Deadlock resolution in wait-for graphs by vertex/arc deletion

Alan Diêgo Aurélio Carneiro (), Fábio Protti () and Uéverton S. Souza ()
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Alan Diêgo Aurélio Carneiro: Fluminense Federal University
Fábio Protti: Fluminense Federal University
Uéverton S. Souza: Fluminense Federal University

Journal of Combinatorial Optimization, 2019, vol. 37, issue 2, No 9, 546-562

Abstract: Abstract A deadlock occurs in a distributed computation if a group of processes wait indefinitely for resources from each other. In this paper we study actions to be taken after deadlock detection, especially the action of searching for a small deadlock-resolution set. More precisely, given a “snapshot” graph G representing a deadlocked state of a distributed computation governed by a certain deadlock model $${\mathbb {M}}$$ M , we investigate the complexity of vertex/arc deletion problems that aim at finding minimum vertex/arc subsets whose removal turns G into a deadlock-free graph (according to model $${\mathbb {M}}$$ M ). Our contributions include polynomial-time algorithms and hardness proofs, for general graphs and for special graph classes. Among other results, we show that the arc deletion problem in the OR model can be solved in polynomial time, and the vertex deletion problem in the OR model remains NP-complete even for graphs with maximum degree $${\varDelta }(G) = 4$$ Δ ( G ) = 4 , but is solvable in $$O (m \sqrt{n})$$ O ( m n ) time for graphs with $${\varDelta }(G)\le 3$$ Δ ( G ) ≤ 3 .

Keywords: Deadlock resolution; Knot; Deadlock recovery; Wait-for graphs; Computational complexity; Vertex deletion; Directed feedback vertex set (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-018-0279-5

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