Author
Lin Chen
Bio: Lin Chen is an academic researcher from Ohio State University. The author has contributed to research in topics: Complete bipartite graph & Maximal independent set. The author has an hindex of 2, co-authored 3 publications receiving 69 citations.
Papers
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TL;DR: 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.
34 citations
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TL;DR: This paper gives the first NC algorithm for recognizing the consecutive 1's property for rows of a (0, 1)-matrix, and shows that the maximum matching problem for arbitrary convex bipartite graphs can be solved within the same complexity bounds.
33 citations
01 Jan 1990
TL;DR: By exhibiting a parallel algorithm, it is shown, for the first time, that the recognition of the consecutive 1's property for rows of a (0,1)-matrix is in NC, and the techniques and methods exhibited can be used to obtain efficient solutions to some other problems.
Abstract: Processor complexity and time complexity are two important measures of the efficiency of parallel algorithms. A problem is said to be in NC if it can be solved in polylogarithmic time using a polynomial number of processors. This dissertation centers on designing efficient parallel algorithms for discrete problems.
By exhibiting a parallel algorithm, we show, for the first time, that the recognition of the consecutive 1's property for rows of a (0,1)-matrix is in NC. The algorithm gives a useful tool for solving many other problems.
Based on the above procedure, we prove to be in NC the recognition of many classes of graphs, e.g., transformable convex bipartite (TCB) graphs, bipartite permutation (BP) graphs, $\Gamma$ circular arc graphs, $\Theta$ circular arc graphs (a.k.a. Helly circular arc graphs), proper circular arc graphs, proper interval graphs, etc. We also present the first NC algorithms for finding a maximum matching, a maximum independent set, and a minimum clique cover in a TCB graph, and for finding a Hamilton path/cycle in a BP graph. We also obtain more efficient parallel algorithms for some problems such as computing maximum cliques on comparability graphs, circle graphs, and circular arc graphs than the predecessors.
Furthermore, we study a well known longstanding open problem, the graph isomorphism problem. We introduce the notion of identification (ID) matrices. We show to be in NC the isomorphism testing for graphs which have ID matrices with the circular 1's property. These graphs include, among others, $\Gamma$ circular arc graphs, $\Theta$ circular arc graphs, and circular convex bipartite graphs. This substantially broadens the class of graphs for which the graph isomorphism problem is known to be in NC, and therefore, in P.
Included in the appendix are efficient sorting algorithms and efficient implementation of the sequential isomorphism testing algorithms, which are by no means less important.
This research has produced many efficient algorithms. They will help us in at least the following two aspects: (0) The algorithms can be used as building blocks to develop some other efficient algorithms; (1) The techniques and methods exhibited can be used to obtain efficient solutions to some other problems.
2 citations
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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.
321 citations
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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.
Abstract: Bipartite permutation graphs have several nice characterizations in terms of vertex ordering. Besides, as AT-free graphs, they have a linear structure in the sense that any connected bipartite permutation graph has a dominating path. In the present paper, we 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. A particular consequence from the obtained characterization is that the clique-width of bipartite permutation graphs is unbounded, which reenes a recent result of Golumbic and Rotics for permutation graphs.
85 citations
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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.
66 citations
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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.
41 citations
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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.
Abstract: We present a logspace algorithm for computing a canonical labeling, in fact, a canonical interval representation, for interval graphs. To achieve this, we compute canonical interval representations of interval hypergraphs. This approach also yields a canonical labeling of convex graphs. As a consequence, the isomorphism and automorphism problems for these graph classes are solvable in logspace. For proper interval graphs we also design logspace algorithms computing their canonical representations by proper and by unit interval systems.
38 citations