals and Related Graphs},
journal = UM,
year = 2005,
note = {\url{http://www.hi.is/~rkk1/SplitSurvey.pdf}}
}
, lien v\'erifi\'e le 16/03/2006
@article{kw1997,
author = {Alexandr V. Kostochka and Douglas B. West},
title = {Total Interval Number for Graphs with Bounded Degree},
journal = JGT,
pages = {79-84},
volume = 25,
year = 1997,
note = {\url{http://citeseer.ifi.unizh.ch/kostochka95total.html}}
}
, lien v\'erifi\'e le 16/03/2006
% décomposition du graphe outerplanar par parcours en largeur
% en ensembles de sommets à distance paire ou non d'une
% racine. Les deux ensembles, unions de chemins disjoints,
% sont placés sur des lignes différentes,
% puis les arêtes entre les 2 ensembles sont traduites
% en utilisant l'intervalle restant des 2-intervalles.
@article{kw1999,
author = {Alexandr V. Kostochka and Douglas B. West},
title = {Every Outerplanar Graph is the Union of Two Interval Graphs},
journal = CN,
volume = 139,
pages = {5-8},
year = 1999,
note = {\url{http://citeseer.ifi.unizh.ch/297772.html}}
}
, lien v\'erifi\'e le 16/03/2006
@article{kw1993,
author = {Thomas M. Kratzke and Douglas B. West},
title = {The total interval number of a graph I: Fundamental Classes},
journal = DM,
volume = 118,
pages = {145-156},
year = 1993,
}
@article{kw1996,
author = {T.M. Kratzke and Douglas B. West},
title = {The total interval number of a graph II: Trees and complexity},
journal = JDM,
volume = 9,
year = 1996,
pages = {339-348},
note = {\url{www.math.uiuc.edu/~west/pubs/titrees.pdf}}
}
, lien v\'erifi\'e le 16/03/2006
@article{op1997,
author = {A.J. Orman and C.N. Potts},
title = {On the Complexity of Coupled-Task Scheduling},
journal = DAM,
volume = 72,
year = 1997,
pages = {141-154}
}
@article{osm1998,
author = {A.J. Orman and A.K. Shahani and A.R. Moore},
title = {Modelling for the control of a complex radar system},
journal = {Computers and operations research},
year = 1998,
note = {\url{http://dx.doi.org/10.1016/S0305-0548(97)00047-6}}
}
, lien v\'erifi\'e le 15/03/2006
@article{shapiro1980,
author = {R.D. Shapiro},
title = {Scheduling Coupled Tasks},
journal = {Naval Research Logistics Quarterly},
volume = 27,
year = 1980,
pages = {489-498},
}
@article{tardos1995,
author = {G. Tardos},
title = {Transversals of 2-intervals, a topological approach},
journal = C,
volume = 15,
number = 1,
year = 1995,
pages = {123-134}
}
@article{Vialette2004,
author = {St{\'e}phane Vialette},
title = {On the computational complexity of 2-interval pattern matching problems},
journal = TCS,
volume = 312,
number = {2-3},
year = 2004,
note = {\url{http://dx.doi.org/10.1016/j.tcs.2003.08.010}}
}
, lien v\'erifi\'e le 15/03/2006
@article{ws1984,
author = {Douglas B. West and David B. Shmoys},
title = {Recognizing graphs with fixed interval number is {NP}-complete},
journal = DAM,
volume = 8,
year = 1984,
pages = {295-305}
}
@book{Fishburn1985,
author = {Peter C. Fishburn},
title = {Interval Orders and Interval Graphs},
publisher = {John Wiley \& Sons},
serie = {Wiley-Interscience Series in Discrete Mathematics},
year = {1985}
}
1 Introduction defines partial orders, weak orders, posets, considers graph as posets
irreflexive binary relation : not xRx
negatively transitive : xRy = > for all z, xRz or zRy
partial order : R irreflexive transitive
weak order : R asymmetric negatively transitive
linear order : R weak complete
2 Interval orders :
< such that (a (a (a define an order <_0 on the endpoints (X,-) = x^- and (X,+) = x^+
<_0 is a weak order if < is an interval order
@TECHREPORT{Gardi2003,
AUTHOR = {Fr\'ed\'eric Gardi},
TITLE = {{A note on the Roberts characterization of proper and unit interval graphs}},
INSTITUTION = {{LIF}},
ADDRESS = {Marseille, France},
TYPE = {Research report},
NUMBER = {11-2003},
MONTH = {January},
YEAR = {2003},
NOTE = {\url{http://www.lif-sud.univ-mrs.fr/Rapports/11-2003.html}},
}
, lien v\'erifi\'e le 10/05/2006
% quite short proof that (proper = unit) interval graphs.
