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Journal of the ACM (JACM)
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ACM Transactions on Programming Languages and Systems (TOPLAS)
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Journal of the ACM (JACM)
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Journal of the ACM (JACM)
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ACM Transactions on Programming Languages and Systems (TOPLAS)
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SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Linear-time algorithms for dominators and related problems
Linear-time algorithms for dominators and related problems
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The disjoint paths problem in quadratic time
Journal of Combinatorial Theory Series B
Finding disjoint paths on directed acyclic graphs
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ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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We present an algorithm that, given two vertices s"1 and s"2 of a directed acyclic graph, constructs in linear time a data structure using linear space that, for each pair (u,v) of two vertices u and v, in constant time can output a tuple (s"1,t"1,s"2,t"2) with {t"1,t"2}={u,v} such that there are two disjoint paths p"1, from s"1 to t"1, and p"2, from s"2 to t"2, if such a tuple exists. The data structure is simpler than such a data structure for general directed graphs that can be obtained from results of Georgiadis and Tarjan. Disjoint can mean vertex- as well as edge-disjoint. As an application and main result we show that the data structure can be used to solve the 2-disjoint paths problem on directed acyclic graphs optimally, i.e., in linear time.