Resilient Level Ancestor, Bottleneck, and Lowest Common Ancestor Queries in Dynamic Trees

TL;DR

This paper introduces a resilient data structure for dynamic trees that maintains key ancestor and bottleneck queries efficiently even under memory corruption, enhancing fault tolerance in tree algorithms.

Contribution

It presents the first resilient data structure supporting level ancestor, LCA, and bottleneck queries in dynamic trees with linear size and $O( ext{corruption})$ worst-case update time.

Findings

Supports resilient queries under memory corruption.

Operates with linear space complexity.

Achieves $O( ext{corruption})$ worst-case update time.

Abstract

We study the problem of designing a \emph{resilient} data structure maintaining a tree under the Faulty-RAM model [Finocchi and Italiano, STOC'04] in which up to $\delta$ memory words can be corrupted by an adversary. Our data structure stores a rooted dynamic tree that can be updated via the addition of new leaves, requires linear size, and supports \emph{resilient} (weighted) level ancestor queries, lowest common ancestor queries, and bottleneck vertex queries in $O(\delta)$ worst-case time per operation.