@manuscript{wood2006,
author = {David R. Wood},
title = {Characterisations of Intersection Graphs by Vertex Orderings},
journal = UM,
year = 2006,
note = {\url{http://arxiv.org/PS_cache/cs/pdf/0404/0404031.pdf}}
}
, lien v\'erifi\'e le 11/05/2006
% bandwidth of a graph: order its vertices, maximum distance between two vertices joined by an edge
% lower bound : degree/2
% upper bounds for interval, proper interval, cocomparability, AT-free, split graphs.
% analysis of the bandwidth of chordal and comparability graphs
@manuscript{dsw2005,
author = {Vida Dujmovi\'c and Matthew Suderman and David R. Wood},
title = {Really Straight Drawings II: Non-Planar Graphs},
journal = UM,
year = 2005,
note = {\url{http://cgm.cs.mcgill.ca/~vida/pubs/papers/ReallyStraight-Nonplanar.pdf}}
}
, lien v\'erifi\'e le 11/05/2006
% slope number : minimum number of different slopes while drawing a graph : upper and lower bounds
% or approximations, for some graph classes.
@article{chorsudan1998,
author = {Benny Chor and Madhu Sudan},
title = {A geometric approach to betweenness},
journal = JDM,
volume = 11,
number = 4,
year = 1998,
note = {\url{http://epubs.siam.org/SIDMA/volume-11/art_29622.html}}
}
lien v\'erifi\'e le 12/05/2006
% reduction of MaxCut to Betweenness
@inproceedings{micalivazirani1980,
author = {Silvio Micali and Vijay V. Vazirani},
title = {An ${O}(\sqrt{|v|} |E|)$ Algorithm for Finding Maximum Matching in General Graphs},
booktitle = {Proceedings of the 21th Annual IEEE Symposium on Foundation of Computer Science},
year = 1980,
pages = {17-27}
}
% difficult algorithm, according to Michel Habib
% implementation here: http://archi.snu.ac.kr/bwkim/free-OR-codes.html#cardmatch
@phdthesis{Evans1999,
author = {Patricia A. Evans},
title = {Algorithms and Complexity for Annotated Sequence Analysis},
year = 1999,
school = {University of Victoria},
note = {\url{http://www.cs.unb.ca/profs/pevans/research/pae-thesis.ps}}
}
lien v\'erifi\'e le 18/05/2006
% Chapter 1 definitions : subsequence, substrings, DNA...
% Chapter 2 "Background" : state of the art on sequence comparison & aligning, protein 3D structure,
parametrized complexity.
% Chapter 3 "Types of annotation" : colouring, arcs and eventual restrictions, edit distances between annotated
sequences.
% Chapter 4 Annotation verification, automatas and coloured regular languages
% Chapter 5 Annotation Creation : format conversions (colourings, arc formats)
% Chapter 6 Comparing coloured sequences : cartesian product of the alphabets or more subtile.
% Chapter 7 Comparing Arc-annotated Sequences, problem \Pi of finding longest common subsequence
between two arc-annotated sequences which respects order and presence of arcs
and various restrictions, NP completeness from IndependentSet for pi(unlim,plain)
from clique for pi(cross,cross), fixed-parameter (cutwidth = max number of arcs
that cross or end at some point in the sequence) algorithm.
% Chapter 8 Variations of the algorithm by weighting the arcs, and/or extending them to cover many
nucleotides.
@article{bkkm1999,
author = {Hajo Broersma and Ton Kloks and Dieter Kratsch and Haiko M\"uller},
title = {Independent sets in asteroidal triple-free graphs},
journal = JDM,
volume = 12,
number = 2,
year = 1999,
pages = {276-287},
note = {\url{http://epubs.siam.org/fulltext/SIDMA/volume-12/32634.pdf}}
}
, lien v\'erifi\'e le 18/05/2006
% O(n^4) algorithm solving IndependentSet on AT-free graphs.
