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Short Regular Expressions from Finite Automata: Empirical Results
 CIAA 2009. LNCS
, 2009
"... Abstract. We continue our work [H. Gruber, M. Holzer: Provably shorter regular expressions from deterministic finite automata (extended abstract). In Proc. DLT, LNCS 5257, 2008] on the problem of finding good elimination orderings for the state elimination algorithm, one of the most popular algorith ..."
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Cited by 5 (2 self)
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Abstract. We continue our work [H. Gruber, M. Holzer: Provably shorter regular expressions from deterministic finite automata (extended abstract). In Proc. DLT, LNCS 5257, 2008] on the problem of finding good elimination orderings for the state elimination algorithm, one of the most popular algorithms for the conversion of finite automata into equivalent regular expressions. Here we tackle this problem both from the theoretical and from the practical side. First we show that the problem of finding optimal elimination orderings can be used to estimate the cycle rank of the underlying automata. This gives good evidence that the problem under consideration is difficult, to a certain extent. Moreover, we conduct experiments on a large set of carefully chosen instances for five different strategies to choose elimination orderings, which are known from the literature. Perhaps the most surprising result is that a simple greedy heuristic by [M. Delgado, J. Morais: Approximation to the smallest regular expression for a given regular language. In Proc. CIAA, LNCS 3317, 2004] almost always outperforms all other strategies, including those with a provable performance guarantee. 1
Approximation algorithms for the Maximum Induced Planar and Outerplanar Subgraph problems
 J. Graph Algorithms Appl
"... The task of finding the largest subset of vertices of a graph that induces a planar subgraph is known as the Maximum Induced Planar Subgraph problem (MIPS). In this paper, some new approximation algorithms for MIPS are introduced. The results of an extensive study of the performance of these and exi ..."
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The task of finding the largest subset of vertices of a graph that induces a planar subgraph is known as the Maximum Induced Planar Subgraph problem (MIPS). In this paper, some new approximation algorithms for MIPS are introduced. The results of an extensive study of the performance of these and existing MIPS approximation algorithms on randomly generated graphs are presented. Efficient algorithms for finding large induced outerplanar graphs are also given. One of these algorithms is shown to find an induced outerplanar subgraph with at least 3n/(d + 5/3) vertices. The results presented in this paper indicate that most existing algorithms perform substantially better than the existing lower bounds indicate. 1
Planarization and acyclic colorings of subcubic clawfree graphs
"... Abstract. We study methods of planarizing and acyclically coloring clawfree subcubic graphs. We give a polynomialtime algorithm that, given such a graph G, produces an independent set Q of at most n/6 vertices whose removal from G leaves an induced planar subgraph P (in fact, P has treewidth at mo ..."
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Abstract. We study methods of planarizing and acyclically coloring clawfree subcubic graphs. We give a polynomialtime algorithm that, given such a graph G, produces an independent set Q of at most n/6 vertices whose removal from G leaves an induced planar subgraph P (in fact, P has treewidth at most four). We further show the stronger result that in polynomialtime a set of at most n/6 edges can be identified whose removal leaves a planar subgraph (of treewidth at most four). From an approximability point of view, we show that our results imply 6/5 and 9/8approximation algorithms, respectively, for the (NPhard) problems of finding a maximum induced planar subgraph and a maximum planar subgraph of a subcubic clawfree graph, respectively. Regarding acyclic colorings, we give a polynomialtime algorithm that finds an optimal acyclic vertex coloring of a subcubic clawfree graph. To our knowledge, this represents the largest known subclass of subcubic graphs such that an optimal acyclic vertex coloring can be found in polynomialtime. We show that this bound is tight by proving that the problem is NPhard for cubic line graphs (and therefore, clawfree graphs) of maximum degree d ≥ 4. An interesting corollary to the algorithm that we present is that there are exactly three subcubic clawfree graphs that require four colors to be acyclically colored. For all other such graphs, three colors suffice. 1
Test Results on the Performance of Approximation Algorithms for the Maximum Induced Planar Subgraph Problem Contents
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The Analysis and Design of Approximation Algorithms for the Maximum Induced Planar Subgraph Problem
, 2005
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