A Note on Dynamic Bidirected Dyck-Reachability with Cycles
Abstract
Recently, Li et al. [2022] presented a dynamic Dyck-reachability algorithm for bidirected graphs. The basic idea is based on updating edge weights in a data structure called the merged graph Gm. As noted in Krishna et al. [2023], the edge deletion procedure described in the algorithm of Li et al. [2022] cannot properly update the weights in the presence of cycles in Gm. This note discusses the cycle case and the time complexity.
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