Connectivity Oracles for Graphs Subject to Vertex Failures
نویسندگان
چکیده
We introduce new data structures for answering connectivity queries in graphs subject to batched vertex failures. Our deterministic structure processes a batch of d ≤ d? failed vertices in Õ(d) time and thereafter answers connectivity queries in O(d) time. It occupies space O(d?m log n). We develop a randomized Monte Carlo version of our data structure with update time Õ(d), query time O(d), and space Õ(m) for any d?. This is the first connectivity oracle for general graphs that can efficiently deal with an unbounded number of vertex failures. Our data structures are based on a new decomposition theorem for an undirected graph G = (V,E), which is of independent interest. It states that for any terminal set U ⊆ V we can remove a set B of |U |/(s − 2) vertices such that the remaining graph contains a Steiner forest for U −B with maximum degree s.
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