@article{dushnikmiller1941,
author = {Ben Dushnik and Edwin W. Miller},
title = {Partially ordered sets},
journal = {American Journal of Mathematics},
volume = 63,
year = 1941,
pages = {600-610}
}
% Some mathematical stuff supposed to prove that a permutation graph = a comparability + cocompar. graph
@manuscript{BiedlLectureNotes,
author = {Therese Biedl},
title = {Graph-theoretic Algorithms},
journal = UM,
year = 2005,
note = {\url{http://www.student.cs.uwaterloo.ca/~cs762/Notes/book.pdf}}
}
lien v\'erifi\'e le 23/05/2006
% course about graphs, lot of stuff on interval graphs in the beginning, planar graphs after that
@phdthesis{Vialette2001,
author = {St\'ephane Vialette},
title = {Aspects algorithmiques de la pr\'ediction des structures secondaires d'ARN},
year = 2001,
school = {Universit{\'e} Paris 7},
note = {\url{http://philippe.gambette.free.fr/LIAFA/Vialette2001.htm}}
}
% Chapter 6 : 2-intervals
@article{trotterharary1979,
author = {William T. Trotter and Frank Harary},
title = {On double and multiple interval graphs},
journal = JGT,
volume = 3,
pages = {205-211},
year = 1979
}
@article{hararykabell1980,
author = {Frank Harary and Jerald Allan Kabell},
title = {An Intuitive Approach to Interval Numbers of Graphs},
journal = {Mathematics Magazine},
volume = 53,
number = 1,
pages = {39-44},
year = 1980
}
@Book{ BLS1999,
author = {Andreas Brandst{\"a}dt and Van Bang Le and Jeremy P. Spinrad},
title = {Graph Classes: a Survey},
publisher = {SIAM Monographs on Discrete Mathematics and Applications},
year = 1999,
}
@misc{isgci,
author = {Andreas Brandst{\"a}dt and Van Bang Le and Thomas Szymczak and Frank Siegemund and H.N. de Ridder and Stefan Knorr and Mirko Rzehak and M. Mowitz and Natalia Ryabova},
title = {{ISGCI}: {Information System on Graph Class Inclusions}},
note = {\url{http://wwwteo.informatik.uni-rostock.de/isgci/classes.cgi}}
}
, lien v\'erifi\'e le 29/05/2006
@article{gll1982,
author = {Udaiprakash I. Gupta and D. T. Lee and Joseph Y.-T Leung},
title = {Efficient Algorithms for Interval Graphs and Circular-Arc Graphs},
journal = {Networks},
volume = 12,
pages = {459-467},
year = 1982
}
@article{fmw1997,
author = {Stefan Felsner and Rudolf M\"uller and Lorenz Wernisch},
title = {Trapezoid Graphs and Generalizations, Geometry and Algorithms},
journal = DAM,
volume = 74,
number = 1,
year = {1997},
pages = {13-32},
note = {\url{ftp://ftp.inf.fu-berlin.de/pub/reports/tr-b-94-02.ps.gz}},
}
, lien v\'erifi\'e le 30/05/2006
@book{CLR1990,
author = {Thomas Cormen and Charles Leiserson and Ronald Rivest},
title = {Introduction to Algorithms},
year = 1990,
publisher = {MIT Press}
}
@article{Edmonds1965,
author = {Jack Edmonds},
title = {Paths, trees and flowers},
journal = {Canadian Journal of Mathematics},
volume = 17,
year = 1965,
pages = {449-467}
}
@article{Galil1986,
author = {Zviv Galil},
title = {Efficient algorithms for finding maximum matching in graphs},
journal = {ACM Computing Surveys},
volume = 18,
number = 1,
year = 1986,
pages = {23-38},
note = {\url{http://doi.acm.org/10.1145/6462.6502}}
}
, lien v\'erifi\'e le 01/06/2006
% weighted or not, edmonds algorithm, idea of Micali & Vazirani
@book{FordFulkerson1962,
author = {Lester R. Ford and Delbert R. Fulkerson},
title = {Flows In Networks},
publisher = {Princeton University Press},
year = {1962}
}
@article{COS1997AT,
author = {Derek G. Corneil and Stephan Olariu and Lorna Stewart},
title = {Asteroidal Triple-Free Graphs},
journal = JDM,
year = {1997},
note = {\url{http://epubs.siam.org/fulltext/SIDMA/volume-10/25012.pdf}}
}
, lien v\'erifi\'e le 01/06/2006
@article{GLS1981,
author = {Martin Gr{\"o}tschel and L{\'a}szlo Lov{\'a}sz and Alexander Schrijver},
title = {The ellipsoid method and its consequences in combinatorial optimization},
journal = C,
volume = 1,
number = 2,
pages = {169-197},
year = 1981,
note = {\url{http://www.zib.de/groetschel/pubnew/paper/groetschellovaszschrijver1981a.djvu}}
}
lien v\'erifi\'e le 01/06/2006
%To find the independent set on i don't remember which kind of graphs (perfect?)
