Deterministic Fully Dynamic Data Structures for Vertex Cover and Matching

Sayan Bhattacharya, Monika Henzinger, Giuseppe F. Italiano

Abstract: We present the first deterministic data structures for maintaining approximate minimum vertex cover and maximum matching in a fully dynamic graph in time per update. In particular, for minimum vertex cover we provide deterministic data structures for maintaining a (2 + ε) approximation in O(log n/ε2) amortized time per update. For maximum matching, we show how to maintain a (3 + e) approximation in O(m1/3/ε2) amortized time per update, and a (4 + ε) approximation in O(m1/3/ε2) worst-case time per update. Our data structure for fully dynamic minimum vertex cover is essentially near-optimal and settles an open problem by Onak and Rubinfeld [13].