Results 1  10
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27
Fixed Parameter Algorithms for Dominating Set and Related Problems on Planar Graphs
, 2002
"... We present an algorithm that constructively produces a solution to the kdominating set problem for planar graphs in time O(c . To obtain this result, we show that the treewidth of a planar graph with domination number (G) is O( (G)), and that such a tree decomposition can be found in O( (G)n) time. ..."
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Cited by 105 (23 self)
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We present an algorithm that constructively produces a solution to the kdominating set problem for planar graphs in time O(c . To obtain this result, we show that the treewidth of a planar graph with domination number (G) is O( (G)), and that such a tree decomposition can be found in O( (G)n) time. The same technique can be used to show that the kface cover problem ( find a size k set of faces that cover all vertices of a given plane graph) can be solved in O(c n) time, where c 1 = 3 and k is the size of the face cover set. Similar results can be obtained in the planar case for some variants of kdominating set, e.g., kindependent dominating set and kweighted dominating set.
Towards PatternBased Design Recovery
"... A method and a corresponding tool is described which assist design recovery and program understanding by recognising instances of design patterns semiautomatically. The approach taken is specifically designed to overcome the existing scalability problems caused by many design and implementation var ..."
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Cited by 59 (12 self)
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A method and a corresponding tool is described which assist design recovery and program understanding by recognising instances of design patterns semiautomatically. The approach taken is specifically designed to overcome the existing scalability problems caused by many design and implementation variants of design pattern instances. Our approach is based on a new recognition algorithm which works incrementally rather than trying to analyse a possibly large software system in one pass without any human intervention. The new algorithm exploits domain and context knowledge given by a reverse engineer and by a special underlying syntax graph. Finally, the paper gives some results and experiences about the application of the approach to the Java AWT and JGL libraries in comparison to other approaches.
A Randomized Parallel 3D Convex Hull Algorithm For Coarse Grained Multicomputers
 In Proc. ACM Symp. on Parallel Algorithms and Architectures
, 1995
"... We present a randomized parallel algorithm for constructing the 3D convex hull on a generic pprocessor coarse grained multicomputer with arbitrary interconection network and n=p local memory per processor, where n=p p 2+ffl (for some arbitrarily small ffl ? 0). For any given set of n points in ..."
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Cited by 50 (11 self)
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We present a randomized parallel algorithm for constructing the 3D convex hull on a generic pprocessor coarse grained multicomputer with arbitrary interconection network and n=p local memory per processor, where n=p p 2+ffl (for some arbitrarily small ffl ? 0). For any given set of n points in 3space, the algorithm computes the 3D convex hull, with high probaility, in O( n log n p ) local computation time and O(1) communication phases with at most O(n=p) data sent/received by each processor. That is, with high probability, the algorithm computes the 3D convex hull of an arbitrary point set in time O( n logn p + \Gamma n;p ), where \Gamma n;p denotes the time complexity of one communication phase. The assumption n p p 2+ffl implies a coarse grained, limited parallelism, model which is applicable to most commercially available multiprocessors. In the terminology of the BSP model, our algorithm requires, with high probability, O(1) supersteps, synchronization period L = \Th...
Upper Bounds for Vertex Cover Further Improved
"... . The problem instance of Vertex Cover consists of an undirected graph G = (V; E) and a positive integer k, the question is whether there exists a subset C V of vertices such that each edge in E has at least one of its endpoints in C with jCj k. We improve two recent worst case upper bounds fo ..."
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Cited by 43 (16 self)
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. The problem instance of Vertex Cover consists of an undirected graph G = (V; E) and a positive integer k, the question is whether there exists a subset C V of vertices such that each edge in E has at least one of its endpoints in C with jCj k. We improve two recent worst case upper bounds for Vertex Cover. First, Balasubramanian et al. showed that Vertex Cover can be solved in time O(kn + 1:32472 k k 2 ), where n is the number of vertices in G. Afterwards, Downey et al. improved this to O(kn+ 1:31951 k k 2 ). Bringing the exponential base significantly below 1:3, we present the new upper bound O(kn + 1:29175 k k 2 ). 1 Introduction Vertex Cover is a problem of central importance in computer science: { It was among the rst NPcomplete problems [7]. { There have been numerous eorts to design ecient approximation algorithms [3], but it is also known to be hard to approximate [1]. { It is of central importance in parameterized complexity theory and has one ...
Fixed parameter algorithms for planar dominating set and related problems
, 2000
"... We present an algorithm that constructively produces a solution to the kdominating set problem for planar graphs in time O(c √ kn), where c = 36√34. To obtain this result, we show that the treewidth of a planar graph with domination number γ(G) is O ( � γ(G)), and that such a tree decomposition ca ..."
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Cited by 35 (10 self)
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We present an algorithm that constructively produces a solution to the kdominating set problem for planar graphs in time O(c √ kn), where c = 36√34. To obtain this result, we show that the treewidth of a planar graph with domination number γ(G) is O ( � γ(G)), and that such a tree decomposition can be found in O ( � γ(G)n) time. The same technique can be used to show that the kface cover problem (find a size k set of faces that cover all vertices of a given plane graph) can be solved √ k in O(c1 n + n2) time, where c1 = 236√34 and k is the size of the face cover set. Similar results can be obtained in the planar case for some variants of kdominating set, e.g., kindependent dominating set and kweighted dominating set. Keywords. NPcomplete problems, fixed parameter tractability, planar graphs, planar dominating set, face cover, outerplanarity, treewidth.
