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 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 \(\mathbb {M}\), 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 \(\mathbb {M}\)). Our contributions include polynomial 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 four, but it is solvable in \(O (m \sqrt{n})\) time for graphs with \(\varDelta \le 3\).
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This research was partially supported by the Brazilian National Council for Scientific and Technological Development (CNPq), the Brazilian National Council for the Improvement of Higher Education (CAPES) and FAPERJ.
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Carneiro, A.D.A., Protti, F., Souza, U.S. (2017). Deletion Graph Problems Based on Deadlock Resolution. In: Cao, Y., Chen, J. (eds) Computing and Combinatorics. COCOON 2017. Lecture Notes in Computer Science(), vol 10392. Springer, Cham. https://doi.org/10.1007/978-3-319-62389-4_7
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