@article{COS1995,
author = {Derek G. Corneil and Stephan Olariu and Lorna Stewart},
title = {Simple Linear Time Recognition of Unit Interval Graphs},
journal = {IPL},
volume = 55,
year = 1995,
pages = {99-104},
note = {\url{http://www.cs.odu.edu/~olariu/uig.ps}}
}
lien v\'erifi\'e le 07/06/2006
Algorithm avoiding to check first that the graph is an interval graph.
It realizes a BFS to check that a characteristic condition for
uig defined by Roberts is verified: there exists an ordering of the vertices such that the
neighbourhood of each vertex is an interval in this ordering (if you have a realization of
the graph, the ordering is for example the ordering on the left endpoints)
@inproceedings{EKSX1996,
author = {Martin Ester and Hans-Peter Kriegel and J\"org Sander and Xiaowei Xu},
title = {A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise},
booktitle = {Proceedings of 2nd International Conference on Knowledge Discovery and Data Mining (KDD96)},
year = 1996,
pages = {226-231},
note = {\url{http://ifsc.ualr.edu/xwxu/publications/kdd-96.pdf}}
}
lien v\'erifi\'e le 08/06/2006
606 Google Scholar Citations in 2006...
criterion to put a point p in a cluster C :
- there are enough points of C in the neighborhood of p
FAILS ! (because of the density of points lower on the frontier
of the cluster).
Instead :
- there is a point q in the neighborhood of p that has enough
points of C in its neighborhood.
= > Efficient implementation (O(n log n)) thanks to efficient
region queries with R* trees.
@inproceedings{BKSS1990,
author = {Norbert Beckmann and Hans-Peter Kriegel and Ralf Schneider and Bernhard Seeger},
title = {The $R^*$-tree: an efficient and robust access method for points and rectangles},
booktitle = {Proceedings of the 1990 ACM SIGMOD international conference on Management of data},
year = 1990,
pages = {322-331},
note = {\url{http://www.sai.msu.su/~megera/postgres/gist/papers/Rstar3.pdf}}
}
lien v\'erifi\'e le 08/06/2006
structure for efficient region queries.
@article{CrickWatson1953,
author = {James D. Watson and Francis H. Crick},
title = {Molecular Structure of nucleic acides, a structure for deoxyribose nucleic acid},
journal = {Nature},
year = 1953,
note = {\url{http://www.annals.org/cgi/reprint/138/7/581.pdf}}
}
lien v\'erifi\'e le 09/06/2006
They explain that they doubt that DNA is a 3-chain molecule and propose their helix structure
with the pairing nucleotides.
