Journal ArticleDOI
Efficient parallel algorithms for bipartite permutation graphs
Lin Chen,Yaacov Yesha +1 more
TLDR
The minimum fill-in problem for bipartite permutation graphs can be solved efficiently by a randomized parallel algorithm and the first efficient parallel algorithms for several problems on bipartitespermutation graphs are given.Abstract:
In this paper, we further study the properties of bipartite permutation graphs. We give first efficient parallel algorithms for several problems on bipartite permutation graphs. These problems include transforming a bipartite graph into a strongly ordered one if it is also a permutation graph; testing isomorphism; finding a Hamiltonian path/cycle; solving a variant of the crossing number problem; and others. All these problems can be solved in O(log2n) time with O(n3) processors on a Common CRCW PRAM. We also show that the minimum fill-in problem for bipartite permutation graphs can be solved efficiently by a randomized parallel algorithm. © 1993 by John Wiley & Sons, Inc.read more
Citations
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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.
Journal Article
On the linear structure and clique-width of bipartite permutation graphs.
TL;DR: This paper elaborate the linear structure of bipartite permutation graphs by showing that any connected graph in the class can be stretched into a "path" with "edges" being chain graphs.
Journal ArticleDOI
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.
Journal ArticleDOI
Permuting matrices to avoid forbidden submatrices
TL;DR: 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.
Journal ArticleDOI
Interval Graphs: Canonical Representations in Logspace
TL;DR: A logspace algorithm for computing a canonical labeling, in fact, a canonical interval representation, for interval graphs, which yields a canonicallabel of convex graphs and isomorphism and automorphism problems for these graph classes are solvable in logspace.
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.
Journal ArticleDOI
Incidence matrices and interval graphs
TL;DR: In this article, the problem of determining when a graph is an interval graph is a special case of the following problem concerning (0, 1)-matrices: when can the rows of such a matrix be permuted so as to make the 1's in each colum appear consecutively.
Journal ArticleDOI
Parallel Prefix Computation
TL;DR: A recurstve construction is used to obtain a product circuit for solving the prefix problem and a Boolean clrcmt which has depth 2[Iog2n] + 2 and size bounded by 14n is obtained for n-bit binary addmon.
Journal ArticleDOI
The NP-completeness column: An ongoing guide
TL;DR: This is the fourteenth edition of a quarterly column that provides continuing coverage of new developments in the theory of NP-completeness, and readers who have results they would like mentioned (NP-hardness, PSPACE- hardness, polynomialtime-solvability, etc.), or open problems they wouldlike publicized, should send them to David S. Johnson.