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Make it Practical: A Generic LinearTime Algorithm for Solving MaximumWeightsum Problems
 In Proceedings of the 5th ACM SIGPLAN International Conference on Functional Programming (ICFP'00
, 2000
"... In this paper we propose a new method for deriving a practical lineartime algorithm from the specification of a maximumweight sum problem: From the elements of a data structure x, find a subset which satisfies a certain property p and whose weightsum is maximum. Previously proposed methods for aut ..."
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Cited by 12 (8 self)
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In this paper we propose a new method for deriving a practical lineartime algorithm from the specification of a maximumweight sum problem: From the elements of a data structure x, find a subset which satisfies a certain property p and whose weightsum is maximum. Previously proposed methods for automatically generating lineartime algorithms are theoretically appealing, but the algorithms generated are hardly useful in practice due to a huge constant factor for space and time. The key points of our approach are to express the property p by a recursive boolean function over the structure x rather than a usual logical predicate and to apply program transformation techniques to reduce the constant factor. We present an optimization theorem, give a calculational strategy for applying the theorem, and demonstrate the effectiveness of our approach through several nontrivial examples which would be difficult to deal with when using the methods previously available.
Excluding a Countable Clique
, 1998
"... We extend the excluded K n minor theorem of Robertson and Seymour to infinite graphs, and deduce a structural characterization of the infinite graphs that have no K #0 minor. The latter is a refinement of an earlier characterization of Robertson, Seymour and the second author. ..."
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Cited by 4 (0 self)
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We extend the excluded K n minor theorem of Robertson and Seymour to infinite graphs, and deduce a structural characterization of the infinite graphs that have no K #0 minor. The latter is a refinement of an earlier characterization of Robertson, Seymour and the second author.
Calculating linear time algorithms for solving maximum weightsum problems
 Computer Software
, 2001
"... In this paper, we propose a new method to derive practical linear time algorithms for maximum weightsum problems. A maximum weightsum problem is specified as follows: given a recursive data x, find an optimal subset of elements of x which not only satisfies certain property p but also maximizes the ..."
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Cited by 1 (1 self)
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In this paper, we propose a new method to derive practical linear time algorithms for maximum weightsum problems. A maximum weightsum problem is specified as follows: given a recursive data x, find an optimal subset of elements of x which not only satisfies certain property p but also maximizes the sum of the weight of elements of the subset. The key point of our approach is to describe the property p as a functional program. This enables us to use program transformation techniques. Based on this approach, we present the optimization theorem, with which we construct a systematic framework to calculate efficient linear time algorithms for maximum weightsum problems on recursive data structures. We demonstrate effectiveness of our approach through several interesting and nontrivial examples, which would be difficult to solve by known approaches.
Excluding Subdivisions of Infinite Cliques
, 1989
"... For every infinite cardinal κ we characterize graphs not containing a subdivision of K_κ. ..."
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Cited by 1 (1 self)
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For every infinite cardinal κ we characterize graphs not containing a subdivision of K_κ.
TreeDecompositions of Graphs
"... Treedecompositions of graphs play an important role in graph structure theory, in the theory of algorithms and in practical computation. ..."
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Treedecompositions of graphs play an important role in graph structure theory, in the theory of algorithms and in practical computation.
Typical Subgraphs of 3 and . . .
, 1990
"... We prove that, for every positive integer k, there is an integer N such that every 3connected graph with at least N vertices has a minor isomorphic to the kspoke wheel or K3,k; and that every internally 4connected graph with at least N vertices has a minor isomorphic to the 2kspoke double wheel ..."
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We prove that, for every positive integer k, there is an integer N such that every 3connected graph with at least N vertices has a minor isomorphic to the kspoke wheel or K3,k; and that every internally 4connected graph with at least N vertices has a minor isomorphic to the 2kspoke double wheel, the krung circular ladder, the krung Möbius ladder, or K4,k. We also prove an analogous result for infinite graphs.