@article{Holyer1981,
author = {Ian Holyer},
title = {The {NP}-completeness of Edge-Colouring},
journal = JOC,
volume = 10,
number = 4,
year = 1981,
pages= {718-720},
note = {\url{http://www.cs.bris.ac.uk/~ian/graphs/edge.pdf}}
}
lien v\'erifi\'e le 15/06/2006
@manuscript{Sloane,
author = {Neil J. A. Sloane},
title = {The on-line encyclopedia of integer sequences},
note = {\url{http://www.research.att.com/~njas/sequences/}}
}
@inproceedings{CHLV2005,
author = {Maxime Crochemore and Danny Hermelin and Gad M. Landau and St{\'e}phane Vialette},
title = {Approximating the 2-Interval Pattern Problem},
booktitle = {Algorithms - ESA 2005, 13th Annual European Symposium},
series = {Lecture Notes in Computer Science},
volume = {3669},
year = {2005},
pages = {426-437},
note = {\url{http://dx.doi.org/10.1007/11561071_39}},
}
, lien v\'erifi\'e le 28/06/2006
@article{Polya1937,
author = {George P{\'o}lya},
title = {Kombinatorische Anzahlbestimmungen f{\"u}r Gruppen, Graphen, und chemische Verbindungen},
journal = {Acta Mathematica},
volume = 68,
pages = {145-254},
year = 1937
}
@book{Harary1969,
author = {Frank Harary},
title = {Graph Theory},
publisher = {Addison-Wesley},
year = 1969
}
@phdthesis{Montgolfier2003,
author = {Fabien de Montgolfier},
title = {D{\'e}composition modulaire des graphes, th{\'e}orie, extensions et algorithmes},
school = {Universit{\'e} Montpellier II},
year = 2003,
note = {\url{http://www.liafa.jussieu.fr/~fm/publications/memoire.pdf}}
}
lien v\'erifi\'e le 03/07/2006
@book{GareyJohnson1979,
author = {Michael~R. Garey and David.~S. Johnson},
title = {Computers and Intractability, a guide to the theory of {NP}-completeness},
publisher = {Bell Telephone Laboratories, Inc.},
year = 1979
}
@article{Lehot1974,
author = {Philippe G. H. Lehot},
title = {An Optimal Algorithm to Detect a Line Graph and Output Its Root Graph},
journal = JACM,
volume = 21,
number = 4,
pages = {569-575},
year = 1974,
note = {\url{http://doi.acm.org/10.1145/321850.321853}}
}
lien v\'erifi\'e le 06/07/2006
@article{Berge1994,
author = {Claude Berge},
title = {Qui a tu{\'e} le duc de {Densmore} ?},
journal = {Biblioth{\`e}que {Oulipienne}},
volume = 67,
year = 1994,
note = {r{\'e}{\'e}dition Castor Astral, 2000}
}
@article{BoothLueker1976,
author = {Kellogg S. Booth and George S. Lueker},
title = {Testing for the consecutive ones property, interval graphs, and graph planarity using {PQ}-tree algorithms},
journal = {J. Comp. Sys. Sci.},
volume = 13,
year = 1976,
pages = {335-379}
}
@article{Kendall1969,
author = {David G. Kendall},
title = {Incidence matrices, interval graphs, and seriation in archaeology},
journal = {Pacific Journal of Mathematics},
volume = 28,
year = 1969,
pages = {565-570},
note = {\url{http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.pjm/1102983306}}
}
lien v\'erifi\'e le 24/07/2006
Tries to solve the "approximate" consecutive ones problems.
Consecutive 1 property = Petrie matrix | Robinson matrix = going left or down from the diagonal, never increase.
sigma0 row permutation applied on M gives a Petrie => sigma0 applied to row and columns of M tM fives a Robinson.
+ proof
Idea of using MultiDimensional Scaling to solve approximate consecutive ones problem.
@article{FG1965,
author = {D. R. Fulkerson and O. A. Gross},
title = {Incidence matrices, interval graphs, and seriation in archaeology},
journal = {Pacific Journal of Mathematics},
volume = 28,
year = 1969,
pages = {565-570},
note = {\url{http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.pjm/1102995572}}
}
lien v\'erifi\'e le 24/07/2006
Tries to solve the "approximate" consecutive ones problems.
Consecutive 1 property = Petrie matrix | Robinson matrix = going left or down from the diagonal, never increase.
sigma0 row permutation applied on M gives a Petrie => sigma0 applied to row and columns of M tM fives a Robinson.
+ proof
Idea of using MultiDimensional Scaling to solve approximate consecutive ones problem.
