Parallel recognition of the consecutive ones property with applications
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Cited by (22)
Circular-arc hypergraphs: Rigidity via connectedness
2017, Discrete Applied MathematicsCitation Excerpt :Note also that Theorem 1.1 is a consequence of Part 2. The proof of each part follows the same scheme, used by Chen and Yesha [4, Theorem 2] for overlap-connected interval hypergraphs. Moreover, the claims about interval hypergraphs easily follow from the analogous claims about CA hypergraphs.
Solving the canonical representation and Star System Problems for proper circular-arc graphs in logspace
2016, Journal of Discrete AlgorithmsCitation Excerpt :For the latter class we have linear-time algorithms for recognition [4] and canonical representation [29] due to the seminal work by Booth and Lueker; logspace algorithms for these tasks are designed in [21]. The aforementioned circular ones property and the related consecutive ones property (requiring that the columns can be permuted so that the 1-entries in each row form a segment) were studied in [4,17,18], where linear-time algorithms are given; parallel AC2 algorithms were suggested in [9,2]. In order to solve the canonical representation problem for CA hypergraphs we have to compute for a given hypergraph some arc representation (if it exists) such that isomorphic CA hypergraphs obtain identical arc models.
On the isomorphism problem for Helly circular-arc graphs
2016, Information and ComputationCitation Excerpt :The latter relation is excluded in interval systems. The following fact about interval systems is due to [3, Theorem 2]; see also [11, Section 2.2]. We are now prepared to prove Theorem 1.1.
A selected tour of the theory of identification matrices
2000, Theoretical Computer ScienceGraph isomorphism and identification matrices: Sequential algorithms
1999, Journal of Computer and System SciencesOptimal computation of shortest paths on doubly convex bipartite graphs
1999, Computers and Mathematics with Applications
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Supported in part by the Office of Research and Graduate Studies of Ohio State University.
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Supported in part by the National Science Foundation under Grant DCR-8606366 at Ohio State University.