Permuting matrices to avoid forbidden submatrices
TLDR
It is proved that the problem is polynomial time solvable for many sets F containing a single, small matrix and some example sets F for which the problems are NP-complete are exhibited.About:
This article is published in Discrete Applied Mathematics.The article was published on 1995-06-23 and is currently open access. It has received 41 citations till now. The article focuses on the topics: Integer matrix & Matrix (mathematics).read more
Citations
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Linear Assignment Problems and Extensions
Rainer E. Burkard,Eranda Çela +1 more
TL;DR: Assignment problems deal with the question how to assign n items to n machines (or workers) in the best possible way and an objective function modeling the ”best way” is modeled.
Journal ArticleDOI
Perspectives of Monge properties in optimization
TL;DR: This paper presents a survey on Monge matrices and related Monge properties and their role in combinatorial optimization, and deals with the following three main topics: fundamental combinatorsial properties of Monge structures, applications of MonGE properties to optimization problems and recognition ofMonge properties.
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On probe interval graphs
TL;DR: It is proved that probe interval graphs are weakly triangulated, and hence are perfect, and characterize probe interval graph by consecutive orders of their intrinsic cliques.
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Incomplete Directed Perfect Phylogeny
TL;DR: This work provides a graph theoretic formulation of the problem of finding a single, general solution tree, from which any other solution can be obtained by node, and gives near-optimal $\tilde{O}(nm)$-time algorithms for the problem.
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On orthogonal ray graphs
TL;DR: The results settle an open question of deciding whether a (0,1)-matrix can be permuted to avoid the submatrices and imply polynomial-time recognition and isomorphism algorithms for 2-directional orthogonal ray graphs.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book
Integer and Combinatorial Optimization
TL;DR: This chapter discusses the Scope of Integer and Combinatorial Optimization, as well as applications of Special-Purpose Algorithms and Matching.
Book
Algorithmic graph theory and perfect graphs
TL;DR: This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems and remains a stepping stone from which the reader may embark on one of many fascinating research trails.
Journal ArticleDOI
Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms
TL;DR: The consecutive ones test for the consecutive ones property in matrices and for graph planarity is extended to a test for interval graphs using a recently discovered fast recognition algorithm for chordal graphs.