Journal ArticleDOI
The Recognition of Series Parallel Digraphs
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TLDR
A linear-time algorithm to recognize the class of vertex series-parallel (VSP) digraphs is presented and efficient methods to compute the transitive closure and transitive reduction of VSPDigraphs are obtained.Abstract:
We present a linear-time algorithm to recognize the class of vertex series-parallel (VSP) digraphs. Our method is based on the relationship between VSP digraphs and the class of edge series-paralle...read more
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Journal ArticleDOI
The NP-completeness column: An ongoing guide
TL;DR: This is the fourteenth edition of a quarterly column that provides continuing coverage of new developments in the theory of NP-completeness, and readers who have results they would like mentioned (NP-hardness, PSPACE- hardness, polynomialtime-solvability, etc.), or open problems they wouldlike publicized, should send them to David S. Johnson.
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Modular decomposition and transitive orientation
TL;DR: This work gives O(n+m) algorithms for modular decomposition and transitive orientation, where n and m are the number of vertices and edges of the graph and linear time bounds for recognizing permutation graphs, maximum clique and minimum vertex coloring on comparability graphs, and other combinatorial problems on comparable graphs and their complements.
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Monadic second-order evaluations on tree-decomposable graphs
Bruno Courcelle,Mohamed Mosbah +1 more
TL;DR: By using monadic second-order logic and semiring homomorphisms, this work describes in a single formalism a large class of functions on graphs that can be computed recursively on the derivation trees of these graphs.
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Linear-time computation of optimal subgraphs of decomposable graphs
TL;DR: This work suggests a general approach for constructing linear-time algorithms in the case where the graph G is defined by certain rules of composition and the desired subgraph H satisfies a property that is “regular” with respect to theserules of composition.
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The discrete time-cost tradeoff problem revisited
TL;DR: This work formally describes the time-cost tradeoff problem, discusses the difficulties associated with its solution, and presents network decomposition/reduction as a convenient basis for solving the problem and analyzing its difficulty.