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Deadlock Detection

Algorithms to identify and resolve situations where transactions are blocked indefinitely, waiting for each other.
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The statement of the theorem

Let G=(V,E)G = (V, E) be a Resource Allocation Graph, where VV is the set of transactions T={t1,t2,…,tn}T = \{t_1, t_2, \dots, t_n\} and EE represents resource dependencies. Define EE such that an edge (ti,tj)(t_i, t_j) exists if transaction tit_i is waiting for a resource currently held by tjt_j. A deadlock D\mathcal{D} occurs if and only if the graph GG contains a cycle: ∃ cycle C=(ti1→ti2→⋯→tik→ti1) in G.\exists \text{ cycle } C = (t_{i_1} \to t_{i_2} \to \dots \to t_{i_k} \to t_{i_1}) \text{ in } G. The detection algorithm must identify such cycles by traversing the dependency graph.
Source: Wikipedia