@inproceedings{KMMS2003,
author = {Dieter Kratsch and Ross M. McConnell and Kurt Mehlhorn and Jeremy P. Spinrad},
title = {Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs},
booktitle = {Proceedings of the fourteenth annual ACM-SIAM Symposium on Discrete algorithms (SODA'03)},
year = 2003,
pages = {158-167},
note = {\url{http://www.cs.colostate.edu/~rmm/certificates.pdf}}
}
algorithm+certificate for permutation and interval graphs in linear time.
lien v\'erifi\'e le 24/07/2006
@article{Spinrad1994,
author = {Jeremy P. Spinrad},
title = {Recognition of circle graphs},
journal = {Journal of Algorithms},
volume = 16,
number = 2,
year = 1994,
pages = {264-282},
}
@phdthesis{Gardi2005,
author = {Fr{\'e}d{\'e}ric Gardi},
title = {Ordonnancement avec exclusion mutuelle par un graphe d'intervalles ou d'une classe apprent{\'e}e :
complexit{\'e} et algorithmes},
school = {Universit{\'e} de la M{\'e}diterran{\'e}e - Aix-Marseille II},
year = 2005,
note = {\url{http://www.lif-sud.univ-mrs.fr/~gardi/downloads/These_Gardi.pdf}}
}
26/07/2006
@article{MS1994,
author = {Tze-Heng Ma and Jeremy P. Spinrad},
title = {On the 2-chain subgraph cover and related problems},
journal = {Journal of Algorithms},
volume = 17,
number = 2,
year = 1994,
pages = {251-268},
}
D'après Corneil, algo un peu compliqué (variation de celui de Cogis qui reconnaît les graphes
de dimension intervallaire 2)
@inproceedings{MS1991,
author = {Tze-Heng Ma and Jeremy P. Spinrad},
title = {An ${O}(n^2)$ time algorithm for the 2-chain cover problem and related problems},
booktitle = {Proceedings of the second annual ACM-SIAM Symposium on Discrete algorithms (SODA'91)},
year = 1991,
pages = {363-372},
note = {\url{http://portal.acm.org/citation.cfm?id=127852}}
}
02/08/2006
@phdthesis{Cogis1980,
author = {Olivier Cogis},
title = {La dimension Ferrers des graphes orient{\'e}s},
school = {Universit{\'e} Pierre et Marie Curie},
year = 1980,
}
@article{Cogis1982,
author = {Olivier Cogis},
title = {Ferrers Dimension of a Digraph},
journal = DM,
volume = 38,
number = 1,
year = 1982,
pages = {47-52},
}
@article{CC1996,
author = {Faithful Hoe Kooi Cheah and Derek Corneil},
title = {On the structure of trapezoid graphs},
journal = DAM,
volume = 66,
number = 2,
year = 1996,
pages = {109-133},
}
@book{Forte1973,
author = {Allen Forte},
title = {The structure of atonal music},
publisher = {Yale University Press},
year = 1973
}
@article{StapleButcher2005,
author = {David W. Staple and Samuel E. Butcher},
title = {Pseudoknots: {RNA} Structures with Diverse Functions},
journal = {{PLoS Biology}},
volume = 3,
number = 6,
year = 2005,
pages = {109-133},
note = {\url{http://biology.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pbio.0030213}}
}
, lien v\'erifi\'e le 07/08/2006
@article{RPPBB1982,
author = {Krijn Rietveld and R. Van Poelgeest and Cornelis W.A. Pleij and J.H. Van Boom and Leendert Bosch},
title = {The {tRNA}-like structure at the 3' terminus of turnip yellow mosaic virus {RNA}, differences and similarities with canonical {tRNA}},
journal = NAR,
volume = 10,
year = 1982,
pages = {1929-1946}
}
++ Dans ~stewart/GRAPH/circle/circle.bib
Independent set in circle graph :
Gavril 73 O(n^3)
Hsu 85 O(n^2+m log log n)
Apostolico, Atallah, Hambrusch O(n^2) clique 1992
Recognition
@article{AAH1992,
author = {Alberto Apostolico and Mikhail J. Atallah and Susanne E. Hambrusch},
title = {New clique and independent set algorithms for circle graphs},
journal = DAM,
volume = 36,
number = 2,
year = 1992,
pages = {1-24}
}
O(n^2)
@inproceedings{Tiskin2006,
author = {Alexander Tiskin},
