Algorithmic Aspects of the Consecutive-Ones Property

Algorithmic Aspects of the Consecutive-Ones Property (2009)

Cached

Download Links

by Michael Dom

Citations:

BibTeX

@MISC{Dom09algorithmicaspects,
    author = {Michael Dom},
    title = {Algorithmic Aspects of the Consecutive-Ones Property},
    year = {2009}
}

Bookmark

OpenURL

Abstract

We survey the consecutive-ones property of binary matrices. Herein, a binary matrix has the consecutive-ones 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.

Citations

8882	Computers and Intractability: A Guide to the Theory of NP-completeness - Garey, Johnson - 1979
7321	Introduction to Algorithms - Cormen, Leiserson, et al. - 2001
3377	Introduction to Automata Theory, Languages, and Computation - Hopcroft, Motwani, et al. - 2003
1232	Theory of Linear and Integer Programming - SCHRIJVER - 1986
1107	Network flows: theory, algorithms and applications - Ahuja, Magnanti, et al. - 1993
991	Algorithmic Graph Theory and Perfect Graphs - Golumbic - 1980
697	Fellows M: Parameterized Complexity - Downey - 1999
406	G.: Testing for the consecutive ones property, interval graphs and graph planarity using PQ-trees - Booth, Lueker - 1976
363	Primal-Dual Interior-Point Methods - Wright - 1960
228	Parameterized Complexity Theory - Flum, Grohe - 2006
190	Invitation to Fixed-Parameter Algorithms - Niedermeier - 2006
160	Incidence matrices and interval graphs - Fulkerson, Gross - 1965
112	Representation of a finite graphs by a set of intervals on the real line - Lekkerkerker, Boland - 1962
110	Interval Orders and Interval Graphs - Fishburn - 1985
62	Indifference graphs - Roberts - 1968
60	Integral boundary points of convex polyhedra - Hoffman, Kruskal - 1956
57	Algorithms for the set covering problem - Caprara, Toth, et al. - 2000
54	On the topology of the genetic fine structure - Benzer - 1959
50	An incremental linear-time algorithm for recognizing interval graphs - Korte, Mohring - 1989
46	R.: Four strikes against physical mapping of DNA - Goldberg, Golumbic, et al. - 1995
46	Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing - Habib, McConnell, et al. - 2000
37	Matrix characterizations of circular-arc graphs, Pacific J.Math., 39 - Tucker - 1971
35	A spectral algorithm for seriation and the consecutive ones problem - Atkins, Boman, et al. - 1998
33	Treybig, Bounds on positive integral solutions of linear diophantine equations - Borosh, B - 1976
31	Balanced matrices - Berge - 1972
30	L.: The ultimate interval graph recognition algorithm? (Extended abstract - Corneil, Olariu, et al. - 1998
28	M.: On the red-blue set cover problem - Carr, Doddi, et al.
26	Caractérisation des matrices totalement unimodulaires - GHOUILA-HOURI - 1962
26	Linear-time recognition of circular-arc graphs - McConnell
24	Balanced matrices - Conforti, Cornuéjols, et al. - 1994
24	A threshold of ln n for approximating Set - Feige
23	Cyclic scheduling via integer programs with circular ones - Bartholdi, Orlin, et al. - 1980
23	A certifying algorithm for the consecutive-ones property, in - McConnell
23	On the consecutive ones property - Meidanis, Telles - 1998
23	An efficient test for circular-arc graphs - Tucker - 1980
22	Interval routing schemes - Flammini, Gambosi, et al. - 1996
22	A simple test for the consecutive ones property - Hsu
22	Certifying algorithms for recognizing interval graphs and permutation graphs - Kratsch, McConnell, et al. - 2003
22	R: SNPs problems, complexity, and algorithms - Lancia, Bafna, et al.
22	PC-trees and circular-ones arrangements - Hsu, McConnell - 2003
21	Constant ratio approximation algorithms for the rectangle stabbing problem and the rectilinear partitioning problem - Gaur, Ibaraki, et al.
21	A Structure Theorem for the Consecutive 1s Property - Tucker - 1972
18	Approximation algorithms for hitting objects with straight lines - Hassin, Megiddo - 1991
18	A simple test for interval graphs - Hsu - 1993
18	O(mn) algorithms for the recognition and isomorphism problems on circular-arc graphs - Hsu - 1995
17	and R.Oppenheim, On balanced matrices - Fulkerson - 1974
17	zur Gathen and M. Sieveking. A bound on solutions of linear integer equalities and inequalities - von - 1978
15	An O(n 2 ) algorithm for circular-arc graph recognition - Eschen, Spinrad - 1993
15	A note on the consecutive ones submatrix problem - Hajiaghayi, Ganjali
15	Uber eine art von graphen - Hajos - 1980