Linear Time Computable Problems and FirstOrder Descriptions
, 1996
"... this article is a proof that each FO problem can be solved in linear time if only relational structures of bounded degree are considered. The basic idea of the proof is a localization technique based on a method that was originally developed by Hanf (Hanf 1965) to show that the elementary theories o ..."
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Cited by 31 (2 self)
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this article is a proof that each FO problem can be solved in linear time if only relational structures of bounded degree are considered. The basic idea of the proof is a localization technique based on a method that was originally developed by Hanf (Hanf 1965) to show that the elementary theories of two structures are equal under certain conditions, i.e., that two structures agree on all firstorder sentences. Fagin, Stockmeyer and Vardi (Fagin et al. 1993) developed a variant of this technique, which is applicable in descriptive complexity theory to classes of finite relational structures of uniformly bounded degree. Variants of this result can also be found in Gaifman (1982) (see also Thomas (1991)). The essential content of this result, which is also called the HanfSphere Lemma, is that two relational structures of bounded degree satisfy the same firstorder sentences of a certain quantifierrank if both contain, up to a certain number m, the same number of isomorphism types of substructures of a bounded radius r. In addition, a technique of model interpretability from Rabin (1965) (see also Arnborg et al. (1991), Seese (1992), Compton and Henson (1987) and Baudisch et al. (1982)) is adapted to descriptive complexity classes, and proved to be useful for reducing the case of an arbitrary class of relational structures to a class of structures consisting only of the domain and one binary irreflexive and symmetric relation, i.e., the class of simple graphs. It is shown that the class of simple graphs is lintimeuniversal with respect to firstorder logic, which shows that many problems on descriptive complexity classes, described in languages extending firstorder logic for arbitrary structures, can be reduced to problems on simple graphs. This paper is organized as f...
Utilizing Constraint Satisfaction Techniques for Efficient Graph Pattern Matching
 IN 6TH INTERNATIONAL WORKSHOP ON THEORY AN APPLICATION OF GRAPH TRANSFORMATIONS (TAGT
, 1998
"... This paper presents a way to represent and solve the problem of graph matching  also known as the subgraph homomorphism problem  as a constraint satisfaction problem (CSP), opening up direct access to the large variety of research findings on optimized solution algorithms for CSPs. By decoupling ..."
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Cited by 25 (0 self)
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This paper presents a way to represent and solve the problem of graph matching  also known as the subgraph homomorphism problem  as a constraint satisfaction problem (CSP), opening up direct access to the large variety of research findings on optimized solution algorithms for CSPs. By decoupling the solution algorithm from the concrete graph model, the approach allows for variations of the model without affecting the algorithm. Furthermore, complementing the standard CSP definition, a query concept is introduced to allow abstract representation of concrete implementation properties for optimization purposes.
A New Planarity Test
, 1999
"... Given an undirected graph, the planarity testing problem is to determine whether the graph can be drawn in the plane without any crossing edges. Linear time planarity testing algorithms have previously been designed by Hopcroft and Tarjan, and by Booth and Lueker. However, their approaches are quite ..."
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Cited by 19 (2 self)
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Given an undirected graph, the planarity testing problem is to determine whether the graph can be drawn in the plane without any crossing edges. Linear time planarity testing algorithms have previously been designed by Hopcroft and Tarjan, and by Booth and Lueker. However, their approaches are quite involved. Several other approaches have also been developed for simplifying the planariy test. In this paper, we developed a very simple linear time testing algorithm based only on a depthfirst search tree. When the given graph is not planar, our algorithm immediately produces explicit Kuratowski's subgraphs. A new data structure, PCtrees, is introduced, which can be viewed as abstract subembeddings of actual planar embeddings. A graphreduction technique is adopted so that the embeddings for the planar biconnected components constructed at each iteration never have to be changed. The recognition and embedding are actually done simultaneously in our algorithm 1 . The implementation of o...
Handling Large Search Space in Patternbased Reverse Engineering
 Proceedings of the 11 th IEEE International Workshop on Program Comprehension (IWPC
, 2003
"... Large industrial legacy systems are challenges of reverseengineering activities. Reverseengineering approaches use textsearch tools based on regular expressions or work on graph representations of programs, such as abstract syntax graphs. Analyzing large legacy systems often fail because of the la ..."
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Cited by 15 (3 self)
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Large industrial legacy systems are challenges of reverseengineering activities. Reverseengineering approaches use textsearch tools based on regular expressions or work on graph representations of programs, such as abstract syntax graphs. Analyzing large legacy systems often fail because of the large search space. Our approach to handle large search space in patternbased reverse engineering is to allow imprecise results in means of false positives. We use the theory of fuzzy sets to express impreciseness and present our approach on the example of recovering associations.
DataFlow Frameworks for WorstCase Execution Time Analysis
 RealTime Systems
, 2000
"... The purpose of this paper is to introduce frameworks based on dataflow equations which provide for estimating the worstcase execution time (WCET) of (realtime) programs. These frameworks allow several different WCET analysis techniques, which range from nave approaches to exact analysis, provided ..."
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Cited by 12 (8 self)
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The purpose of this paper is to introduce frameworks based on dataflow equations which provide for estimating the worstcase execution time (WCET) of (realtime) programs. These frameworks allow several different WCET analysis techniques, which range from nave approaches to exact analysis, provided exact knowledge on the program behaviour is available. However, dataflow frameworks can also be used for symbolic analysis based on information derived automatically from the source code of the program. As a byproduct we show that slightly modified elimination methods can be employed for solving WCET dataflow equations, while iteration algorithms cannot be used for this purpose.