Finding paths and deleting edges in directed acyclic graphs
Information Processing Letters
On paths avoiding forbidden pairs of vertices in a graph
Discrete Applied Mathematics
On Two Problems in the Generation of Program Test Paths
IEEE Transactions on Software Engineering
Predicting gene structures from multiple RT-PCR tests
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Parameterized complexity of eulerian deletion problems
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Theoretical Computer Science
Complexity of the path avoiding forbidden pairs problem revisited
Discrete Applied Mathematics
Kernel bounds for path and cycle problems
Theoretical Computer Science
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Given a graph G=(V,E), two fixed vertices s,t@?V and a set F of pairs of vertices (called forbidden pairs), the problem of a path avoiding forbidden pairs is to find a path from s to t that contains at most one vertex from each pair in F. The problem is known to be NP-complete in general and a few restricted versions of the problem are known to be in P. We study the complexity of the problem for directed acyclic graphs with respect to the structure of the forbidden pairs. We write x@?y if and only if there exists a path from x to y and we assume, without loss of generality, that for every forbidden pair (x,y)@?F we have x@?y. The forbidden pairs have a halving structure if no two pairs (u,v),(x,y)@?F satisfy v@?x or v=x and they have a hierarchical structure if no two pairs (u,v),(x,y)@?F satisfy u@?x@?v@?y. We show that the PAFP problem is NP-hard even if the forbidden pairs have the halving structure and we provide a surprisingly simple and efficient algorithm for the PAFP problem with the hierarchical structure.