title = {Semi-local longest common subsequences and maximum cliques in circle graphs},
booktitle = {Proceedings of CPM2006, Lecture Notes in Computer Science},
volume = 4009,
year = 2006,
pages = {271-282},
note = {\url{http://www.dcs.warwick.ac.uk/~tiskin/pub/2006/circle.pdf}}
}
lien v\'erifi\'e le 24/08/2006
O(n^2)
@inproceedings{LiLi2006,
author = {Shuai-Cheng Li and Ming Li},
title = {On the Complexity of the Crossing Contact Map Pattern Matching Problem},
booktitle = {Proceedings of 6th Workshop on Algorithms in Bioinformatics (WABI 2006)},
year = 2006
}
This problem is in fact NP-complete, bugged alggorithm in Gramm2002
@inproceedings{Gramm2004,
author = {Jens Gramm},
title = {A polynomial-time algorithm for the matching of crossing contact-map patterns},
booktitle = {Proceedings of the 4th International Workshop on Algorithms in Bioinformatics (WABI 2004), Lecture Notes in Bioinformatics},
volume = 3240,
year = 2004,
pages = {38-49},
note = {\url{http://portal.acm.org/citation.cfm?id=1042198.1042361}}
}
lien v\'erifi\'e le 25/08/2006
@mastersthesis{Bouvel2006,
author = {Mathilde Bouvel},
title = {Autour des permutations s{\'e}parables},
year = 2006,
school = {ENS Cachan, MPRI},
note = {\url{http://philippe.gambette.free.fr/LIAFA/Bouvel2006.htm}},
}
@article{YannakakisGavril1980,
author = {Mihalis Yannakakis and Fanica Gavril},
title = {Edge dominating sets in graphs},
journal = JAM,
volume = 38,
number = 3,
pages = {364-372},
year = 1980,
note = {\url{http://www.jstor.org/view/00361399/di974726/97p0339h/}}
}
26/08/2006
@article{HTC1992,
author = {Ju Yuan Hsiao and Chuan Yi Tang and Ruay Shiung Chang},
title = {An Efficient Algorithm for Finding a Maximum Weight 2-Independent
Set on Interval Graphs},
journal = IPL,
volume = {43},
number = {5},
year = {1992},
pages = {229-235},
}
@article{Lin2006,
author = {Yaw-Ling Lin},
title = {Circular and Circle Trapezoid Graphs},
journal = {Journal of Science and Engineering Technology},
volume = 2,
number = 2,
year = 2006,
pages = {11-17},
note = {\url{http://journal.dyu.edu.tw/dyujo/document/s2-2-11-17.pdf}}
}
26/08/2006
@article{APT1979,
author = {Bengt Aspvall and Michael F. Plass and Robert E. Tarjan},
title = {A linear-time algorithm for testing the truth of certain quantified boolean formulas},
journal = IPL,
year = 1979,
}
Nice algorithm to solve 2-SAT using an digraph.
@article{CPS2006,
author = {Peter Cameron and Thomas Prellberg and Dudley Stark},
title = {Asymptotic enumeration of incidence matrices},
journal = {Journal of Physics: Conference Series},
volume = {42},
pages = {59-70},
year = 2006,
note = {\url{http://ej.iop.org/links/r8JtBU4n_/st_AleI52xG2ZV7Sav5vpA/jpconf6_42_007.pdf}}
}
01/09/2006
nice maths (Möbius inversion, sum re-indicing) to enumerate certain adjacency matrices
@article{BenderGoldman1975,
author = {Edward A. Bender and Jay R. Goldman},
title = {On the Applications of Moebius Inversion in Combinatorial Analysis},
journal = {American Mathematical Monthly},
volume = {82},
number = {8},
pages = {789-803},
year = 1975,
note = {\url{http://www.citeulike.org/user/euclid/article/775065}}
}
01/09/2006
@inproceedings{KMR1972,
author = {Richard M. Karp and Raymond E. Miller and Arnold L. Rosenberg},
title = {Rapid identification of repeated patterns in strings, trees and arrays},
booktitle = {Proceedings of the 4th Annual ACM Symposium},
pages = {125-136},
year = 1972,
note = {\url{http://doi.acm.org/10.1145/800152.804905}}
}
@manuscript{Makinen1999,
author = {Erkki M{\"a}kinen},
title = {On The Longest Upsequence Problem For Permutations},
year = 1999,
note = {\url{http://citeseer.ist.psu.edu/225912.html}}
}
03/09/2006